U.S. patent application number 12/989344 was filed with the patent office on 2012-02-09 for audio processing device and audio processing method.
This patent application is currently assigned to JAPAN SCIENCE AND TECHNOLOGY AGENCY. Invention is credited to Masakazu Higuchi, Yasuo Morooka, Mitsuaki Nakamura, Kazuo Toraichi.
Application Number | 20120033830 12/989344 |
Document ID | / |
Family ID | 41255161 |
Filed Date | 2012-02-09 |
United States Patent
Application |
20120033830 |
Kind Code |
A9 |
Toraichi; Kazuo ; et
al. |
February 9, 2012 |
AUDIO PROCESSING DEVICE AND AUDIO PROCESSING METHOD
Abstract
There is provided a sound processing apparatus and a sound
processing method which are capable of reproducing discrete data
with a high-quality sound matching users' preferences. In a sound
processing means 2, since an interpolation value reflecting a value
of a variable parameter .alpha. by which the value of a control
sampling function c.sub.0(t) is multiplied can be calculated, an
analog signal obtained through the interpolation performed in a
sampling function s.sub.N(t) can be regulated in accordance with
the variable parameter .alpha. by changing the value of the
variable parameter .alpha.. In this way, by allowing the user to
appropriately change the variable parameter .alpha. in accordance
with various conditions including music reproduction environments,
sound sources, musical tones and so on, it becomes possible to
reproduce high-quality-sound music in which its frequency
characteristics of the analog signal have changed and a high
quality desired by the user is obtained.
Inventors: |
Toraichi; Kazuo; (Ibaraki,
JP) ; Higuchi; Masakazu; (Ibaraki, JP) ;
Morooka; Yasuo; (Ibaraki, JP) ; Nakamura;
Mitsuaki; (Ibaraki, JP) |
Assignee: |
JAPAN SCIENCE AND TECHNOLOGY
AGENCY
|
Prior
Publication: |
|
Document Identifier |
Publication Date |
|
US 20110058686 A1 |
March 10, 2011 |
|
|
Family ID: |
41255161 |
Appl. No.: |
12/989344 |
Filed: |
May 1, 2009 |
PCT Filed: |
May 1, 2009 |
PCT NO: |
PCT/JP2009/058567 PCKC 00 |
371 Date: |
November 24, 2010 |
Current U.S.
Class: |
381/98 |
Current CPC
Class: |
H04S 3/002 20130101;
H03H 17/0294 20130101; B60D 1/58 20130101; G10L 19/04 20130101;
G06F 17/17 20130101; B62D 12/02 20130101 |
Class at
Publication: |
381/98 |
International
Class: |
H03G 5/00 20060101
H03G005/00 |
Foreign Application Data
Date |
Code |
Application Number |
May 1, 2008 |
JP |
2008-119923 |
May 12, 2008 |
JP |
2008-124906 |
Oct 6, 2008 |
JP |
2008-259780 |
Claims
1. A sound processing apparatus comprising a function processing
means for calculating interpolation values among discrete data, by
applying the convolution operation to a plurality of
temporally-ordered discrete data, using a sampling function made up
of a linear combination of a fundamental sampling function and a
control sampling function which are each expressed by a piecewise
polynomial of finite support.
2. The sound processing apparatus according to claim 1, wherein
after applying the convolution operation to each of said discrete
data, using said fundamental sampling function and said control
sampling function, said function processing means calculates said
interpolation values by linearly adding calculated results obtained
by said convolution operation using said sampling function.
3. The sound processing apparatus according to claim 1 further
comprising a band separation means for separating said discrete
data into a plurality of frequency bands to produce a plurality of
band by band signals, wherein said function processing means
performs an interpolating process individually for each of said
band-by-band signals to produce synthesized signals by synthesizing
interpolation processing signals produced for each of said
frequency bands.
4. The sound processing apparatus according to claim 1 further
comprising a discrete data extraction means for extracting a given
number of said discrete data existing in such a manner as to
sandwich a marked point where said interpolation values are
calculated, wherein said function processing means is equipped with
a fundamental term calculation means for calculating a value of
said fundamental sampling function, using a distance to said marked
point determined for each of said discrete data extracted by said
discrete data extraction means and then calculating a fundamental
interpolation value at said marked point, by applying the
convolution operation to a value of said fundamental sampling
function allowed to correspond to each of said discrete data; a
control term calculation means for calculating a value of said
control sampling function, using a distance to said marked point
determined for each of said discrete data extracted by said
discrete data extraction means and then calculating a control
interpolation value at said marked point by applying the
convolution operation to a value of said control sampling function
allowed to correspond to each of said discrete data; and a linear
adding means for calculating said interpolation values by linearly
adding said fundamental interpolation value calculated by said
fundamental term calculation means and said control interpolation
value calculated by said control term calculation means.
5. The sound processing apparatus according to claim 1, wherein
said function processing means includes a coefficient
multiplication means for multiplying said control sampling function
by a variable parameter settable as an arbitrary value by a
user.
6. The sound processing apparatus according to claim 1 further
comprising a discrete data extraction means for extracting a given
number of said discrete data existing in such a manner as to
sandwich a marked point where said interpolation values are
calculated, wherein said function processing means is equipped with
a function calculation means in which said sampling function
produced by linearly adding said fundamental sampling function and
said control sampling function in advance is stored and which
calculates a value of said sampling function, using a distance to
said marked point determined for each of said discrete data; and
the convolution operation means for calculating an interpolation
value at said marked point by applying the convolution operation to
a value of said sampling function allowed to correspond to each of
said discrete data.
7. The sound processing apparatus according to claim 1, wherein
said fundamental sampling function is a function which can be
expressed by a piecewise polynomial once differentiable at an
interval [-1, 1] of a sampling position of said discrete data and
is expressed invariably as 0 in the other interval, while said
control sampling function is a function which can be expressed by a
piecewise polynomial once differentiable at an interval [-2, 2] of
a sampling position of said discrete data and is expressed
invariably as 0 in the other intervals.
8. The sound processing apparatus according to claim 1, wherein
when a sampling position of said discrete data is defined as t,
said fundamental sampling function is defined as f(t) and then said
fundamental sampling function is expressed by the following formula
20, f ( t ) = { 0 t .di-elect cons. ( - .infin. , - 1 ) 2 ( t + 1 )
2 t .di-elect cons. [ - 1 , - 1 2 ) - 2 t 2 + 1 t .di-elect cons. [
- 1 2 , 1 2 ) 2 ( - t + 1 ) 2 t .di-elect cons. [ 1 2 , 1 ) 0 t
.di-elect cons. [ 1 , .infin. ) , [ Formula 20 ] ##EQU00017## and
in said control sampling function, when C.sub.0(t)=C.sub.r(t)+(-t)
are set, said C.sub.r(t) is expressed by the following formula 21.
c r ( t ) = { 0 t .di-elect cons. ( - .infin. , 0 ) - t 2 t
.di-elect cons. [ 0 , 1 2 ) 3 ( - t + 1 ) 2 - 2 ( - t + 1 ) t
.di-elect cons. [ 1 2 , 1 ) - 3 ( t - 1 ) 2 + 2 ( t - 1 ) t
.di-elect cons. [ 1 , 3 2 ) ( - t + 2 ) 2 t .di-elect cons. [ 3 2 ,
2 ) 0 t .di-elect cons. [ 2 , .infin. ) [ Formula 21 ]
##EQU00018##
9. The sound processing apparatus according to claim 1, wherein a
selector is provided in which a plurality of said variable
parameters different in value is stored in advance and any one of
said variable parameters to be multiplied by said control sampling
function is selected from a plurality of said variable
parameters.
10. The sound processing apparatus according to claim 1, wherein
said function processing means is programmed in a programmable
signal processing device for forming a calculating configuration
with a controlling formation desired by a user, based on program
data specified by a user.
11. The sound processing apparatus according to claim 1, wherein
after tabulating values calculated in advance according to a given
number of sectioned portions among said discrete data marked, said
fundamental sampling function and said control sampling function
apply the convolution operation between said tabulated values and
said discrete data, the multiplication of said variable parameters
and said linear adding every time said discrete data are input,
thus outputting said interpolation values.
12. The sound processing apparatus according to claim 11, wherein
when the number of said sectioned portions among said discrete data
is plural, said tabulated values are calculated in advance using
the lowest common multiple in the number of said sectioned portions
and thereafter according to the number of said sectioned portions
set at the start of inputting said discrete data, said tabulated
values are selected to perform convolution operations between said
tabulated values and said discrete data.
13. The sound processing apparatus according to claim 3 further
comprising a sound pressure regulating means for multiplying any
one of said band-by-band signal and said interpolation processing
signal by a sound pressure parameter to produce a regulated
band-by-band signal whose sound pressure level is regulated for
each of said frequency bands, wherein when multiplying said
band-by-band signal by said sound pressure parameter, said
interpolation processing means performs said interpolation process
individually for each of said regulated band-by-band signals.
14. The sound processing apparatus according to claim 13, wherein
said sound pressure parameter different in each of said
band-by-band signals is settable.
15. A sound processing method including a function processing step
for calculating said interpolation values among said discrete data
by a function processing unit, by applying the convolution
operation to a plurality of temporally-ordered discrete data, using
said sampling function made up of a linear combination of a
fundamental sampling function and a control sampling function which
are each expressed by a piecewise polynomial of a finite order.
16. The sound processing method according to claim 15 further
including the convolution operation step for applying the
convolution operation to each of said discrete data, using said
fundamental sampling function and said control sampling function;
and a linear adding step for calculating said interpolation values
by linearly adding calculated results obtained by said convolution
operation using said sampling function.
17. The sound processing method according to claim 15 further
including a band separating step for separating said discrete data
into a plurality of frequency bands to produce a plurality of
band-by-band signals, wherein said function processing step
includes: an interpolation processing step for performing an
interpolating process individually for each of said band-by-band
signals to produce interpolation signals for each of said frequency
bands, and a band synthesizing step for producing synthesized
signals by synthesizing a plurality of said interpolation
processing signals produced for each of said frequency bands.
18. The sound processing method according to claim 15 further
including a discrete data extraction step for extracting said given
number of said discrete data existing in such a manner as to
sandwich a marked point where said interpolation values are
calculated, wherein said function processing step includes: a
fundamental term calculation step for calculating a value of said
fundamental sampling function, using a distance to said marked
point determined for each of said discrete data extracted by said
discrete data extracting means and then calculating a value of a
basic interpolation value at said marked point by applying the
convolution operation to said fundamental sampling function allowed
to correspond to each of said discrete data; a control term
calculation step for calculating a value of said control sampling
function, using a distance to said marked point determined for each
of said discrete data extracted by said discrete data extraction
means and then calculating a control interpolation value at said
marked point by applying the convolution operation to a value of
said control sampling function allowed to correspond to each of
said discrete data; and a linear adding step for calculating said
interpolation value by linearly adding said fundamental
interpolation value calculated by said fundamental term calculation
means and said control interpolation value calculated by said
control term calculation means.
19. The sound processing method according to claim 15, wherein said
function processing step includes a coefficient multiplication step
for multiplying said control sampling function by a variable
parameter settable as an arbitrary numerical value by a user.
20. The sound processing method according to claim 15 further
including a discrete data extraction step for extracting a given
number of said discrete data existing in such a manner as to
sandwich a marked point where said interpolation values are
calculated, wherein said function processing step includes: a
function calculation step for storing in advance said sampling
function produced by linearly adding said fundamental sampling
function and said control sampling function and thereafter
calculating a value of said sampling function, using a distance to
said marked point determined for each of said discrete data; and
the convolution operation step for calculating an interpolation
value at said marked point by applying the convolution operation to
a value of said sampling function allowed to correspond to each of
said discrete data.
21. The sound processing method according to claim 15, wherein said
fundamental sampling function is a function which is expressed by a
piecewise polynomial once differentiable at an interval [-1, 1] of
a sampling position of said discrete data and is expressed
invariably as 0 at the other intervals, while said control sampling
function is a function which can be expressed by a piecewise
polynomial once differentiable at an interval [-2, 2] of a sampling
position of said discrete data and is expressed invariably as 0 at
the other intervals.
22. The sound processing method according to claim 15, wherein when
a sampling position of said discrete data is defined as t, said
fundamental sampling function is defined as f(t) and then said
fundamental sampling function is expressed by the following formula
22, f ( t ) = { 0 t .di-elect cons. ( - .infin. , - 1 ) 2 ( t + 1 )
2 t .di-elect cons. [ - 1 , - 1 2 ) - 2 t 2 + 1 t .di-elect cons. [
- 1 2 , 1 2 ) 2 ( - t + 1 ) 2 t .di-elect cons. [ 1 2 , 1 ) 0 t
.di-elect cons. [ 1 , .infin. ) , [ Formula 22 ] ##EQU00019## and
in said control sampling function, when
C.sub.0(t)=C.sub.r(t)+C.sub.r(-t) are set, said C.sub.r(t) is
expressed by the following formula 23. c r ( t ) = { 0 t .di-elect
cons. ( - .infin. , 0 ) - t 2 t .di-elect cons. [ 0 , 1 2 ) 3 ( - t
+ 1 ) 2 - 2 ( - t + 1 ) t .di-elect cons. [ 1 2 , 1 ) - 3 ( t - 1 )
2 + 2 ( t - 1 ) t .di-elect cons. [ 1 , 3 2 ) ( - t + 2 ) 2 t
.di-elect cons. [ 3 2 , 2 ) 0 t .di-elect cons. [ 2 , .infin. ) [
Formula 23 ] ##EQU00020##
23. The sound processing method according to claim 15, wherein in
said parameter setting step, any one of a plurality of said
variable parameters to be multiplied by said control sampling
function is selected from a plurality of said variable parameters
which are stored in advance and are different in said numerical
value.
24. The sound processing method according to claim 15, wherein said
function processing step is performed by a calculation circuit
configuration with a controlling formation which is desired by a
user and is programmed in a programmable signal processing device
based on program data specified by a user.
25. The sound processing method according to claim 15, wherein in
said function processing step, after tabulating calculated values
of said fundamental sampling function and said control sampling
function, in advance according to a given number of sectioned
portions among said discrete data marked, said fundamental sampling
function and said control sampling function apply the convolution
operation between said tabulated values and said discrete data,
multiplications of said variable parameters and said linear adding
every time said discrete data are input, thus outputting said
interpolation values.
26. The sound processing method according to claim 25, wherein in
said function processing step, when the number of said sectioned
portions among said discrete data is plural, said tabulated values
are calculated in advance using the lowest common multiple in the
number of said sectioned portions, and thereafter according to the
number of said sectioned portions set at the start of inputting
said discrete data, said tabulated values are selected to perform
convolution operations between said tabulated values and said
discrete data.
27. The sound processing method according to claim 17 further
including a sound pressure regulating step provided behind any one
of said band separation step and interpolating processing step,
wherein said sound pressure regulating step is intended for
multiplying said band-by-band signal by a sound pressure parameter
behind said band separation step and further multiplying said
interpolation processing signal by a sound pressure parameter
behind said interpolation processing step to produce regulated
band-by-band signals behind said interpolation processing step,
while said interpolation processing means performs said
interpolation process independently for each of said regulated
band-by-band signals when multiplying said band-by-band signal by
said sound pressure parameter.
28. The sound processing method according to claim 27 further
including a sound pressure parameter setting step, wherein said
sound pressure parameter different in each of said band-by-band
signals is settable by a setting unit.
Description
TECHNICAL FIELD
[0001] The present invention relates to a sound processing
apparatus and a sound processing method, which are suitably
applicable, e.g., when intervals among temporally ordered discrete
data sampled at a predetermined frequency are interpolated to
produce new discrete data by a higher sampling frequency than that
of the input original discrete data or produce analogue signals. In
addition, in this specification, a process in which signals are
produced at high-frequency discrete intervals and a process in
which analogue signals are produced are defined as the same
processing and are referred to as "the production of analogue
signals, thus giving this description. Further, the description, in
this specification shall be given with the case where a function
value has a finite value other than 0 in a localized region and
becomes 0 at a region other than the localized region, referred to
as "finite support".
BACKGROUND ART
[0002] Heretofore, when analogue data are created from discrete
data such as digital data, Shannon's sampling function has been
extensively utilized which was derived based on Shannon's sampling
theorem. Here, the Shannon's sampling function becomes equals to 1
only at a sample point t=0 as shown in FIG. 22 and becomes 0 at all
the other sampling points, exhibiting a waveform whose vibration
theoretically continues to infinity from -.infin. to +.infin..
Accordingly, when utilizing various processors to actually perform
an interpolation process among discrete data using Shannon's
sampling function, the interpolation process is forcibly truncated
within a finite interval. As a result, there has been the issue
that an error was generated due to the truncation.
[0003] Further, when utilizing such a Shannon's sampling function,
since analogue signals reproduced were subjected to band
limitation, when discrete data recorded on. e.g., a CD (Compact
Disc) and a DVD (Digital versatile Disc) were converted into
analogue signals to be reproduced, high frequencies not less than
22.5 KHz were unable to reproduce, posing the issue that natural
sounds containing the sounds with frequencies not less than 22.5
KHz could not be reproduced.
[0004] Here, to solve such an issue, the error due to the
truncation does not occur and therefore a sampling function has
been evolved which is capable of reproducing farther higher
frequency range components and converges within a finite range
(e.g., see patent document 1). This sampling function converges to
0 at the second sampling positions anteroposterior to the original
point and hence signal reproduction can be performed with a small
amount of calculations, thus making it possible to ascertain that
farther higher-frequency range d is contained. [0005] Reference
document 1: International unexamined patent application publication
No. 99/38090
DISCLOSURE OF THE INVENTION
Problem to be Solved by the Invention
[0006] An audio system using such a sampling function, however,
cannot vary high-frequency range components depending on a wide
variety of users such as hearing-impaired persons, aged persons and
so on and various types of conditions such as music reproduction
environments, sound sources, musical tones or the like. Therefore,
a frequency characteristic cannot be freely regulated depending on
the situations. On the other hand, in recent years, a tailor-made
audio system in which users are able to freely regulate by oneself
its sound quality including high-frequency range components
depending on users' preferences and types of music has been desired
to provide.
[0007] With the view of the above needs, it is an object of the
present invention to provide a sound processing apparatus and a
sound processing method which are capable of reproducing discrete
data with excellent quality depending on users' preferences.
Means for Solving the Problem
[0008] To solve the issue like this, a first aspect of the present
invention provides a sound processing apparatus, which is equipped
with a function processing means for calculating interpolation
values among discrete data, by applying the convolution operation
to a plurality of the discrete data temporally-ordered, using a
sampling function made up of a liner combination of a fundamental
sampling function and a control sampling function which are each
expressed by a piecewise polynomial of finite support.
[0009] A second aspect of the present invention is a sound
processing apparatus in which after applying the convolution
operation to each of the discrete data, using the fundamental
sampling function and the control sampling function, the function
processing means calculates the interpolation values by linearly
adding calculated results obtained by the convolution operation
using the sampling function.
[0010] A third aspect of the present invention is a sound
processing apparatus equipped with a band separation means for
separating the discrete data into a plurality of frequency bands to
produce a plurality of band-by-band signals. Then, the function
processing means performs an interpolation process individually for
each of the band-by-band signals to produce synthesized signals by
synthesizing interpolation processing signals produced for each of
the frequency bands,
[0011] A fourth aspect of the present invention is a sound
processing apparatus equipped with a discrete data extraction means
for extracting a given number of the discrete data existing in such
a manner as to sandwich a marked point where the interpolation
values are calculated. Then, the function processing means is
equipped with a fundamental term calculation means for calculating
a value of the fundamental sampling function, using a distance to
the marked point determined for each of the discrete data extracted
by the discrete data extraction means, and then calculating a
fundamental interpolation value at the marked point, by applying
the convolution operation to a value of the fundamental sampling
function allowed to correspond to each of the discrete data; a
control term calculation means for calculating a value of the
control sampling function, using a distance to the marked point
determined for each of the discrete data extracted by the discrete
data extraction means and then calculating a control interpolation
value at the marked point by applying the convolution operation to
a value of the control sampling function allowed to correspond to
each of the discrete data; and a linear adding means for
calculating the interpolation value by linearly adding the
fundamental interpolation value calculated by the fundamental term
calculation means and the control interpolation value calculated by
the control term calculation .means.
[0012] A fifth aspect of the present invention is a sound
processing apparatus in which the function processing means
includes a coefficient multiplication means for multiplying the
control sampling function by a variable parameter settable as an
arbitrary value by a user.
[0013] A sixth aspect of the present invention is a sound
processing apparatus equipped with a discrete data extraction means
for extracting a given number of the discrete data existing in such
a manner as to sandwich a marked point where the interpolation
values are calculated. Then, the function processing means is
equipped with a function calculation means in which the sampling
function produced by linearly adding the fundamental sampling
function and the control sampling function in advance is stored and
which calculates a value of the sampling function, using a distance
to the marked point determined for each of the discrete data; and
the convolution operation means for calculating an interpolation
value at the marked point by applying the convolution operation to
a value of the sampling function allowed to correspond to each of
the discrete data.
[0014] A seventh aspect of the present invention is a sound
processing apparatus in which the fundamental sampling function is
a function which can be expressed by a piecewise polynomial once
differentiable at an interval [-1, 1] of a sampling position of the
discrete data and is expressed invariably as 0 at the other
intervals. Further, the control sampling function is a function
which can be expressed by a piecewise polynomial once
differentiable at an interval [-2, 2] of a sampling position of the
discrete data and is expresses invariably as 0 at the other
intervals.
[0015] A eighth aspect of the present invention is a sound
processing apparatus in which when a sampling position of the
discrete data is defined as t, the fundamental sampling function is
defined as f(t) and then the fundamental sampling function is
expressed by the following formula 1.
f ( t ) = { 0 t .di-elect cons. ( - .infin. , - 1 ) 2 ( t + 1 ) 2 t
.di-elect cons. [ - 1 , - 1 2 ) - 2 t 2 + 1 t .di-elect cons. [ - 1
2 , 1 2 ) 2 ( - t + 1 ) 2 t .di-elect cons. [ 1 2 , 1 ) 0 t
.di-elect cons. [ 1 , .infin. ) , [ Formula 1 ] ##EQU00001##
Then, the control sampling function is set as
C.sub.0(t)=C(t)+C.sub.r(-t) and C.sub.r(t) is expressed by the
following formula 2.
c r ( t ) = { 0 t .di-elect cons. ( - .infin. , 0 ) - t 2 t
.di-elect cons. [ 0 , 1 2 ) 3 ( - t + 1 ) 2 - 2 ( - t + 1 ) t
.di-elect cons. [ 1 2 , 1 ) - 3 ( t - 1 ) 2 + 2 ( t - 1 ) t
.di-elect cons. [ 1 , 3 2 ) ( - t + 2 ) 2 t .di-elect cons. [ 3 2 ,
2 ) 0 t .di-elect cons. [ 2 , .infin. ) [ Formula 2 ]
##EQU00002##
[0016] A ninth aspect of the present invention is a sound
processing apparatus which includes a selector in which a plurality
of variable parameters different in the numerical value are stored
in advance and any one of the variable parameters to be multiplied
by the control sampling function is selected from among a plurality
of the variable parameters.
[0017] A tenth aspect of the present invention is a sound
processing apparatus in which the function processing means is
programmed in a programmable signal processing device for forming a
calculation configuration with a controlling formation desired by a
user, based on program data specified by a user.
[0018] An eleventh aspect of the present invention is a sound
processing apparatus in which after tabulating values calculated in
advance according to a given number of sectioned portions among the
discrete data marked, the fundamental sampling function and the
control sampling function apply the convolution operation between
the tabulated values and the discrete data, multiplication of the
variable parameters and said linear adding every time the discrete
data are input, thus outputting the interpolation values.
[0019] A twelfth aspect of the present invention is a sound
processing apparatus in which when the number of the sectioned
portions among the discrete data is plural, the tabulated values
are calculated in advance using the lowest common multiple in the
number of the sectioned portions and thereafter according to the
number of the sectioned portions set at the start of inputting the
discrete data, the tabulated values are selected to perform
convolution operations between said tabulated values and the
discrete data.
[0020] A thirteenth aspect of the present invention is a sound
processing apparatus equipped with a sound pressure regulating
means for multiplying any one of the band-by-band signal and the
interpolation processing signal by a sound pressure parameter to
produce a regulated band-by-band signal whose sound pressure level
is regulated for each of the frequency bands. When multiplying the
band-by-band signal by the sound pressure parameter, the
interpolation processing means performs the interpolation process
individually for each of the regulated band-by-band signals.
[0021] A fourteenth aspect of the present invention is a sound
processing apparatus in which the sound pressure parameter
different in each of band-by-band signals is settable.
[0022] A fifteenth aspect of the present invention is a sound
processing method which includes a function processing step for
calculating interpolation values among the discrete data by a
function processing means, by applying the convolution operation to
a plurality of temporally-ordered discrete data, using the sampling
function made up of the linear combination of a fundamental
sampling function and a control sampling function which are each
expressed by a piecewise polynomial of finite support.
[0023] A sixteenth aspect of the present invention is a sound
processing method in which the function processing step includes
the convolution operation step for applying the convolution
operation to each of the discrete data, using the fundamental
sampling function and the control sampling function; and a linear
adding step for calculating the interpolation values by linearly
adding the calculated result obtained by the convolution operation
using the sampling function.
[0024] A seventeenth aspect of the present invention is a sound
processing method which includes a band separating step for
separating the discrete data into a plurality of frequency bands to
produce a plurality of band-by-band signals. The function
processing step includes an interpolation processing step for
performing an interpolation process individually for each of the
band-by-band signals to produce interpolation signals for each of
the frequency bands, and a band synthesizing step for producing
synthesized signals by synthesizing a plurality of the
interpolation processing signals produced for each of the frequency
bands.
[0025] A eighteenth aspect of the present invention is a sound
processing method which includes a discrete data extraction step
for extracting a given number of the discrete data existing in such
a manner as to sandwich a marked point where the interpolation
values are calculated. Then, the function processing step includes
a fundamental term calculation step for calculating a value of the
fundamental sampling function, using a distance to the marked point
determined for each of the discrete data extracted by the discrete
data extraction means and then calculating a value of a fundamental
interpolation value at the marked point, by applying the
convolution operation to the fundamental sampling function allowed
to correspond to each of the discrete data; a control term
calculating step for calculating a value of the control sampling
function, using a distance to the marked point determined for each
of the discrete data extracted by the discrete data extraction
means, by applying the convolution operation to a value of the
control sampling function allowed to correspond to each of the
discrete data; and a linearly adding step for calculating the
interpolation value by linearly adding the fundamental
interpolation value calculated by the fundamental term calculation
means and the control interpolation value calculated by the control
term calculation means.
[0026] A nineteenth aspect of the present invention is a sound
processing method in which the function processing step includes a
coefficient multiplication step for multiplying the control
sampling function by a variable parameter settable as an arbitrary
numerical value by a user.
[0027] A twentieth aspect of the present invention is a sound
processing method which includes a discrete data extraction step
for extracting a given number of the discrete data existing in such
a manner as to sandwich a marked point where the interpolation
values are calculated. Then, the function processing step includes
a function calculation step for storing in advance the sampling
function produced by linearly adding the fundamental sampling
function and the control sampling function and thereafter
calculating a value of the sampling function, using a distance to
the marked point determined for each of the discrete data; and the
convolution operation step for calculating an interpolation value
at the marked point by applying the convolution operation to a
value of the sampling function allowed to correspond to each of the
discrete data.
[0028] A twenty-first aspect of the present invention is a sound
processing method in which the fundamental sampling function is a
function which is expressed by a piecewise polynomial once
differentiable at an interval [-1, 1] of a sampling position of the
discrete data and is expressed invariably as 0 in the other
intervals. Further, the control sampling function is a function
which is expressed by a piecewise polynomial once differentiable at
an interval [-2, 2] of a sampling position of the discrete data and
is expressed invariably as 0 at the other interval.
[0029] A twenty-second aspect of the present invention is a sound
processing method in which when the sampling position of the
discrete data is defined as t, the fundamental sampling function is
defined as f(t) and then the fundamental sampling function is
expressed by the following formula 3.
f ( t ) = { 0 t .di-elect cons. ( - .infin. , - 1 ) 2 ( t + 1 ) 2 t
.di-elect cons. [ - 1 , - 1 2 ) - 2 t 2 + 1 t .di-elect cons. [ - 1
2 , 1 2 ) 2 ( - t + 1 ) 2 t .di-elect cons. [ 1 2 , 1 ) 0 t
.di-elect cons. [ 1 , .infin. ) , [ Formula 3 ] ##EQU00003##
The control sampling function, C.sub.0(t)=C.sub.r(t)+C.sub.r(-t)
are set and then C.sub.r(t) is expressed by the following formula
4.
c r ( t ) = { 0 t .di-elect cons. ( - .infin. , 0 ) - t 2 t
.di-elect cons. [ 0 , 1 2 ) 3 ( - t + 1 ) 2 - 2 ( - t + 1 ) t
.di-elect cons. [ 1 2 , 1 ) - 3 ( t - 1 ) 2 + 2 ( t - 1 ) t
.di-elect cons. [ 1 , 3 2 ) ( - t + 2 ) 2 t .di-elect cons. [ 3 2 ,
2 ) 0 t .di-elect cons. [ 2 , .infin. ) [ Formula 4 ]
##EQU00004##
[0030] A twenty-third aspect of the present invention is a sound
processing method in which in the parameter setting step, any one
of variable parameters to be multiplied by the control sampling
function is selected from among a plurality of variable parameters
which are stored in advance and are different in the numerical
value.
[0031] A twenty-fourth aspect of the present invention is a sound
processing method in which the function processing step is
performed by a calculation circuit configuration with a controlling
formation, desired by a user, which is programmed in a programmable
signal processing device based on program data specified by a
user.
[0032] A twenty-fifth aspect of the present invention is a sound
processing method in which in the function processing step, after
tabulating calculated values of said fundamental sampling function
and said control sampling function in advance according to a given
number of sectioned portions among said discrete data marked, the
convolution operation between said tabulated values and said
discrete data, multiplications of said variable parameters and said
linear adding are performed every time said discrete data are
input, thus outputting the interpolation values.
[0033] A twenty-sixth aspect of the present invention is a sound
processing method in which in the function processing step, when
the number of sectioned portions among the discrete data is plural,
the tabulated values are calculated in advance using the lowest
common multiple in the number of sectioned portions and thereafter
according to the number of the sectioned portions set at the start
of inputting the discrete data, the tabulated values are selected
to apply the convolution operation between the tabulted values and
the discrete data.
[0034] A twenty-seventh aspect of the present invention is a sound
processing method including a sound pressure regulating step behind
any one of the band separation step and the interpolation
processing step. The sound pressure regulating step multiplies the
band-by-band signal by a sound pressure parameter behind the band
separation step and further multiplies the interpolation processing
signal by a sound pressure parameter to produce the regulated
band-by-band signal whose sound pressure level is regulated for
each of the frequency bands by the sound pressure parameter. When
multiplying the band-by-band signal by a sound pressure parameter,
the interpolation processing means performs the interpolation
process individually for each of the regulated band-by-band
signals.
[0035] A twenty-eighth aspect of the present invention is a sound
processing method which includes a sound pressure parameter setting
process in which the sound pressure parameter different in each of
the band-by-band signals is settable by a setting unit.
Effects of the Invention
[0036] According to the sound processing apparatus of the first
aspect of the present invention and according to the sound
processing method of the fifteenth aspect of the present invention,
the interpolation value reflected by the numerical value of the
variable parameter by which the control sampling function is
multiplied is allowed to be calculated and thereby the numerical
value of the variable parameter is varied. Therefore, the
interpolated value obtained by performing the interpolation process
by means of the sampling function can be regulated depending on the
variable parameter. Thus, a user varies appropriately the variable
parameter depending on various types of conditions such as music
reproduction environments, sound sources, musical tones or the like
and as a consequence, the frequency characteristics of the signals
produced based on the interpolated values varies. Hence, a
high-quality-sound music with a sound quality desired by a user can
be reproduced.
BRIEF DESCRIPTION OF THE DRAWINGS
[0037] FIG. 1 is a schematic view illustrating a relationship
between a waveform of a fundamental sampling function and a
waveform of a control sampling function, according to the present
invention.
[0038] FIG. 2 is a block diagram illustrating a circuit
configuration of an audio apparatus according to a first
embodiment.
[0039] FIG. 3 is a block diagram illustrating a circuit
configuration of a sound processing means according to the first
embodiment.
[0040] FIG. 4 is a schematic view illustrating a positional
relationship between four discrete data and a marked point.
[0041] FIG. 5 is a block diagram illustrating a detailed
configuration of the sound processing means.
[0042] FIG. 6 is a schematic view illustrating an interpolation
process using the fundamental sampling function, which is performed
by a sound processing means 2, according to the present
invention.
[0043] FIG. 7 is a schematic view illustrating an interpolation
process using the control sampling function, which is performed by
a sound processing means 2, according to the present invention.
[0044] FIG. 8 is a schematic view illustrating waveforms of the
sampling function when a variable parameter is varied.
[0045] FIG. 9 is a schematic view illustrating frequency
characteristics when a variable parameter is varied.
[0046] FIG. 10 is a schematic view illustrating signal levels when
a numerical value of a variable parameter is varied with a
reproduced frequency fixed.
[0047] FIG. 11 is a block diagram illustrating a circuit
configuration of a sound processing means according to other
embodiment.
[0048] FIG. 12 is a schematic view illustrating a positional
relationship between four discrete data and a marked point, and
interpolation positions.
[0049] FIG. 13 is a block diagram illustrating a detailed
configuration of the sound processing means according to other
embodiment.
[0050] FIG. 14 is a block diagram illustrating a circuit
configuration of an audio apparatus according to a second
embodiment.
[0051] FIG. 15 is a block diagram illustrating a circuit
configuration of a sound processing means according to a second
embodiment.
[0052] FIG. 16 is a schematic view illustrating a waveform of the
fundamental sampling function and a waveform of the control
sampling function, which are used in a band interpolation means
according to the present invention.
[0053] FIG. 17 is a block diagram illustrating a circuit
configuration of the band interpolation means.
[0054] FIG. 18 is a schematic view illustrating a positional
relationship between four band-by-band data and a marked point,
[0055] FIG. 19 is a block diagram illustrating a detailed
configuration of the band interpolation means.
[0056] FIG. 20 is a schematic view illustrating an interpolation
process using the fundamental sampling function, which is performed
by the band interpolation means according to the present
invention.
[0057] FIG. 21 is a schematic view illustrating an interpolation
process using the control sampling function, which is performed by
the band interpolation value unit according to the present
invention.
[0058] FIG. 22 is a schematic view illustrating a waveform of a
traditional sampling function according to Shannon.
BEST MODE FOR CARRYING OUT THE INVENTION
[0059] Hereunder is a detailed description of embodiments based on
the accompanying drawings.
First Embodiment
[0060] (1) The Fundamental Concept of the Present Invention
[0061] FIG. 1 shows each of waveforms exhibited by a fundamental
sampling function f(t) and a control sampling function c.sub.0(t)
which make up a sampling function used for an interpolation process
according to the present invention. In addition, in FIG. 1, the
abscissa axis denotes a sampling position t of discrete data and
the ordinate axis denotes each of values of the sampling function.
Here, the sampling position of discrete data is defined as t. A
sampling function s.sub.2(t) made up of the fundamental sampling
function f(t) and the control sampling function c.sub.0(t) which
exist among sampling positions [-2, 2] of the discrete data is
expressed by the following formula 5.
s.sub.2(t)=f(t)+.alpha.c.sub.0(t) [Formula 5] [0062] where
c.sub.0(t)=c.sub.r(t)+c.sub.r(-t) and when a general control
sampling function is defined as c.sub.k(t) and
c.sub.k(t)=c.sub.r(t-k)+c.sub.r(-t-k) are set, among the sampling
positions [-N, N] of the discrete data,a sampling function
s.sub.N(t) is expressed by the following formula 6.
[0062] S N ( t ) = f ( t ) + k = 0 N - 2 .alpha. k c k ( t ) [
Formula 6 ] ##EQU00005##
[0063] In addition, .alpha..sub.k denotes a variable parameter
described below and an arbitrary numerical value settable by a user
and .alpha..sub.k may be invariable by k as a result of setting
.alpha..sub.1=.alpha..sub.2=.alpha..sub.3.
[0064] Here, the fundamental sampling function f(t) is a function
expressed by a piecewise polynomial of finite support focused on
differentiability. This function, e.g., is only once differentiable
over its whole range and has a finite value other than 0 when a
sampling position t along the abscissa axis exists in the range of
-1 to 1 (that is, an interval [-1, 1]) and in the other regions, is
expressed invariably as 0. Specifically, the fundamental sampling
function f(t) is in the form of an n-order polynomial function in
each short section produced by sectioning the interval [-1, 1] into
two or more sections and at the boundaries among the short
sections, the fundamental sampling function f(t) is continuous (a
value and slope of the function are each continuous). This
fundamental sampling function f(t) exhibits a concave and undulate
waveform differentiable n-1 (n is an integer not less than 2) times
over its whole range. Further, this fundamental sampling function
f(t) becomes 1 only at the sampling position and converges to 0
toward t=.+-.1 and keeps 0 further toward t=.+-.2.
[0065] Further, this fundamental sampling function f(t) may be a
function of an impulse response waveform of finite support and
further may be a continuous n-order piecewise polynomial function
which is at least once differentiable at an arbitrary position
within a sampling position interval.
[0066] Specifically, the fundamental sampling function f(t) like
this is expressed as the following formula 7.
f ( t ) = { 0 t .di-elect cons. ( - .infin. , - 1 ) 2 ( t + 1 ) 2 t
.di-elect cons. [ - 1 , - 1 2 ) - 2 t 2 + 1 t .di-elect cons. [ - 1
2 , 1 2 ) 2 ( - t + 1 ) 2 t .di-elect cons. [ 1 2 , 1 ) 0 t
.di-elect cons. [ 1 , .infin. ) , [ Formula 7 ] ##EQU00006##
[0067] Then, by performing overlapping operations, using this
fundamental sampling function f(t), based on each discrete data,
the temporary interpolation is possible using a function in which
values among discrete data can be only once differentiated.
[0068] At the same time, the control sampling function c.sub.0(t)
is a function expressed by a piecewise polynomial of finite support
focused on differentiability and is expressed by an n-order
polynomial function like the fundamental sampling function. The
control sampling function c.sub.0(t) is, e.g., only once
differentiable over its whole range and has a finite value other
than 0 when a sampling position t along the abscissa axis exists in
the range of -2 to 2 (that is, an interval [-2, 2]) and in the
other ranges, is expressed invariably as 0. Further, the control
sampling function c.sub.0(t) exhibits an undulate form only once
differentiable over its whole range and becomes 0 at each of the
sampling positions t=0, .+-.1, .+-.2. Furthermore, this control
sampling function c.sub.0(t) may be a function of an impulse
response waveform of finite support and further may be an n-order
continuous piecewise polynomial function at least once
differentiable at an arbitrary position within the sampling
position interval.
[0069] Here, the control sampling function c.sub.0(t) is expressed
as the control sampling function c.sub.0(t)=c.sub.r(t)+c.sub.r(-t)
and this c.sub.r(t) is expressed by the following formula 8.
c r ( t ) = { 0 t .di-elect cons. ( - .infin. , 0 ) - t 2 t
.di-elect cons. [ 0 , 1 2 ) 3 ( - t + 1 ) 2 - 2 ( - t + 1 ) t
.di-elect cons. [ 1 2 , 1 ) - 3 ( t - 1 ) 2 + 2 ( t - 1 ) t
.di-elect cons. [ 1 , 3 2 ) ( - t + 2 ) 2 t .di-elect cons. [ 3 2 ,
2 ) 0 t .di-elect cons. [ 2 , .infin. ) [ Formula 8 ]
##EQU00007##
Then, by performing overlapping operations using this control
sampling function c.sub.0(t) based on each discrete data, the
temporary interpolation is possible using a function in which
values among discrete data can be only once differentiated.
[0070] By linearly adding the temporary interpolation value
(hereunder, referred to as a fundamental interpolation value)
calculated in this manner based on the fundamental sampling
function f(t) and the temporary interpolation value (hereunder,
referred to as a control interpolation value) calculated in this
manner based on the control sampling function c.sub.0(t), the
interpolation of the value at an arbitrary position among discrete
data is possible using the function only once differentiable.
[0071] Incidentally, in the linear combination of the fundamental
sampling function f(t) and the control sampling function
c.sub.0(t), these functions must be satisfied by the following six
conditions. First, S.sub.2(0)=1, S.sub.2(.+-.1)=S.sub.2(.+-.2)=0
are satisfied; second, these functions are each an even function
(that is, the function symmetric about the y axis); third, within
the sampling position intervals [-.infin., -2], [2, .infin.], these
functions are invariably 0; fourth, in each of the intervals [n/2,
(n+1)/2] (-4.ltoreq.n.ltoreq.3), these functions are at most
quadratic polynomial; fifth, over the whole range, C1 class is
satisfied for these functions, that is, only once differentiable,
and sixth, within the sampling position interval [-1/2, -2], the
following formula 9 is satisfied.
k = - 2 2 s 2 ( t - k ) .ident. 1 [ Formula 9 ] ##EQU00008##
[0072] In addition, the sampling function s.sub.2(t) when N=2 is
hereunder described simply as a sampling function s.sub.N(t) for
convenience sake.
[0073] Further, in addition to this, at this time, the control
sampling function c.sub.0(t) can be multiplied by a variable
parameter .alpha. set as an arbitrary value by a user. Accordingly,
the control sampling function c.sub.0(t) can be varied in amplitude
of its waveform according to a numerical value of the variable
parameter .alpha. between sampling positions from -2 to +2 with the
control sampling function c.sub.0(t) kept 0 at the sampling
positions t=0, .+-.1, .+-.2. As a result, the control sampling
function c.sub.0(t) is able to vary the result calculated by the
convolution operation between itself and the fundamental sampling
function f(t). Thus, the variable parameter .alpha. is varied in
numerical value and thereby varies the frequency characteristic of
analogue signals obtained by the calculation performed by the
sampling function s.sub.N(t), thus permitting the signal levels of
high-frequency components to be regulated.
[0074] N Consequently, in the present invention, when the
convolution operation is applied to the results calculated by the
fundamental sampling function f(t) and the control sampling
function c.sub.0(t) to determine interpolation values, the
interpolation values can be regulated by the variable parameter
.alpha. which is multiplied by the control sampling function
c.sub.0(t). Therefore, in the present invention, the frequency
characteristic of the analogue signals produced by interpolating
positions among discrete data by the interpolation values can be
freely regulated by the variable parameter .alpha..
[0075] (2) Overall Architecture of an Audio Apparatus
[0076] Next, a description is hereunder given about an audio
apparatus in which an interpolation process is performed using the
sampling function s.sub.N(t) described above. In FIG. 2, numeral
symbol 1 denotes the audio apparatus and its sound processing means
2 is programmed in a field programmable gate array (hereunder,
referred to as FPGA) 3. Incidentally, in the FPGA 3 acting as a
programmable signal processing device, a plurality of circuit
blocks and interconnection blocks is regularly arranged on a chip.
A plurality of devices in which an electrical connection or
electrical nonconnection of a circuit is programmable is arranged
inside the circuit block and the interconnection block. A user
programs (defines) these devices and thereby insides of the blocks
and interconnections between the blocks are able to be designed in
the field (a utilization site).
[0077] For reference's sake, in this audio apparatus 1, various
types of other sampling functions such as Shannon's sampling
function, the sampling function described above in the formula 9
according to the present invention, sampling functions different
entirely from these sampling functions or the like are programmed
in the FPGA 3 from a personal computer 5 via an external interface
4. Therefore, by altering the connections between the circuit
blocks and the interconnection blocks in the FPGA 3, the circuit
configuration of the audio apparatus 1 can be varied into the
hardware capable of performing an interpolation process using
various types of sampling functions. Thus, in the audio apparatus
1, the circuit configuration in the FPGA 3 can be changed into one
desired by a user only by simply programming the FPGA 3. Hence,
when searching an optimal sampling function, a circuit board need
not be actually fabricated in each case according to various types
of sampling functions, thus attaining a reduction in cost just as
much.
[0078] In addition, in the embodiment described above, the FPGA 3
is applied in FIG. 2 to suggest an implementation method using the
FPGA 3. The present invention is, however, not limited to this
method and can be realized by a programmable signal processing
device such as a DSP (Digital Signal Processor). For example, some
controller made up of a CPU (Central Processing Unit), memories or
the like may be applicable.
[0079] Here, in the audio apparatus 1 according to the present
invention, the sampling function f(t) expressed by the formula 7
and the control sampling function c.sub.0(t), in which c.sub.r(t)
is expressed by the formula 8, which satisfy the condition of the
sampling function s.sub.N(t) in the formula 9 described above can
be programmed in the FPGA 3 from the personal computer 5 via the
external interface 4.
[0080] Consequently, the FPGA 3 integrally controls the whole of
the audio apparatus 1 according to a given program, and thereby the
audio apparatus 1 reproduces, e.g., various recording media such as
CDs, DVDs or the like by an input unit 6 to sequentially output a
plurality of temporally-ordered discrete data obtained by the
reproduction to the sound processing means 2. For reference's sake,
discrete data mean data obtained by smoothly sampling varying
continuous signals at a certain time intervals and then quantizing
the sampled data obtained by that sampling.
[0081] Now, a parameter setting unit 7 by which a user can freely
set a numerical value of the variable parameter .alpha. is
connected with the FPGA 3. When a user sets the variable parameter
.alpha. as an arbitrary value by the parameter setting unit 7,
information indicating the numerical value that has been set can be
output from the parameter setting unit 7 to the sound processing
means 2. When interpolating positions among discrete data using the
sampling function s.sub.N(t) to increase the sampling frequency in
a pseudo manner, that is, performing a so-called oversampling
process, the sound processing means 2 acting as a sound processing
apparatus calculates interpolation values reflected by the
numerical value of the variable parameter .alpha. to output the
interpolation values to an output unit 8.
[0082] When the interpolation values have been input at given
intervals from the sound processing means 2, the output unit 8
converts the interpolated signals into analogue signals
corresponding to the interpolation values, thereby permitting the
signals to be output as music sounds based on the analogue signals.
In this manner, by varying the numerical value of the variable
parameter .alpha., the sound apparatus 1 can produce analogue
signals with high-quality sounds which have been reflected by the
numerical value of the variable parameter .alpha. and are desired
by users.
[0083] Further, a selector 10 equipped with a plurality of buttons
9a, 9b, 9c is connected with the FPGA 3. The selector 10 is
incorporated with variable parameters which are different in
numerical value and are preliminarily associated with each of the
selector buttons 9a, 9b, 9c. Then, by selecting any one of the
buttons 9a, 9b, 9c, a numerical value of the corresponding variable
parameter .alpha. is multiplied by the control sampling function
c.sub.0(t), allowing the interpolation process to be performed by
the sampling function s.sub.N(t).
[0084] Specifically, in this embodiment, when the selector button
9a, e.g., is selected, the interpolation process is performed by
the sampling function s.sub.N(t) whose variable parameter .alpha.
is set as -1.5, while when another selector button 9b is selected,
the interpolation process is performed by the sampling function
s.sub.N(t) whose variable parameter .alpha. is set as -2.5 and when
yet another button 9c is selected, the interpolation process is
performed by the sampling function s.sub.N(t) whose variable
parameter .alpha. is set as 1.5.
[0085] Consequently, in the audio apparatus 1, users can set a
numerical value of the variable parameter .alpha. as an arbitrary
value by the parameter setting unit 7. At the same time, any one of
the buttons 9a, 9b, 9c is only selected and thereby without finely
setting the variable parameter by the parameter setting unit 7 in
each case, the interpolation process using a desired variable
parameter .alpha. can be easily performed.
[0086] (3) Circuit Configuration of the Sound Processing Means
[0087] (3-1) General Description of the Interpolation Process in
the Sound Processing Means
[0088] Practically, the sound processing means 2 with a circuit
configuration as shown in FIG. 3 can be programmed in the FPGA 3.
The sound processing means 2 comprises a discrete data extraction
means 15 for extracting a given number (here, four) of discrete
data in series to hold the discrete data and a function processing
means 14 for receiving at a time a given number of discrete data
which has been extracted to be held by the discrete data extraction
means 15 to perform an interpolation process using these discrete
data received. Thus, positions among discrete data input in series
from the input unit 6 can be interpolated at given time
intervals.
[0089] The function processing means 14 comprises a fundamental
term calculation means 16 for calculating terms of the fundamental
sampling function f(t) among the sampling function s.sub.N(t) based
on discrete data, a control term calculation means 17 for
calculating terms of the control sampling function c.sub.0(t) among
the sampling function s.sub.N(t) based on the discrete data, a
coefficient multiplication means 18 for multiplying the calculated
results of the control term calculation means 17 by a variable
parameter .alpha., and a linear adding means 19 for linearly adding
the calculated results of the fundamental term calculation means 16
and the calculated results of the coefficient multiplication means
18.
[0090] In this embodiment, the discrete data extraction means 15
extracts the last four discrete data from among the discrete data
input in series to hold the four discrete data until new discrete
data are next input and then delivers these four discrete data to
each of the fundamental term calculation means 16 and the control
term calculation means 17.
[0091] The fundamental term calculation means 16 has stored the
fundamental sampling function f(t) in a given storage means (not
shown) and when an interpolation position is specified among the
discrete data, calculates a value of the fundamental sampling
function f(t) based on a distance between this interpolation
position and the discrete data. This fundamental term calculation
means 16 can calculate a value of the fundamental sampling function
f(t) for each of the four discrete data delivered from the discrete
data extraction means 15. Further, the fundamental term calculation
means 16 multiples each of the four values, obtained for each of
the discrete data, of the fundamental sampling function f(t) by a
value of the discrete data corresponding to each of the four values
of the discrete data and thereafter applies convolution operations
to these four discrete data to deliver the calculated results of
the convolution operations to the linear adding means 19.
[0092] At the same time, the control term calculation means 17 has
stored the control sampling function c.sub.0(t) in a given storage
means (not shown) and when an interpolation position is specified,
calculates a value of the control sampling function c.sub.0(t)
based on the distance between this interpolation position and the
discrete data. This control term calculation means 17 can calculate
a value of the control sampling function c.sub.0(t) for each of the
four discrete data delivered from the discrete data extraction
means 15. Further, the control term calculation means 17 multiples
each of the four values, obtained for each of the discrete data, of
the control sampling function c.sub.0(t) by a value of the discrete
data corresponding to each of the discrete data and thereafter
applies convolution operations to the four discrete data by adding
the multiplied values to deliver the results of the convolution
operations to the coefficient multiplication means 18.
[0093] The coefficient multiplication means 18 receives, from the
control term calculation means 17, the calculated results of the
convolution operations applied to the control sampling function
c.sub.0(t) and then multiplies the calculated results by a variable
parameter .alpha. to deliver the obtained multiplied results by the
variable parameter to the linear adding means 19. The linear adding
means 19 receives the multiplied results of the convolution
operations applied to the fundamental sampling function f(t) from
the fundamental term calculation means 16 and the multiplied
results by the variable parameter .alpha. from the coefficient
multiplication means 18 and then adds linearly the calculated
results and the multiplied results to thereby obtain the linearly
added results corresponding to the four discrete data. The value
thus obtained by the linearly adding acts as an interpolation value
at the interpolation positions between given two discrete data. For
reference's sake, this interpolation position is updated at preset
intervals, specifically every period of T/N, produced by
multiplying a period T, corresponding to the input interval of
discrete data, by 1/N, corresponding to each input interval of the
discrete data.
[0094] (3-2) Specific Example for Determining an Interpolation
Value Based on the Four Discrete Data
[0095] Next, using FIG. 4 showing a positional relationship between
the four continuous discrete data and a marked point acting as an
interpolation position, a description is hereunder given about an
interpolation process for calculating an interpolation value
between given two discrete data based on the temporally-ordered
four discrete data. In FIG. 4, each of discrete data d1, d2, d3, d4
which are input in series corresponding to sampled positions t1,
t2, t3, t4 are defined as Y(t1), Y(t2), Y(t3), Y(t4). A given
position t0 (a distance from t2 is b) between sampling positions t2
and t3 is defined as an interpolation position and a case of
determining a interpolation value y corresponding to this
interpolation position is looked at.
[0096] The sampling function s.sub.N(t) used in the present
embodiment converges to 0 at the sampling positions t=.+-.2 and
hence the discrete data d1, d2, d3, d4 between t=.+-.2 may be taken
into account. Accordingly, when the interpolation value y shown in
FIG. 4 is determined, only four discrete data d1, d2, d3, d4
corresponding to t1, t2, t3, t4 may be eventually taken into
account, thus allowing the calculation amount to be substantially
reduced. Additionally, as for the discrete data equal to or out of
t=.+-.3 (not shown), the discrete data are essentially
considerable, but these discrete data are not ignored in
consideration of a calculation amount, a calculation accuracy or
the like and in fact, no truncation error occurs due to no need for
theoretically taking into account the discrete data.
[0097] As shown in FIG. 5, the discrete data extraction means 15 is
equipped with three shift circuits 20a, 20b, 20c and when
continuous discrete data are input, the discrete data are shifted
in each of the shift circuits 20a, 20b, 20c, e.g., at the sampling
period (44.1 kHz) used for CDs, the discrete data extraction means
15 can extract and retain each one of the last discrete data d1,
d2, d3, d4 in each of the shift circuits 20a, 20b, 20c. That is,
when the continuous four discrete data d1, d2, d3, d4 are input,
the discrete data extraction means 15 delivers the last discrete
data d4 directly to a fundamental term calculation circuit 21a of
the fundamental term calculation means 16 and a control term
calculation circuit 22a of the control term calculation means
17.
[0098] Further, the discrete data extraction means 15 delivers a
discrete data sequence comprising the continuous four discrete data
d1, d2, d3, d4 to the shift circuit 20a to shift the discrete data
sequence by the shift circuit 2b and thereby extract the second
last discrete data d3 in relation to the last discrete data d4 to
deliver the discrete data d3 to both the fundamental term
calculation circuit 21b of the fundamental term calculation means
16 and a control term calculation circuit 22b of the control term
calculation means 17.
[0099] Furthermore, the discrete data extraction means 15 continues
to deliver the discrete data sequence in series also to the
remaining shift circuits 20b, 20c to further shift the discrete
data sequence by the shift circuit 20b to deliver the third last
discrete data d2 in relation to the last discrete data d4 to both
the fundamental term calculation circuit 21c and the control term
calculation circuit 22c and furthermore shift the discrete data
sequence by the shift circuit 20c to deliver the fourth last
discrete data d1 in relation to the last discrete data d4 to both
the fundamental term calculation circuit 21d and the control term
calculation circuit 22d.
[0100] Here, FIG. 6 and FIG. 7 are schematic views illustrating the
interpolation process for a given position t0 in the fundamental
term calculation means 16 and the control term calculation means
17. With regard to the content of the interpolation process, first,
as described above, performed are a calculation process for
calculating a fundamental interpolation value in the fundamental
term calculation means 16 (hereunder, referred to as simply a
fundamental interpolation value calculation process) and a
calculation process for calculating a control interpolation value
in the control term calculation means 17 and the coefficient
multiplication means 18 (hereunder, referred to as simply a control
interpolation value calculation process). Hereunder, using FIG. 6
and FIG. 7, the fundamental interpolation value calculation process
and the control interpolation value calculation process are
described.
[0101] (3-2-1) Fundamental Interpolation Value Calculation
Process
[0102] With regard to the content of the fundamental interpolation
value calculation process, as shown in FIGS. 6(A) to 6(D), a peak
height at t=0 (a central position) in the fundamental sampling
function f(t) is allowed to coincide with each of the sampling
positions t1, t2, t3, t4 and then each value of the fundamental
sampling function f(t) is determined at the interpolation position
t0 at that time.
[0103] Focusing on the discrete data d1 at the sampling position t1
shown in FIG. 6(A), a distance between the interpolation position
t0 and the sampling position t1 becomes 1+b. Accordingly, a value
of the fundamental sampling function f(t) at the interpolation
position t0 when allowing the central position of the fundamental
sampling function f(t) to coincide with the sampling position t1
becomes f(1+b). Practically, the peak height at the central
position of the fundamental sampling function f(t) is adjusted so
as to coincide with the value Y(t1) of the discrete data d1 and
hence a value of (1+b)Y(t1), produced by multiplying f(1+b)
described above by Y(t1), becomes a desired value. The calculation
of f(1+b) is performed in the fundamental term calculation circuit
21a of the fundamental term calculation means 16, while the
calculation of multiplying f(1+b) by Y(t1) is performed in a
fundamental term multiplying circuit 23a of the fundamental term
calculation means 16 (see FIG. 5).
[0104] Similarly, focusing on a value Y(t2) of the discrete data d2
at the sampling position t2 shown in FIG. 6(B), a distance between
the interpolation position t0 and the sampling position t2 becomes
b. Accordingly, a value of the fundamental sampling function f(t)
at the interpolation position t0 when allowing the central position
of the fundamental sampling function f(t) to coincide with the
sampling position t2 becomes f(b). Practically, the peak height at
the central position of the fundamental sampling function f(t) is
adjusted so as to coincide with the value Y(t2) of the discrete
data d2 and hence a value of f(b)Y(t2), produced by multiplying
f(b) described above by Y(t2), becomes a desired value. The
calculation of f(b) is performed in the fundamental term
calculation circuit 21b of the fundamental term calculation means
16, while the calculation of multiplying f(b) by Y(t2) is performed
in a fundamental term circuit multiplying circuit 23b of the
fundamental term calculation means 16 (see FIG. 5).
[0105] Focusing on a value Y(t3) of the discrete data d3 at the
sampling position t3 shown in FIG. 6(C), a distance between the
interpolation position t0 and the sampling position t3 becomes 1-b.
Accordingly, a value of the fundamental sampling function f(t) at
the interpolation position t0 when allowing the central position of
the fundamental sampling function f(t) to coincide with the
sampling position t3 becomes f(1-b). Practically, the peak height
at the central position of the fundamental sampling function f(t)
is adjusted so as to coincide with the value Y(t3) of the discrete
data d3 and hence a value of f(1-b)Y(t3), produced by multiplying
f(1-b) described above by Y(t3), becomes a desired value. The
calculation of f(1-b) is performed in the fundamental term
calculation circuit 21c of the fundamental term calculation means
16, while the calculation of multiplying f(1-b) by Y(t3) is
performed in a fundamental term multiplying circuit 23c of the
fundamental term calculation means 16 (see FIG. 5).
[0106] Focusing on a value Y(t4) of the discrete data d4 at the
sampling position t4 shown in FIG. 6(D), a distance between the
interpolation position t0 and the sampling position t4 becomes 2-b.
Accordingly, a value of the fundamental sampling function f(t) at
the interpolation position t0 when allowing the central position of
the fundamental sampling function f(t) to coincide with the
sampling position t4 becomes f(2-b). Practically, the peak height
at the central position of the fundamental sampling function f(t)
is adjusted so as to coincide with the value Y(t4) of the discrete
data d4 and hence a value of f(2-b)Y(t4), produced by multiplying
f(2-b) described above by Y(t4), becomes a desired value. The
calculation of f(2-b) is performed in the fundamental term
calculation circuit 21d of the fundamental term calculation means
16, while the calculation of multiplying f(2-b) by Y(t4) is
performed in a fundamental term multiplying circuit 23d of the
fundamental term calculation means 16 (see FIG. 5).
[0107] Then, in a fundamental term convolution operation circuit
24, the fundamental term calculation means 16 applies the
convolution operation to the four values f(1+b)Y(t1), f(b)Y(t2),
f(1-b)Y(t3), f(2-b)Y(t4) which are obtained corresponding to the
marked point of the interpolation position t0 and as a result, a
fundamental interpolation value ya corresponding to the marked
point is calculated. In addition, a calculation performed by the
whole of the fundamental term calculation means 16 is the
convolution operation, whereas the fundamental term convolution
operation circuit 24 simply adds the multiplied results in each of
the fundamental term multiplying circuits 23a to 23d. For
reference's sake, in the present embodiment, the values of
f(1+b)Y(t1) and f(2-b)Y(t4) become 0 as shown in FIGS. 6(A), 6(D)
and therefore {f(b)Y(t2)}+{f(1-)Y(t3)} becomes effective as the
fundamental interpolation value ya.
[0108] (3-2-2) Control Interpolation Value Calculation Process
[0109] With regard to the content of the control interpolation
value calculation process, as shown in FIGS. 7(A) to 7(D), t=0 (a
central position) of the control sampling function c.sub.0(t) is
allowed to coincide with each of the sampling positions t1, t2, t3,
t4 to apply multiplication to values Y(t1), Y(t2), Y(t3), Y(t4) of
the discrete data d1, d2, d3, d4 corresponding to the control
sampling function c.sub.0(t) and thereby determine each value of
the control sampling function c.sub.0(t) at the interpolation
position t0 at that time.
[0110] Focusing on a value Y(t1) of the discrete data d1 at the
sampling position t1 shown in FIG. 7(A), a distance between the
interpolation position t0 and the sampling position t1 becomes 1+b.
Accordingly, a value of the control sampling function c.sub.0(t) at
the interpolation position t0 when allowing the central position of
the control sampling function c.sub.0(t) to coincide with the
sampling position t1 becomes c.sub.0(1+b). Practically, the
waveform height of the control sampling function c.sub.0(t) is
adjusted so as to be allowed to correspond to the value Y(t1) of
the discrete data d1 and hence a value of c.sub.0(1+b)Y(t1),
produced by multiplying c.sub.0(1+b) described above by Y(t1),
becomes a desired value. The calculation of c.sub.0(1+b) is
performed in the control term calculation circuit 22a of the
control term calculation means 17, while the calculation of
multiplying c.sub.0(1+b) by Y(t1) is performed in a control term
multiplying circuit 25a of the control term calculation means 17
(see FIG. 5).
[0111] Similarly, focusing on a value Y(t2) of the discrete data d2
at the sampling position t2 shown in FIG. 7(B), a distance between
the interpolation position t0 and the sampling position t2 becomes
b. Accordingly, a value of the control sampling function c.sub.0(t)
at the interpolation position t0 when allowing the central position
of the control sampling function c.sub.0(t) to coincide with the
sampling position t2 becomes c.sub.0(b). Practically, the waveform
height of the control sampling function c.sub.0(t) is adjusted so
as to be allowed to correspond to the value Y(t2) of the discrete
data d2 and hence a value of c.sub.0(b)Y(t2), produced by
multiplying c.sub.0(b) described above by Y(t2), becomes a desired
value. The calculation of c.sub.0(b) is performed in the control
term calculation circuit 22b of the control term calculation means
17, while the calculation of multiplying c.sub.0(b) by Y(t2) is
performed in a control term multiplication circuit 25b of the
control term calculation means 17 (see FIG. 5).
[0112] Focusing on a value Y(t3) of the discrete data d3 at the
sampling position t3 shown in FIG. 7(C), a distance between the
interpolation position t0 and the sampling position t3 becomes 1-b.
Accordingly, a value of the control sampling function c.sub.0(t) at
the interpolation position t0 when allowing the central position of
the control sampling function c.sub.0(t) to coincide with the
sampling position t3 becomes c.sub.0(1-b). Practically, the
waveform height of the control sampling function c.sub.0(t) is
adjusted so as to be allowed to correspond to the value Y(t3) of
the discrete data d3 and hence a value of c.sub.0(1-b)Y(t3),
produced by multiplying c.sub.0(1-b) described above by Y(t3),
becomes a desired value. The calculation of c.sub.0(1-b) is
performed in the control term calculation circuit 22c of the
control term calculation means 17, while the calculation of
multiplying c.sub.0(1-b) by Y(t3) is performed in a control term
multiplication circuit 25c of the control term calculation means 17
(see FIG. 5).
[0113] Focusing on a value Y(t4) of the discrete data d4 at the
sampling position t4 shown in FIG. 7(D), a distance between the
interpolation position t0 and the sampling position t4 becomes 2-b.
Accordingly, a value of the control sampling function c.sub.0(t) at
the interpolation position t0 when allowing the central position of
the control sampling function c.sub.0(t) to coincide with the
sampling position t4 becomes c.sub.0(2-b). Practically, the
waveform height of the control sampling function c.sub.0(t) is
adjusted so as to be allowed to correspond to the value Y(t4) of
the discrete data d4 and hence a value of c.sub.0(2-b)Y(t4),
produced by multiplying c.sub.0(2-b) described above by Y(t4),
becomes a desired value. The calculation of c.sub.0(2-b) is
performed in the control term calculation circuit 22d of the
control term calculation means 17, while the calculation of
multiplying c.sub.0(2-b) by Y(t4) is performed in a control term
multiplying circuit 25d of the control term calculation means 17
(see FIG. 5).
[0114] Then, using a control term convolution operation circuit 26,
the control term calculation means 17 applies the convolution
operation to the four values c.sub.0(1+b)Y(t1), c.sub.0(b)Y(t2),
c.sub.0(1-b)Y(t3), c.sub.0(2-b)Y(t4) which are obtained
corresponding to the marked point of the interpolation position t0
and thereafter the results of the convolution operation are
multiplied by the variable parameter .alpha. by means of the
coefficient multiplication means 18 to thereby calculate a control
interpolation value yb corresponding to the marked point. In
addition, a calculation performed by the whole of the control term
calculation means 17 is the convolution operation, whereas the
control term convolution operation circuit 26 simply adds the
multiplied results in each of the control term multiplication
circuits 25a to 25d.
[0115] (3-2-3) Interpolation Value Calculation Process
[0116] The linear adding means 19 linearly adds the fundamental
interpolation value ya which is calculated by the fundamental term
calculation means 16 and corresponds to the marked point and the
control interpolation value yb which is calculated by the control
term calculation means 17 and the coefficient multiplication means
18 and corresponds to the marked point. As a result, an
interpolation value y at the interpolation position t0 can be
output.
[0117] (3-3) Interpolation Process Result when a Value of the
Variable Parameter is Varied
[0118] In addition to such a configuration, in the sound processing
means 2, a value of the variable parameter .alpha. in the
coefficient multiplication means 18 is varied by the parameter
setting unit 7 and thereby a value of the sampling function
s.sub.N(t) is changed. As a result, the interpolation value y
alters, enabling a frequency characteristic of analogue signals to
be varied. Now, it is described hereunder, focusing on a waveform
produced by synthesizing a waveform exhibited by the fundamental
sampling function f(t) shown in FIG. 1 and a waveform exhibited by
the control sampling function c.sub.0(t), how the sampling function
s.sub.N(t) varies when the variable parameter .alpha. is
changed.
[0119] A waveform of the sampling function s.sub.N(t) produced by
synthesizing the waveform exhibited by the fundamental sampling
function f(t) and the waveform exhibited by the control sampling
function c.sub.0(t) is, as shown in FIG. 8, considerably different
according to a value of the variable parameter a. In the present
embodiment, it was verified that when sequentially varying the
variable parameter .alpha. in the order of -1.5, -0.25, 1.5, the
amplitude of a wavelength of the sampling function s.sub.N(t)
gradually increased both in a region of -2.ltoreq.t.ltoreq.-1 and
in a region of 1.ltoreq.t.ltoreq.2, so that the polarity of the
waveform was inverted. On the other hand, it was verified that the
amplitude of the wavelength of the sampling function s.sub.N(t)
gradually decreased both in a region of -1.ltoreq.t.ltoreq.0 and in
a region of 0.ltoreq.t.ltoreq.1, so that the polarity of the
waveform was inverted.
[0120] Next, as a test piece, the piece for violin "Zigeunerweisen"
recorded on a CD was reproduced for about 23 seconds in the audio
apparatus 1, At this time, in the sound processing means 2, the
variable parameter .alpha. was set at -0.25, -1.5 and 1.5 to
interpolate the discrete data input for about 23 seconds. The
frequency characteristics of the analogue signals interpolated at
this time by each of the sampling functions s.sub.N(t) were
compared to one another and then the results shown in FIG. 9 were
obtained.
[0121] As shown in FIG. 9, in the interpolation process using each
of the sampling functions s.sub.N(t) in which these values of the
variable parameter .alpha. were varied, it was verified that even
if the value of the variable parameter .alpha. was varied, at any
values of the variable parameter .alpha., the signal level
increased at a high-frequency range not less than 20 kHz and as a
result, high-frequency components could be reproduced as compared
to the case where the traditional Shannon's sampling function was
used. Further, it was also verified that when the variable
parameter .alpha. was set at 1.5, the signal level decreased at
frequencies less than about 26 kHz, the signal level, however,
increased at higher-frequencies not less than 26 kHz except at the
vicinity of 44.1 kHz and higher-frequency components could be
reproduced as compared to the case where the variable parameter
.alpha. was set at -0.25 and -1.5.
[0122] On the other hand, it was verified that when the variable
parameter .alpha. was set at -1.5, the signal level sharply
decreased in the vicinity of about 26 kHz, and the signal level,
however, increased as a whole at frequencies less than 26 kHz and
besides the signal level increased at higher frequencies than 26
kHz except at the vicinity of 44.1 kHz and then as a result,
high-frequency components could be reproduced at a different signal
level as compared to the case where the variable parameter .alpha.
was set at -0.25 and -1.5.
[0123] Further, it was verified that when the variable parameter
.alpha. was set at -0.25, the signal level increased as a whole
except at the vicinity of 44.1 kHz and as a result, high-frequency
components could be reproduced at a different signal level as
compared to the case where the variable parameter .alpha. was set
at 1.5 and -1.5.
[0124] Next, as test pieces, its sounds whose reproducing
frequencies were fixed at 10 kHz and 20 kHz were reproduced in the
audio apparatus 1. At this time, in the sound processing means 2,
the value of the variable parameter .alpha. was switched in the
range of -5 to 5 in series to interpolate the discrete data input
in series from the input unit 6. Then, the signal levels of
analogue signals obtained by interpolating discrete data with each
of the sampling functions s.sub.N(t) different in the variable
parameter .alpha. was compared to one another and then the results
shown in FIG. 10 was obtained.
[0125] As shown in FIG. 10, it was verified that in the case of the
reproducing frequency of 10 kHz, when the variable parameter
.alpha. is allowed to continue to increase, the signal level
gradually decreased, and when the variable parameter .alpha. was
between 2 and 3, the signal level rapidly decreased and thereafter
sharply increased again. On the other hand, it was verified that in
the case of the reproducing frequency of 20 kHz, when the variable
parameter .alpha. was allowed to continue to increase, the signal
level gradually decreased and when the variable parameter .alpha.
was at the vicinity of 4, the signal level rapidly decreased and
thereafter sharply increased again. Thus, in the sound processing
means 2, by varying the variable parameter .alpha., even at the
same reproducing frequency, the analogue signals could be
reproduced at a different signal level.
[0126] (4) Behavior and Effect
[0127] In the scheme described above, in the sound processing means
2, the fundamental sampling function f(t) is stored in the
fundamental term calculation means 16 in advance and the distance
to the interpolation position t0 is defined as t for each of the
discrete data d1, d2, d3, d4 extracted by the discrete data
extraction means 15 to calculate a value of the fundamental
sampling function f(t) and then apply the convolution operation to
the values of the fundamental sampling function f(t) allowed to
correspond to each of the discrete data d1, d2, d3, d4, thereby
calculating the fundamental interpolation value ya at the
interpolation position W.
[0128] Further, aside from this, in the sound processing means 2,
the control sampling function c.sub.0(t) is stored in the control
term calculation means 17 in advance and the distance to the
interpolation position t0 is defined as t for each of the discrete
data d1, d2, d3, d4 extracted by the discrete data extraction means
15 to calculate a value of the control sampling function c.sub.0(t)
and then apply the convolution operation to the values of the
control sampling function c.sub.0(t) allowed to correspond to each
of the discrete data d1, d2, d3, d4 and thereafter by multiplying
the results of the convolution operations of the control sampling
function c.sub.0(t) by the variable parameter .alpha. set as an
arbitrary value by a user, thereby calculating the control
interpolation value yb at the interpolation position t0.
[0129] Then, in the sound processing means 2, by linearly adding
the fundamental interpolation value ya and the control
interpolation value yb, the interpolation value y among the
discrete data is calculated. As a result, the interpolation value y
can be calculated which is reflected by the value of the variable
parameter .alpha. by which the control sampling function c.sub.0(t)
is multiplied
[0130] Accordingly, in the sound processing means 2, by varying the
value of the variable parameter .alpha., the interpolation value y
obtained by the interpolation process performed by the sampling
function s.sub.N(t) can be regulated depending on the variable
parameter .alpha.. Thus, a user varies appropriately the variable
parameter .alpha. depending on music reproduction environments,
sound sources, musical tones or the like, thereby making it
possible to reproduce high-quality-sound music with a sound
quality, desired by a user, whose frequency characteristic of
analogue signals is regulated.
[0131] Further, in the sound processing means 2, using the
fundamental sampling function f(t) and the control sampling
function c.sub.0(t) which are only once differentiable in their
whole ranges as the sampling function s.sub.N(t) and have finite
support, the control sampling function c.sub.0(t) is multiplied by
the variable parameter .alpha.. Hence, a calculation amount
required for the interpolation process among the discrete data can
be significantly reduced as compared to the case where the
traditional Shannon's sampling function is used and further the
truncation error does not occur which is generated in the case of
using Shannon's sampling function, thus permitting aliasing
distortion to be prevented from occurring.
[0132] In the present embodiment, a value of the waveform of the
sampling function s.sub.N(t) can be converged to 0 at a range
between each set of ambilateral two sampling positions particularly
sandwiching the interpolation position t0 or in a narrower range
than the above range. Hence, when performing a data interpolation
process or the like using this sampling function s.sub.N(t), each
set of the ambilateral two discrete data of the marked point, that
is, the use of only total four discrete data may be sufficient for
the interpolation process, thus enabling a processing burden to be
markedly reduced as compared to the case where Shannon's sampling
function is used.
[0133] Further, in the present embodiment, the sampling function
s.sub.N(t) is separated into the fundamental sampling function f(t)
and the control sampling function c.sub.0(t) and thereby the two
functions are separately stored and then each of the functions
applies the convolution operation individually to the discrete
data. Then, the calculated results of the convolution operations
between the control sampling function c.sub.0(t) and the discrete
data are multiplied by the variable parameter .alpha. to add the
multiplied results of the convolution operations between the
sampling function s.sub.N(t) and the discrete data to the above
multiplied results and thereby obtain output signals. Hence, only
one control sampling function c.sub.0(t) may be sufficient to
enable formulae to be simplified as much as possible, permitting
the variable control of the sampling function c.sub.0(t) to be
easily performed.
[0134] (5) Other Embodiment
[0135] In addition, in the above embodiment, it has been described
that a plurality of interpolation values among the discrete data is
calculated one by one in series by the fundamental term calculation
means 16 and the control term calculation means 17. The present
invention, however, is not limited to this scheme and a plurality
of the interpolation values among the discrete data may be
calculated in a lump.
[0136] In this case, as shown in FIG. 11 showing its contents with
the same reference symbols attached to portions the same as in FIG.
5, a sound processing means 30 comprises the discrete data
extraction means 15 and a conversion function matrix calculation
means 31. In the conversion function matrix calculation means 31,
by multiplying values Y(t1), Y(t2), Y(t3), Y(t4) of the discrete
data d1, d2, d3, d4, respectively and a conversion matrix A
(described below), a plurality of interpolation values
y.sub.k-2(1), y.sub.k-2(2), . . . , y.sub.k-2(n) among the discrete
data can be calculated in series or in a lump.
[0137] For reference's sake, in this embodiment, it is described
below that as shown in FIG. 12 showing its contents with the same
reference symbols attached to corresponding portions in FIG. 4,
among the four continuous discrete data d1, d2, d3, d4, a position
between the second last discrete data d2 and the third last
discrete data d3 is partitioned into up to 1-n to section the
position with a given sectioned number (in this case, n+1) and then
calculate the interpolation values y.sub.k-2(1), y.sub.k-2(2), . .
. , y.sub.k-2(n) at each position.
[0138] Here, the conversion matrix A is expressed by the following
formula 10.
A = [ S 1 ( n + 1 ) S 2 ( 1 ) S 3 ( n - 1 ) S 4 ( 2 n - 1 ) S 1 ( n
+ 2 ) S 2 ( 2 ) S 3 ( n - 2 ) S 4 ( 2 n - 2 ) S 1 ( n + 3 ) S 2 ( 3
) S 3 ( n - 3 ) S 4 ( 2 n - 3 ) S 1 ( 2 n ) S 2 ( n ) S 3 ( 0 ) S 4
( n ) ] [ Formula 10 ] ##EQU00009##
[0139] This conversion matrix A calculates the sampling function
s.sub.N(t) using the four discrete data d1, d2, d3, d4 and further
calculates n pieces of interpolation values y.sub.k-2(1),
y.sub.k-2(2), . . . , y.sub.k-2(n) among the discrete data d2 and
d3. Hence, the conversion matrix A comprises n rows and 4 columns
with the sampling function s.sub.N(t) defined as elements. Then,
the conversion matrix A is multiplied by a matrix X of one column
having, as its elements, the values Y(t1), Y(t2), Y(t3), Y(t4) of
the discrete data d1, d2, d3, d4 to thereby enable the
interpolation values y.sub.k-2(1), y.sub.k-2(2), . . . ,
y.sub.k-2(n) to be determined. Namely, the interpolation values
y.sub.k-2(1), y.sub.k-2(2), . . . , y.sub.k-2(n) can be determined
by the following formula 11.
[ y k - 2 ( 1 ) y k - 2 ( 2 ) y k - 2 ( 3 ) y k - 2 ( n ) ] = AX =
[ S 1 ( n + 1 ) S 2 ( 1 ) S 3 ( n - 1 ) S 4 ( 2 n - 1 ) S 1 ( n + 2
) S 2 ( 2 ) S 3 ( n - 2 ) S 4 ( 2 n - 2 ) S 1 ( n + 3 ) S 2 ( 3 ) S
3 ( n - 3 ) S 4 ( 2 n - 3 ) S 1 ( 2 n ) S 2 ( n ) S 3 ( 0 ) S 4 ( n
) ] [ Y ( t 1 ) Y ( t 2 ) Y ( t 3 ) Y ( t 4 ) ] [ Formula 11 ]
##EQU00010##
[0140] Here, the conversion matrix A is the sum of the fundamental
term matrix B expressed by the following formula 11 and control
term matrix C expressed by the following formula 13 multiplied by
the variable parameter .alpha. and therefore the conversion matrix
A is expressed by A=B+.alpha.C.
B = [ f 1 ( n + 1 ) f 2 ( 1 ) f 3 ( n - 1 ) f 4 ( 2 n - 1 ) f 1 ( n
+ 2 ) f 2 ( 2 ) f 3 ( n - 2 ) f 4 ( 2 n - 2 ) f 1 ( n + 3 ) f 2 ( 3
) f 3 ( n - 3 ) f 4 ( 2 n - 3 ) f 1 ( 2 n ) f 2 ( n ) f 3 ( 0 ) f 4
( n ) ] [ Formula 12 ] C = [ c 1 ( n + 1 ) c 2 ( 1 ) c 3 ( n - 1 )
c 4 ( 2 n - 1 ) c 1 ( n + 2 ) c 2 ( 2 ) c 3 ( n - 2 ) c 4 ( 2 n - 2
) c 1 ( n + 3 ) c 2 ( 3 ) c 3 ( n - 3 ) c 4 ( 2 n - 3 ) c 1 ( 2 n )
c 2 ( n ) c 3 ( 0 ) c 4 ( n ) ] [ Formula 13 ] ##EQU00011##
[0141] The fundamental sampling function f(t) acts as the elements
of the fundamental term matrix B, while the control sampling
function c(t) acts as the elements of the control term matrix C (t
demotes a distance between an interpolation point and a sampling
position). Accordingly, the interpolation values y.sub.k-2(1),
y.sub.k-2(2), . . . , y.sub.k-2(n) are expressed by the following
formula 14.
[ y K - 2 ( 1 ) y K - 2 ( 2 ) y K - 2 ( 3 ) y K - 2 ( n ) ] = [ S 1
( n + 1 ) S 2 ( 1 ) S 3 ( n - 1 ) S 4 ( 2 n - 1 ) S 1 ( n + 2 ) S 2
( 2 ) S 3 ( n - 2 ) S 4 ( 2 n - 2 ) S 1 ( n + 3 ) S 2 ( 3 ) S 3 ( n
- 3 ) S 4 ( 2 n - 3 ) S 1 ( 2 n ) S 2 ( n ) S 3 ( 0 ) S 4 ( n ) ] [
Y ( t 1 ) Y ( t 2 ) Y ( t 3 ) Y ( t 4 ) ] = [ f 1 ( n + 1 ) f 2 ( 1
) f 3 ( n - 1 ) f 4 ( 2 n - 1 ) f 1 ( n + 2 ) f 2 ( 2 ) f 3 ( n - 2
) f 4 ( 2 n - 2 ) f 1 ( n + 3 ) f 2 ( 3 ) f 3 ( n - 3 ) f 4 ( 2 n -
3 ) f 1 ( 2 n ) f 2 ( n ) f 3 ( 0 ) f 4 ( n ) ] [ Y ( t 1 ) Y ( t 2
) Y ( t 3 ) Y ( t 4 ) ] + .alpha. [ c 1 ( n + 1 ) c 2 ( 1 ) c 3 ( n
- 1 ) c 4 ( 2 n - 1 ) c 1 ( n + 2 ) c 2 ( 2 ) c 3 ( n - 2 ) c 4 ( 2
n - 2 ) c 1 ( n + 3 ) c 2 ( 3 ) c 3 ( n - 3 ) c 4 ( 2 n - 3 ) c 1 (
2 n ) c 2 ( n ) c 3 ( 0 ) c 4 ( n ) ] [ Y ( t 1 ) Y ( t 2 ) Y ( t 3
) Y ( t 4 ) ] [ Formula 14 ] ##EQU00012##
[0142] Practically, the conversion function matrix calculation
means 31 comprises, as shown in FIG. 13, a fundamental term matrix
calculation circuit 32 acting as a fundamental term calculation
means for calculating the fundamental term matrix B and the matrix
X, a control term matrix calculation means 33 acting as a control
term calculation means for calculating the control term matrix C
and the matrix X, a plurality of coefficient multiplication means
18a1, 18a2, . . . , 18an for multiplying the calculated results of
the control term matrix calculation means 33 by the variable
parameter .alpha., and a plurality of the linear adding means 19a1,
19a2, . . . , 19an for linearly adding the calculated results from
the fundamental term matrix calculation circuit 32 and the
calculated results from the coefficient multiplication means 18a1,
18a2, . . . , 18an.
[0143] The fundamental term matrix calculation circuit 32
calculates in advance the fundamental term matrix B acting as the
fundamental sampling function, depending on a sectioned number
among the discrete data and then stores the fundamental matrix B
created by tabulating the calculated values thus obtained in a
given storage means. Then, when receiving the discrete data d1, d2,
d3, d4 from the discrete data extraction means 15, the fundamental
term matrix calculation circuit 32 multiplies the fundamental term
matrix B acting as the tabulated value stored in advance in a given
storage means by the values Y(t1), Y(t2), Y(t3), Y(t4) of the
discrete data d1, d2, d3, d4, with the values of the discrete data
defined as a matrix X of one row. Afterward, the fundamental term
matrix calculation circuit 32 delivers values of each column of the
matrix obtained by the multiplied results to the corresponding
linear adding means 19a1, 19a2, . . . , 19an. Specifically, the
fundamental term matrix calculation circuit 32 delivers the first
column of the matrix obtained as the calculated result,
{f.sub.1(n+1)Y(t1)}+{f.sub.2(1)Y(t2)}+{f.sub.3(n-1)Y(t3)}+{f.sub.4(2n-1)Y-
(t4)} to the linear adding means 19a1 and delivers the second
column of the matrix,
{f.sub.1(n+2)Y(t1)}+{f.sub.2(2)Y(t2)}+{f.sub.3(n-2)Y(t3)}+{f.sub.4(2n-2).-
about.Y(t4)} to the linear adding means 19a2 and afterward delivers
each of values in the third to an n-th column to each of the linear
adding means 19a, . . . , 19an.
[0144] On the other hand, the control term matrix calculation
circuit 33 calculates in advance the control term matrix C, acting
as the control sampling function, depending on the sectioned number
among the discrete data and then stores the control matrix C
created by tabulating the calculated values thus obtained in a
given storage means. Then, when receiving the discrete data d1, d2,
d3, d4 from the discrete data extraction means 15, the control term
matrix calculation circuit 33 multiplies the control term matrix C,
acting as the tabulated value stored in advance in a given storage
means, by the values Y(t1), Y(t2), Y(t3), Y(t4) of the discrete
data d1, d2, d3, d4, with the values of the discrete data defined
as a matrix X of one row. Afterward, the control term matrix
calculation circuit 33 delivers each of column values of the matrix
obtained by the multiplied results to the corresponding coefficient
multiplication means 18a1, 18a2, . . . , 18an. Specifically, the
control term matrix calculation circuit 33 delivers the first
column of the matrix obtained as the calculated result,
{c.sub.1(n+1)Y(t1)}+{c.sub.2(1)Y(t2)}+{c.sub.3(n-1)Y(t3)}+{c.sub.4(2n-1)Y-
(t4)} to the coefficient multiplication means 18a1 and delivers the
second column of the matrix,
{c.sub.1(n+2)Y(t1)}+{c.sub.2(2)Y(t2)}+{c.sub.3(n-2)Y(t3)}+{c.sub.4(2n2)Y(-
t4)} to the coefficient multiplication means 18a2 and afterward
delivers each of values in the third to the n-th column to the
coefficient multiplication means 18a3, . . . , 18an.
[0145] Each of the coefficient multiplication means 18a1, 18a2, . .
. , 18an multiplies each value of the columns of the matrix
calculated in the control term matrix calculation circuit 33 by the
variable parameter .alpha. set by a user in the parameter setting
unit 7 to deliver the multiplied values to the corresponding linear
adding means 19a1, 19a2, . . . , 19an. Each of the linear adding
means 19a1, 19a2, . . . , 19an linearly adds the calculated results
received from the fundamental term matrix calculation circuit 32
and the calculated results received from the coefficient
multiplying calculation means 18a1, 18a2, . . . , 18an, thereby
permitting the interpolation values y.sub.k-2(1), y.sub.k-2(2), . .
. , y.sub.k-2(n) to be produced.
[0146] In the scheme described above, in the sound processing means
30, in addition to the effect the same as in the above embodiment,
the fundamental term matrix B is stored in the fundamental term
matrix calculation circuit 32 and besides the control term matrix C
is stored in the control term matrix calculation circuit 33. Then,
the values Y(t1), Y(t2), Y(t3), Y(t4) of the discrete data d1, d2,
d3, d4 are subjected to multiplication as the matrix X of one row.
Hence, the interpolation values y.sub.k-2(1), y.sub.k-2(2), . . . ,
y.sub.k-2(n) existing among the interpolation positions 1 to n
between given discrete data d2 and d3 among the continuous four
discrete data d1, d2, d3, d4 can be easily calculated in a
lump.
[0147] In addition, in the above embodiment, it has been described
that the fundamental term matrix B and the control term matrix C
were used which were applicable to only the discrete data sequence
in which the sectioned number among the marked discrete data was
n+1 that is a constant value. The present invention, however, is
not limited to this case and a fundamental term matrix and a
control term matrix may be used which are applicable to a plurality
of discrete data sequences different in sectioned number among the
marked discrete data. Specifically, in this case, in the conversion
function matrix calculation means, in order apply to a plurality of
the discrete data sequences different in sectioned number, the
fundamental term matrix B and the control term matrix C are
calculated in advance using a sectioned number of the lowest common
multiple in a plurality of sectioned numbers to be tabulated. Then,
according to the sectioned number set at the start of inputting the
discrete data, a calculated value corresponding to the sectioned
number is selected as a tabulated number from among the fundamental
term matrix B and the control term matrix C and thereafter the
convolution operation is applied between the selected tabulated
value and the discrete data. As a result, the conversion function
matrix calculation means has stored only one set of the fundamental
term matrix B and control term matrix C in advance, thereby making
it possible to correspond to a plurality of the discrete data
sequences different in the sectioned number. Hence, the storage
capacity in a storage means can be reduced, permitting a processing
burden in the whole of the apparatus to be decreased.
[0148] Further, the present invention is not limited to the present
embodiment and various modifications are possible within the scope
of the gist of the present invention. For example, as the sampling
function s.sub.N(t), a piecewise polynomial of finite support only
once differentiable in the whole range has been used. However, the
number of times of differentiability may be set twice or more.
[0149] Furthermore, in the above embodiment, it has been described
that the sampling function s.sub.N(t) was used to perform the
interpolation process, producing the analogue signals. The present
invention is not limited to this case and an oversampling process
is simply performed by performing the interpolation process using
the sampling function s.sub.N(t) and thereafter the analogue
signals may be produced by means of an digital-to-analogue
conversion device.
[0150] Moreover, in the above embodiment, it has been described
that the sampling function s.sub.N(t) was allowed to converge to 0
at t=.+-.2. The present invention is, however, not limited to this
case and the sampling function s.sub.N(t) may be allowed to
converge to 0 at t=.+-.3 or more. For example, when doing so, the
last six discrete data are extracted by the discrete data
extraction means 15 and thereby the values of the sampling function
s.sub.N(t) can be calculated for these six discrete data by the
function processing means 14.
[0151] Further, in the above embodiment, it has been described that
the fundamental sampling function f(t) is stored in the fundamental
term calculation means 16 and aside from this, the control sampling
function c.sub.0(t) is stored in the control term calculation means
17 in advance. Then, the convolution operation is applied to the
discrete data d1, d2, d3, d4 for each of the fundamental sampling
function f(t) and control sampling function c.sub.0(t) to calculate
the fundamental interpolation value ya and the control
interpolation value yb and thereafter the fundamental interpolation
value ya and the control interpolation value yb are linearly added
to calculate the interpolation value y. The present invention is,
however, not limited to this case. The fundamental sampling
function f(t) and the control sampling function c.sub.0(t) may be
stored as one sampling function s.sub.N(t) in advance and using a
sampling function s.sub.N(t) in which the variable parameter
.alpha. is varied, the convolution operation may be applied to the
discrete data d1, d2, d3, d4 to calculate directly the
interpolation value y.
[0152] In this case, as a specified configuration, the function
processing means stores the sampling function s.sub.N(t) produced
by linearly adding the fundamental sampling function f(t) and the
control sampling function c.sub.0(t) in advance and may includes a
calculation means for calculating a value of the sampling function
s.sub.N(t) using a distance to the marked point determined for each
of the discrete data and the convolution operation means for
calculating an interpolation value at the marked point by applying
the convolution operation to the sampling function s.sub.N(t)
allowed to correspond to each of the discrete data. As a result, in
the function processing means, the sampling function s.sub.N(t) is
calculated in advance and hence the number of times of
multiplication is reduced as compared to a case where the
fundamental sampling function f(t) and the control sampling
function c.sub.0(t) are independently calculated and thereby the
number of times of multiplication is reduced and hence the number
of times of calculation and the number of multipliers can be
reduced, thus leading to the adaptability when a low-speed
calculating device is used.
Second Embodiment
[0153] Next, a second embodiment different from the first
embodiment discussed above is explained hereinafter. Here, instead
of using the aforementioned FIG. 1 to 7, FIG. 10 to 13, new
drawings are used for explanation. In the following drawings,
although reference numbers identical to those in FIG. 1 to 7, FIG.
10 to 13 are found, such reference numbers are specifically
provided to describe the configuration of an audio device according
to the second embodiment explained hereinafter.
(1) Overall Configuration of the Audio Device
[0154] In FIG. 14, reference number 1 is the whole of an audio
device comprising a sound processing unit 3 according to the
present invention. This audio device 1 reproduces various recording
media including CD, DVD and so on by means of an input unit 2, and
sequentially sends out to a sound processing unit 3 a plurality of
discrete data thus obtained and temporally-ordered. In fact, the
discrete data is obtained by, for example, sampling at constant
time interval continuous signals which vary smoothly, and
quantizing the sampling data thus obtained.
[0155] The sound processing unit 3 acting as a sound processing
apparatus comprises: a band separation means 4 for separating the
discrete data into three frequency bands including, for example, a
low-frequency range, an mid-frequency range and a high-frequency
range; a sound pressure regulating unit 5 for regulating the sound
pressure level with respect to the three frequency bands of the
low-frequency range, the mid-frequency range and the high-frequency
range; an interpolation processing unit 6 for individually
performing interpolation with respect to each frequency band using
a predetermined sampling function (explained later) individually
set for each frequency band; a setting unit 7 which allows the user
to freely set a sound pressure level and the sampling function with
respect to each frequency band; and a band synthesizing unit 8 for
producing an analog signal acting as a synthesized signal by
synthesizing interpolation processed signal produced with respect
to each frequency band.
[0156] In fact, as shown in FIG. 15, the sound processing unit 3
has a band separation means 4 comprising a digital low-pass filter
4a, a digital band-pass filter 4b and a digital high-pass filter
4c, and is capable of separating the discrete data into the
frequency bands of the low-frequency range, the mid-frequency range
and the high-frequency range. Further, although this embodiment
describes a case in which FIR (Finite duration Impulse Response)
filter is employed as the digital low-pass filter 4a, the digital
band-pass filter 4b and the digital high-pass filter 4c, the
present invention is not limited to such a configuration and
various kinds of other digital filters such as IIR (Infinite
Impulse Response) filter may also be employed.
[0157] The band separation means 4 produces a band-by-band signal
of the low-frequency range in which a high-frequency range
component has been removed, by capturing a predetermined number of
the discrete data by means of the digital low-pass filter 4a and
averaging the discrete data thus captured. The band separation
means 4 then sends out such a band-by-band signal to the sound
pressure regulating unit 5 and the digital band-pass filter 4b.
[0158] The digital high-pass filter 4c produces from the discrete
data a band-by-band signal of the high-frequency range in which a
preset low-frequency range component has been removed, by adding or
subtracting the discrete data and a newly inputted discrete data
with a preset weighting ratio. The digital high-pass filter 4c then
sends out such a band-by-band signal to the sound pressure
regulating unit 5 and the digital band-pass filter 4b.
[0159] The digital band-pass filter 4b produces a band-by-band
signal of the remaining mid-frequency range in which both the low-
and high-frequency range components have been removed, by
subtracting from the value of the discrete data the values of the
corresponding band-by-band signals of the low- and high-frequency
range. The digital band-pass filter 4b then sends out such a
band-by-band signal to the sound pressure regulating unit 5.
[0160] The sound pressure regulating unit 5 is equipped with three
amplifiers 5a, 5b and 5c corresponding to each of the low-frequency
range, the mid-frequency range and the high-frequency range,
respectively. An amplification coefficient for amplifying the sound
pressure level of the band-by-band signal can be individually set
with respect to each of the amplifier 5a, 5b and 5c by virtue of a
sound pressure level regulating command from the setting unit
7.
[0161] Accordingly, in the sound pressure regulating unit 5, the
amplifier 5a can amplify the band-by-band signal of the
low-frequency range by multiplying only the band-by-band signal by
a predetermined amplification coefficient. The amplifier 5b can
amplify the band-by-band signal of the mid-frequency range by
multiplying only the band-by-band signal by a predetermined
amplification coefficient. The amplifier 5c can amplify the
band-by-band signal of the high-frequency range by multiplying only
the band-by-band signal by a predetermined amplification
coefficient. Therefore, once the amplification coefficient has been
set by a user having comparative difficulty in catching the
low-frequency range so that only the sound pressure level of the
band-by-band signal of the low-frequency range is amplified, the
sound pressure regulating unit 5 produces a band-by-band regulated
signal whose sound pressure has been amplified in accordance with
the aforementioned amplification coefficient.
[0162] In this way, each of the amplifiers 5a, 5b, and 5c amplifies
the sound pressure level of each band-by-band signal to a
predetermined value based on the amplification coefficient acting
as a predetermined sound pressure parameter individually set in
advance, and individually sends out each band-by-band regulated
signal thus produced to the interpolation processing unit 6. Here,
the interpolation processing unit 6 is equipped with three
band-by-band-by-band interpolation units 6a, 6b and 6c
corresponding to each of the low-frequency range, the mid-frequency
range and the high-frequency range, respectively. Further, a
predetermined sampling function for performing interpolation on
each band-by-band-by-band regulated signal can be individually set
with respect to each band-by-band interpolation unit 6a, 6b and 6c
by virtue of an interpolation processing selection command from the
setting unit 7.
[0163] Accordingly, the band-by-band interpolation unit 6a performs
interpolation only on the band-by-band regulated signal of the
low-frequency range based on the sampling function set by the
setting unit 7 in advance, and by interpolating a
band-by-band-by-band data composing the band-by-band regulated
signal, increases a sampling frequency in a pseudo manner to
produce an interpolation processed signal. The band-by-band
interpolation unit 6a then sends out the interpolation processed
signal thus obtained to the band synthesizing unit 8. Further, at
that time, the band-by-band interpolation unit 6b performs
interpolation only on the band-by-band regulated signal of the
mid-frequency range based on a sampling function set by the setting
unit 7 independently from sampling functions provided for other
band-by-band interpolation units 6a, 6c, and increases a sampling
frequency in a pseudo manner to produce an interpolation processed
signal by interpolating the band-by-band-by-band data composing the
band-by-band regulated signal. The band-by-band interpolation unit
6b then sends out the interpolation processed signal thus obtained
to the band synthesizing unit 8. In addition, at that time, the
band-by-band interpolation unit 6c performs interpolation only on
the band-by-band regulated signal of the high-frequency range based
on a sampling function set by the setting unit 7 independently from
those provided for other band-by-band interpolation units 6a, 6b,
and by interpolating the band-by-band-by-band data composing the
band-by-band regulated signal, increases a sampling frequency in a
pseudo manner to produce an interpolation processed signal. The
band-by-band interpolation unit 6c then sends out the interpolation
processed signal thus obtained to the band synthesizing unit 8.
[0164] The band synthesizing unit 8 produces one analog signal
having all frequency bands by synthesizing a plurality of the
interpolation processed signals produced in each of the
band-by-band interpolation units 6a, 6b and 6c, and sends out such
an analog signal to an output unit 9. In this sense, since the
interpolation processing unit 6 of the sound processing unit 3
individually performs interpolation with respect to each frequency
band, different sampling function can be freely set with respect to
each frequency band. Therefore, the sound processing unit 3
regulates an interpolation value for interpolating the band-by-band
data with respect to each band-by-band regulated signal by
appropriately modifying the sampling function, thereby enabling an
interpolation processed signal regulated to be produced with
respect to each frequency band, and thus making it possible to
reproduce from the output unit 9 music having a sound quality
desired by a user, in which the frequency characteristic of the
analog signals has been finely regulated.
(2) Interpolation Process in the Band-by-Band Interpolation
Unit
[0165] Next, the concept of the interpolation process carried out
in each band-by-band interpolation unit 6a, 6b and 6c is described
hereinafter. A sampling function S.sub.N(t) employed in the
band-by-band interpolation unit 6a, 6b and 6c includes a
fundamental sampling function f(t) and a control sampling function
c.sub.0(t). Here, when the sampling position of the discrete data
is t, the sampling function S.sub.2(t) composed of the fundamental
sampling function f(t) and the control sampling function c.sub.0(t)
is expressed by the following formula 15, between the sampling
position [-2, 2] of the discrete data
s.sub.2(t)=f(t)+.alpha.c.sub.0(t) [Formula 15] [0166] where
c.sub.0(t)=c.sub.r(t)+c.sub.r(-t)
[0167] And, when a general control sampling function is c.sub.k(t)
and when c.sub.k(t)=c.sub.r(t-k)+c.sub.r(-t-k), the sampling
function S.sub.N(t) between the sampling positions [-N, N] of the
aforementioned discrete data is expressed by the following
formula.
S N ( t ) = f ( t ) + k = 0 N - 2 .alpha. k c k ( t ) [ Formula 16
] ##EQU00013##
[0168] However, .alpha..sub.k represents a variable parameter
described later, and is an arbitrary value settable by a user.
Further, .alpha..sub.k may also be an identical number which does
not change in accordance with k, for example
.alpha..sub.1=.alpha..sub.2=.alpha..sub.3 . . . . Further, the
sampling function S.sub.2(t) when N=2 is described below simply as
the sampling function S.sub.N(t) for the sake of simplicity. With
the use of the sampling function S.sub.N(t), an interpolation value
reflecting the value of the variable parameter .alpha. can be
calculated, thereby making it possible to regulate the
interpolation processed signal with respect to each frequency band
by changing the value of the variable parameter .alpha.. The wave
shapes of the fundamental sampling function f(t) and the control
sampling function C.sub.o(t) are shown in FIG. 16, and the
amplitude of the wave shape of the control sampling function
C.sub.o(t) may increase or decrease in accordance with the value of
the variable parameter .alpha..
[0169] The fundamental sampling function f(t) is expressed in the
form of a piecewise polynomial function of finite support focusing
on the differentiability thereof, and can be differentiated only
once in the entire interval. Further, the fundamental sampling
function f(t) has a finite value other 0 when the sampling position
t along the abscissa axis is between -1 and +1 (Namely, interval
[-1, 1]), and invariably takes the value of 0 in the other
intervals. Specifically, the representative functional form of the
fundamental sampling function f(t) is a second-order polynomial.
The fundamental sampling function f(t) has a convex wave shape
differentiable only once in the entire interval, takes the value of
1 only at the sampling position t=0, converges toward 0 when
proceeding to t=.+-.1, and remains 0 until the sampling position
becomes t=.+-.2.
[0170] Further, this fundamental sampling function f(t) may be an
n-order impulse response function of finite support as long as it
is an n-order piecewise polynomial function that is continuous in
an interval defined by sampling points. Specifically, when such a
fundamental sampling function f(t) is a second-order piecewise
polynomial function, it is expressed by the following formula
17.
f ( t ) = { 0 t .di-elect cons. ( - .infin. , - 1 ) 2 ( t + 1 ) 2 t
.di-elect cons. [ - 1 , - 1 2 ) - 2 t 2 + 1 t .di-elect cons. [ - 1
2 , 1 2 ) 2 ( - t + 1 ) 2 t .di-elect cons. [ 1 2 , 1 ) 0 t
.di-elect cons. [ 1 , .infin. ) , [ Formula 17 ] ##EQU00014##
[0171] Furthermore, using this fundamental sampling function f(t),
superposition is carried out based on each band-by-band data
composing the band-by-band regulated signal, thereby making it
possible to temporarily interpolate the values between the
band-by-band data of the band-by-band regulated signal with the
function differentiable only once.
[0172] Meanwhile, the control sampling function c.sub.o(t) is
expressed in the form of a piecewise polynomial function of finite
support focusing on the differentiability thereof, and can be
differentiated only once in the entire interval. Further, the
control sampling function c.sub.o(t) has a finite value other 0
when the sampling position t along the abscissa axis is between -2
and +2 (Namely, an interval [-2, 2]), and invariably takes the
value of 0 in the other intervals. Further, the control sampling
function c.sub.o(t) has a wave shape differentiable only once in
the entire interval, and takes the value of 0 at the sampling
positions t=0, .+-.1 and .+-.2.
[0173] Further, this control sampling function c.sub.o(t) may be an
n-order impulse response function of finite support as long as it
is an n-order piecewise polynomial function that is continuous at
an interval defined by sampling points. Here, the control sampling
function c.sub.o(t) is expressed as a control sampling function
c.sub.o(t)=c.sub.r(t)+c.sub.r(-t) as described above, and this
c.sub.r(t) is specifically expressed by the following formula
18.
c r ( t ) = { 0 t .di-elect cons. ( - .infin. , 0 ) - t 2 t
.di-elect cons. [ 0 , 1 2 ) 3 ( - t + 1 ) 2 - 2 ( - t + 1 ) t
.di-elect cons. [ 1 2 , 1 ) - 3 ( t - 1 ) 2 + 2 ( t - 1 ) t
.di-elect cons. [ 1 , 3 2 ) ( - t + 2 ) 2 t .di-elect cons. [ 3 2 ,
2 ) 0 t .di-elect cons. [ 2 , .infin. ) [ Formula 18 ]
##EQU00015##
[0174] Furthermore, using this control sampling function
c.sub.o(t), superposition is carried out based on each band-by-band
data composing the band-by-band regulated signal, thereby making it
possible to temporarily interpolate the value between the
band-by-band data of the band-by-band regulated signal with the
function differentiable only once.
[0175] The sampling function S.sub.N(t) is expressed as a linear
combination of the fundamental sampling function f(t) and the
control sampling function C.sub.o(t). An actual interpolation
calculation is carried by linearly adding a temporary interpolation
value (referred to as a fundamental interpolation value hereunder)
obtained through the convolution operation of the fundamental
sampling function f(t) and the discrete data (sampled value), and a
temporary interpolation value (referred to as a control
interpolation value hereunder) obtained through the convolution
operation of the control sampling function c.sub.o(t) and the
discrete data (sampled value), thereby making it possible to
interpolate the value between the band-by-band data of the
band-by-band regulated signal with the function differentiable only
once.
[0176] In fact, the function expressed by the linear combination of
the fundamental sampling function f(t) and the control sampling
function c.sub.o(t) satisfies six conditions described below: first
of all, S.sub.2(0)=1, S.sub.2(.+-.1) =S.sub.2(.+-.2)=0; second, the
function is an even function symmetric about the y-axis; third, the
function invariably takes the value of 0 at the sampling position
intervals [-.infin., -2], [2, .infin.]; fourth, the function is at
most a second-order polynomial at each of intervals [n/2, (n+1)/2]
(-4.ltoreq.n.ltoreq.3); fifth, the function is a class C1 function
at the entire interval, and is therefore continuously
differentiable only once; sixth, the function in the sampling
position interval [-1/2, 1/2] is expressed by the following formula
19.
k = - 2 2 s 2 ( t - k ) .ident. 1 [ Formula 19 ] ##EQU00016##
[0177] In addition, at that time, the control sampling function
c.sub.o can be multiplied by the variable parameter .alpha.
arbitrarily set by a user. In this way, with the control sampling
function c.sub.o fixed as the value of 0 at sampling positions t=0,
.+-.1, .+-.2, the amplitude of the wave shape of the control
sampling function c.sub.o can vary between the sampling positions
-2 and +2 in accordance with the value of the aforementioned
variable parameter .alpha.. As a result, the control sampling
function c.sub.o(t) can change the result of the convolution
operation between itself and the discrete data (sample value). In
this way, since the value of the variable parameter .alpha. can be
changed, the frequency characteristic of the interpolation
processed signal calculated by the sampling function S.sub.N(t) can
also be changed, thereby making it possible to regulate the signal
level of the high-frequency range components with respect to each
frequency band.
[0178] Accordingly, the present invention regulates the
interpolation processed signal with respect to each frequency band
by changing the variable parameter .alpha. by which the control
sampling function c.sub.o(t) is multiplied, and produces the analog
signal by synthesizing a plurality of the interpolation processed
signals produced in each frequency band, thereby making it possible
to produce analog signals having the sound quality desired by the
user, in which the high-frequency range has been finely regulated
with respect to each frequency band.
(3) Circuit Configuration of the Band-by-Band Interpolation
Unit
(3-1) Overview of the Interpolation Process in the Band-by-Band
Interpolation Unit
[0179] The three band-by-band interpolation units 6a, 6b and 6c
differ from each other in that the variable parameter .alpha. of
the sampling function S.sub.N(t) for performing interpolation is
individually set, and that the band-by-band regulated signals for
performing the interpolation are different from each other.
However, the band-by-band interpolation units 6a, 6b and 6c are
identical to each other in the rest part of the configuration
thereof. In this sense, explanation is made hereinafter focusing on
the band-by-band interpolation unit 6a for interpolating the
band-by-band regulated signal of the low-frequency range.
[0180] As shown in FIG. 17, the band-by-band interpolation unit 6a
comprises: a data extraction means 15 for sequentially extracting
and retaining a predetermined number (four in this case) of a
band-by-band data composing the band-by-band regulated signal; and
a function processing means 14 for receiving at one time a
predetermined number of the band-by-band data which were extracted
by the data extraction means 15 and were retained therein, and
enabling interpolation using such band-by-band data. The
band-by-band interpolation unit 6a can interpolate the band-by-band
data sequentially inputted from the amplifier 5a at a predetermined
time interval.
[0181] The function processing means 14 comprises a fundamental
term calculation means 16 for processing the convolution operation
of the terms of the fundamental sampling function f(t) among the
sampling function S.sub.N(t), based on the band-by-band data; a
control term calculation means 17 for processing the convolution
operation of the terms of the control sampling function c.sub.o(t)
among the sampling function S.sub.N(t), based on the band-by-band
data; a coefficient multiplication means 18 for multiplying the
result of the calculation completed by the control term calculation
means 17 by the variable parameter .alpha.; and an adding means 19
for linearly adding the result of the calculation completed by the
fundamental term calculation means 16 and the result of the
calculation completed by the coefficient multiplication means
18.
[0182] In the case of this embodiment, the data extraction means 15
extracts the last four band-by-band data from the band-by-band data
inputted in series, retains these four band-by-band data until new
band-by-band data has been inputted, and sends out the four
band-by-band data to the fundamental term calculation means 16 and
the control term calculation means 17
[0183] The fundamental term calculation means 16 stores the
fundamental sampling function f(t) in a predetermined storage means
(not shown), and calculates a value of the fundamental sampling
function f(t) based on a distance between the interpolation
position and the band-by-band data once the interpolation position
between the band-by-band data has been specified. The fundamental
term calculation means 16 can calculate the value of the
fundamental sampling function f(t) individually with respect to
each one of the four band-by-band data sent out by the data
extraction means 15. Further, the fundamental term calculation
means 16 multiplies the four values of the fundamental sampling
function f(t) obtained with respect to each band-by-band data, by
the corresponding values of the band-by-band data, followed by
applying the convolution operation to the four band-by-band data
and sending out the result of this convolution operation to the
adding means 19.
[0184] At the same time, the control term calculation means 17
stores the control sampling function c.sub.o(t) in a predetermined
storage means (not shown), and calculates a value of the control
sampling function c.sub.o(t) based on a distance between the
interpolation position and the band-by-band data once the
interpolation position has been specified. The control term
calculation means 17 can individually calculate the value of the
control sampling function c.sub.o(t) with respect to each one of
the four band-by-band data sent out by the data extraction means
15. Further, the control term calculation means 17 multiplies the
four values of the control sampling function c.sub.o(t) obtained
with respect to each band-by-band data, by the corresponding values
of the band-by-band data, followed by applying the convolution
operation to the four band-by-band data and sending out the result
of this convolution operation to the coefficient multiplication
means 18.
[0185] The coefficient multiplication means 18 multiplies the
result of the convolution operation of the control sampling
function c.sub.o(t), which has received from the control term
calculation means 17, by the variable parameter .alpha., and sends
out to the adding means 19 the result of the multiplication by the
variable parameter. The adding means 19 obtains calculation results
corresponding to the four band-by-band data by linearly adding the
result of the convolution operation of the fundamental sampling
function f(t) received from the fundamental term calculation means
16 and the result of the multiplication by the variable parameter
received from the coefficient multiplication means 18. The value
obtained through the linear adding becomes the interpolation value
of an interpolation position between the predetermined two
band-by-band data. In fact, the value of the interpolation position
is renewed with respect to a predetermined time interval set in
advance, specifically with respect to a value obtained by
multiplying a period T by 1/N (=T/N) corresponding to an input
interval of the band-by-band data.
(3-2) Specific Example for Obtaining the Interpolation Value Based
on the Four Band-by-Band Data
[0186] Next, an explanation is performed hereunder about the
interpolation process for calculating the interpolation value
between the predetermined two band-by-band data based on the
temporally-ordered four band-by-band data, using FIG. 18 showing
the positional relationship between the consecutive four
band-by-band data and the interpolation position which is the
marked point. FIG. 18 shows that each of the values of the
band-by-band data d1, d2, d3, d4 sequentially inputted with respect
to the sampling positions t1, t2, t3, t4 are represented by Y(t1),
Y(t2), Y(t3), Y(t4), respectively, thus describing a case in which
an interpolation value y corresponding to a predetermined position
t0 (namely, interpolation position (a distance b from t2)) between
a sampling positions t2 and t3 is obtained.
[0187] Since the sampling function S.sub.N(t) employed in the
present embodiment converges toward 0 at the sampling position of
t=.+-.2, the band-by-band data d1, d2, d3, d4 within t=.+-.2 may be
considered. Accordingly, when obtaining the interpolation value y
shown in FIG. 18, only the four band-by-band data d1, d2, d3, d4
corresponding to t=t1, t2, t3, t4, respectively may be considered,
thus drastically reducing the calculation amount. In fact,
respective band-by-band data (not shown) at t=.+-.3 or more should
essentially be considered. But, such band-by-band data are
disregarded here not because the calculation amount and accuracy or
the like is considered, but because, theoretically, such
band-by-band data do not need to be considered, and truncation
errors do not occur.
[0188] As shown in FIG. 19, the data extraction means 15 comprises
three shift circuits 20a, 20b, and 20c. Once the consecutive
band-by-band data have been inputted, the data extraction means 15
shifts the band-by-band data in each shift circuit 20a, 20b, and
20c at, for example, a sampling period of CD (44.1 kHz). The data
extraction means 15 can extract and retain the last band-by-band
data d1, d2, d3, and d4 one by one in each shift circuit 20a, 20b
and 20c. Namely, once the four consecutive band-by-band data d1,
d2, d3 and d4 have been inputted, the data extraction means 15
sends out the last band-by-band data d4 directly to a fundamental
term calculation circuit 21a of the fundamental term calculation
means 16 and a control term calculation circuit 22a of the control
term calculation means 17.
[0189] Further, the data extraction means 15 sends out to the shift
circuit 20a a band-by-band data sequence consisting of the four
consecutive band-by-band data d1, d2, d3 and d4, and extracts the
band-by-band data d3 which is the second last band-by-band data in
relation to the last band-by-band data d4 after shifting the
band-by-band data sequence by means of the shift circuit 20b. The
data extraction means 15 then sends out the band-by-band data d3 to
a fundamental term calculation circuit 21b of the fundamental term
calculation means 16 and a control term calculation circuit 22b of
the control term calculation means 17.
[0190] Furthermore, the data extraction means 15 sequentially sends
out the band-by-band data sequence to the other shift circuits 20b,
20c also, and sends out the band-by-band data d2, which is the
third last band-by-band data in relation to the last band-by-band
data d4, to a fundamental term calculation circuit 21c and a
control term calculation circuit 22c after further shifting the
band-by-band data sequence in the shift circuit 20b. The data
extraction means 15 further sends out the band-by-band data d1,
which is the fourth last band-by-band data in relation to the last
band-by-band data d4, to a fundamental term calculation circuit 21d
and a control term calculation circuit 22d after further shifting
the band-by-band data sequence in the shift circuit 20c.
[0191] Here, FIG. 7 and FIG. 8 are the diagrams showing the concept
of the interpolation process regarding the predetermined
interpolation position t0 in the fundamental term calculation means
16 and the control term calculation means 17 of the present
embodiment. With regard to the content of the interpolation
process, two calculation processes are carried out in the beginning
as described above. One of them is a calculation process for
calculating a fundamental interpolation value in the fundamental
term calculation means 16 (simply referred to as fundamental
interpolation value calculation process, hereunder), and the other
is a calculation process for calculating a control interpolation
value in the control term calculation means 17 and the coefficient
multiplication means 18 (simply referred to as control
interpolation value calculation process, hereunder). Explanation is
performed hereunder about the fundamental interpolation value
calculation process and the control interpolation value calculation
process, using FIG. 20 and FIG. 21.
(3-2-1) Fundamental Interpolation Value Calculation Process
[0192] With regard to the content of the fundamental interpolation
value calculation process, as shown in FIGS. 20(A) to (D), the peak
height of the fundamental sampling function f(t) when t=0 (a center
position) is shifted with respect to each of the sampling positions
t1, t2, t3, and t4, and the value of each fundamental sampling
function f(t) at the interpolation position t0 at that time is
obtained.
[0193] When focusing on the band-by-band data d1 at the sampling
position t1 in FIG. 20(A), the distance between the interpolation
position t0 and the sampling position t1 is 1+b. Accordingly, the
value of the fundamental sampling function f(t) is f(1+b) at the
interpolation position t0 when the center position of the
fundamental sampling function f(t) is located at the sampling
position t1. In fact, since the peak height of the center position
of the fundamental sampling function f(t) is allowed to become
identical with the value Y(t1) of the band-by-band data d1, a value
f(1+b)Y(t1) obtained by multiplying the aforementioned f(1+b) by
Y(t1) is the value to be obtained. The calculation of f(1+b) is
carried out in the fundamental term calculation circuit 21a of the
fundamental term calculation means 16, and the calculation in which
f(1+b) is multiplied by Y(t1) is carried out in a fundamental term
multiplication circuit 23a of the fundamental term calculation
means 16 (FIG. 19).
[0194] Similarly, when focusing on the value Y(t2) of the
band-by-band data d2 at the sampling position t2 in FIG. 20(B), the
distance between the interpolation position t0 and the sampling
position t2 is b. Accordingly, the value of the fundamental
sampling function f(t) is f(b) at the interpolation position t0
when the center position of the fundamental sampling function f(t)
is located at the sampling position t2. In fact, since the peak
height of the center position of the fundamental sampling function
f(t) is allowed to become identical with the value Y(t2) of the
band-by-band data d2, a value f(b)Y(t2) obtained by multiplying the
aforementioned f(b) by Y(t2) is the value to be obtained. The
calculation of f(b) is carried out in the fundamental term
calculation circuit 21b of the fundamental term calculation means
16, and the calculation in which f(b) is multiplied by Y(t2) is
carried out in a fundamental term multiplication circuit 23b of the
fundamental term calculation means 16 (FIG. 19).
[0195] When focusing on the value Y(t3) of the band-by-band data d3
at the sampling position t3 in FIG. 20(C), the distance between the
interpolation position t0 and the sampling position t3 is 1-b.
Accordingly, the value of the fundamental sampling function f(t) is
f(1-b) at the interpolation position t0 when the center position of
the fundamental sampling function f(t) is located at the sampling
position t3. In fact, since the peak height of the center position
of the fundamental sampling function f(t) is allowed to become
identical with the value Y(t3) of the band-by-band data, a value
f(1-b)Y(t3) obtained by multiplying the aforementioned f(1-b) by
Y(t3) is the value to be obtained. The calculation of f(1-b) is
carried out in the fundamental term calculation circuit 21c of the
fundamental term calculation means 16, and the calculation in which
f(1-b) is multiplied by Y(t3) is carried out in a fundamental term
multiplication circuit 23c of the fundamental term calculation
means 16 (FIG. 19).
[0196] When focusing on the value Y(t4) of the band-by-band data d4
at the sampling position t4 in FIG. 20(D), the distance between the
interpolation position t0 and the sampling position t4 is 2-b.
Accordingly, the value of the fundamental sampling function f(t) is
f(2-b) at the interpolation position t0 when the center position of
the fundamental sampling function f(t) is located at the sampling
position t4. In fact, since the peak height of the center position
of the fundamental sampling function f(2-b) is allowed to become
identical with the value Y(t4) of the band-by-band data d4, a value
f(2-b).about.Y(t4) obtained by multiplying the aforementioned
f(2-b) by Y(t4) is the value to be obtained. The calculation of
f(2-b) is carried out in the fundamental term calculation circuit
21d of the fundamental term calculation means 16, and the
calculation in which f(2-b) is multiplied by Y(t4) is carried out
in a fundamental term multiplication circuit 23d of the fundamental
term calculation means 16 (FIG. 19).
[0197] In addition, the fundamental term calculation means 16
applies the convolution operation of the four values,
f(1+b).about.Y(t1), f(b)Y(t2), f(1-b)Y(t3), f(2-b).about.Y(t4)
obtained with respect to the marked points of the interpolation
position t0, in a fundamental term convolution circuit 24, and a
fundamental interpolation value ya is calculated in the
low-frequency range. In fact, in the case of this embodiment, since
the values f (l+b)Y(t1) and f(2-b)Y(t4) obtained with respect to
the marked points of the interpolation position t0 are 0 as shown
in FIGS. 20(A) and (D), the fundamental interpolation value ya
becomes {f(b)Y(t2)}+{f(1-b)Y(t3)}.
(3-2-2) Control Interpolation Value Calculation Process
[0198] Meanwhile, with regard to the content of the control
interpolation value calculation process, as shown in FIGS. 21(A) to
(D), the control sampling function c.sub.o(t) when t=0 (a center
position) is allowed to become identical with each of the sampling
positions t1, t2, t3, and t4, and is multiplied by the values,
Y(t1), Y(t2), Y(t3), Y(t4) of the band-by-band data d1, d2, d3, d4
corresponding to each control sampling function c.sub.o(t). The
value of each control sampling function c.sub.o(t) at the
interpolation position t0 at that time is to be obtained.
[0199] When focusing on the value Y(t1) of the band-by-band data d1
at the sampling position t1 in FIG. 21(A), the distance between the
interpolation position t0 and the sampling position t1 is 1+b.
Accordingly, the value of the control sampling function c.sub.o(t)
is c.sub.o(1+b) at the interpolation position t0 when the center
position of the control sampling function c.sub.o(t) is located at
the sampling position t1. In fact, since the height of the wave
shape of the control sampling function c.sub.o(t) is allowed to
become identical with the value Y(t1) of the band-by-band data d1,
a value c.sub.o(1+b)Y(t1) obtained by multiplying the
aforementioned c.sub.o(1+b) by Y(t1) is the value to be obtained.
The calculation of c.sub.o(1+b) is carried out in the control term
calculation circuit 22a of the control term calculation means 17,
and the calculation in which c.sub.o(1+b) is multiplied with Y(t1)
is carried out in a control term multiplication circuit 25a of the
control term calculation means 17 (FIG. 19).
[0200] Similarly, when focusing on the value Y(t2) of the
band-by-band data d2 at the sampling position t2 in FIG. 21(B), the
distance between the interpolation position t0 and the sampling
position t2 is b. Accordingly, the value of the control sampling
function c.sub.o(t) is c.sub.o(b) at the interpolation position t0
when the center position of the control sampling function
c.sub.o(t) is located at the sampling position t2. In fact, since
the height of the wave shape of the control sampling function
c.sub.o(t) is allowed to become identical with the value Y(t2) of
the band-by-band data d2, a value c.sub.o(b)Y(t2) obtained by
multiplying the aforementioned c.sub.o(b) by Y(t2) is the value to
be obtained. The calculation of c.sub.o(b) is carried out in the
control term calculation circuit 22b of the control term
calculation means 17, and the calculation in which c.sub.o(b) is
multiplied with Y(t2) is carried out in a control term
multiplication circuit 25b of the control term calculation means 17
(FIG. 19).
[0201] When focusing on the value Y(t3) of the band-by-band data d3
at the sampling position t3 in FIG. 21(C), the distance between the
interpolation position t0 and the sampling position t3 is 1-b.
Accordingly, the value of the control sampling function c.sub.o(t)
is c.sub.o(1-b) at the interpolation position t0 when the center
position of the control sampling function c.sub.o(t) is located at
the sampling position t3. In fact, since the height of the wave
shape of the control sampling function c.sub.o(t) is allowed to
become identical with the value Y(t3) of the band-by-band data d3,
a value c.sub.o(1-b)Y(t3) obtained by multiplying the
aforementioned c.sub.o(1-b) by Y(t3) is the value to be obtained.
The calculation of c.sub.o(1-b) is carried out in the control term
calculation circuit 22c of the control term calculation means 17,
and the calculation in which c.sub.o(1-b) is multiplied with Y(t3)
is carried out in a control term multiplication circuit 25c of the
control term calculation means 17 (FIG. 19).
[0202] When focusing on the value Y(t4) of the band-by-band data d4
at the sampling position t4 in FIG. 21(D), the distance between the
interpolation position t0 and the sampling position t4 is 2-b.
Accordingly, the value of the control sampling function c.sub.o(t)
is c.sub.o(2-b) at the interpolation position t0 when the center
position of the control sampling function c.sub.o(t) is located at
the sampling position t4. In fact, since the height of the wave
shape of the control sampling function c.sub.o(2-b) is allowed to
become identical with the value Y(t4) of the band-by-band data d4,
a value c.sub.o(2-b).about.Y(t4) obtained by multiplying the
aforementioned c.sub.o(2-b) by Y(t4) is the value to be obtained.
The calculation of c.sub.o(2-b) is carried out in the control term
calculation circuit 22d of the control term calculation means 17,
and the calculation in which c.sub.o (2-b) is multiplied with Y(t4)
is carried out in a control term multiplication circuit 25d of the
control term calculation means 17 (FIG. 19).
[0203] In addition, a control term convolution operation circuit 26
of the control term calculation means 17 performs convolution
operations of the four values, c.sub.o(1+b)Y(t1), c.sub.o(b)Y(t2),
c.sub.o(1-b)Y(t3), c.sub.o(2-b)Y(t4) obtained with respect to the
marked points of the interpolation position t0. The result thus
obtained is further multiplied with the variable parameter .alpha.
in the coefficient multiplication means 18. In this way, a control
interpolation value yb in the frequency band of the low-frequency
range is calculated.
(3-2-3) Interpolation Value Calculation Process
[0204] The adding means 19 can output an interpolation value y of
the interpolation position t0 in the low-frequency range by
linearly adding the fundamental interpolation value ya, which is
calculated by the fundamental term calculation means 16 and
corresponds to the marked point, and the control interpolation
value yb, which is calculated by the control term calculation means
17 and the coefficient multiplication means 18 and corresponds to
the marked points. In this way, the interpolation values of all the
other interpolation positions between the band-by-band data d2 and
d3 are calculated in the same way, and the same method for
processing interpolation can be carried out also in the
band-by-band interpolation unit 6b, 6c, using sampling functions
set with respect to the mid-frequency range and the high-frequency
range.
(3-3) Result of the Interpolation Process when the Value of the
Variable Parameter has Been Changed
[0205] In addition to such configuration, in the sound processing
unit 3, the value of the variable parameter .alpha. of the
coefficient multiplication means 18 is changed with respect to each
band-by-band interpolation unit 6a, 6b, and 6c via the setting unit
7, thereby allowing the values of the sampling function S.sub.N(t)
to be changed with respect to each band-by-band interpolation unit
6a, 6b and 6c, thus making it possible to regulate the
interpolation value y with respect to each frequency band. As a
result, the frequency characteristics of the analog signal produced
in the band synthesizing unit 8 can be regulated by changing the
value of the variable parameter .alpha. with respect to each
frequency band. Here, explanation is made hereunder about how the
sampling function S.sub.N(t) changes when the variable parameter
.alpha. has been changed, while focusing on the wave shape
combining the wave shape of the fundamental sampling function f(t)
with the wave shape of the control sampling function c.sub.o(t) as
shown in FIG. 16
[0206] As shown in FIG. 8 of the first embodiment described above,
the wave shape of the sampling function S.sub.N(t) combining the
wave shape of the fundamental sampling function f(t) with the wave
shape of the control sampling function c.sub.o(t) drastically
varies in accordance with the value of the variable parameter
.alpha.. Here, a wave shape having the characteristics as shown in
FIG. 9 described in the aforementioned first embodiment is produced
in a similar way even when the band-by-band data produced by
separating the discrete data into the frequency bands of the
low-frequency range, the mid-frequency range and the high-frequency
range have been interpolated, thereby making it possible to
reproduce the high-frequency range component within each range of
the low frequency, the mid-frequency and the high frequency, as
compared to the conventional case in which Shannon's sampling
function is used.
[0207] Further, as shown in FIG. 9, when the variable parameter
.alpha. was set to 1.5, -1.5, or -0.25, the wave shape of each
signal level was found to be different from each other. But, a wave
shape having such characteristics is produced in a similar way even
when the band-by-band data produced by separating the discrete data
into the frequency bands of the low-frequency range, the
mid-frequency range and the high-frequency range have been
interpolated. Accordingly, in the second embodiment, the signal
level within each frequency band of the low-frequency range, the
mid-frequency range and the high-frequency range can be regulated
individually by appropriately changing the value of the variable
parameter .alpha. with respect to each frequency band of the
low-frequency range, the mid-frequency range and the high-frequency
range.
[0208] In this sense, the sound processing unit 3 can finely
regulate the signal level with respect to each frequency band by
changing the variable parameter .alpha. of the sampling function
S.sub.N(t) with respect to each frequency band, thereby allowing
the user to further finely regulate the frequency characteristics
with ease. In this way, in the present invention, each
interpolation processed signal is individually regulated by
changing the variable parameter .alpha. with respect to each
frequency band. An analog signal is then produced by synthesizing a
plurality of the interpolation processed signals regulated in a
manner as described earlier, thereby making it possible to produce
an analog signal whose high-frequency range has been finely
regulated with respect to each frequency band.
(4) Calculation and Effect
[0209] With regard to the aforementioned configuration, in the
sound processing unit 3, the discrete data are separated into each
frequency band of the low-frequency range, the mid-frequency range
and the high-frequency range. Further, the band-by-band
interpolation units 6a, 6b and 6c are provided with respect to a
plurality of the band-by-band regulated signals produced in each
frequency band, thereby making it possible to individually
interpolate the band-by-band regulated signal via each band-by-band
interpolation unit 6a, 6b and 6c. In this way, in the sound
processing unit 3, the sampling function used for performing
interpolation with respect to each frequency band can be changed.
And, by changing such sampling function with respect to each
frequency band, the interpolation processed signal obtained through
interpolation can be finely regulated with respect to each
frequency band. Therefore, by synthesizing a plurality of the
interpolation processed signals obtained through such
interpolation, the frequency characteristics of the analog signal
can be finely changed as necessary, thereby making it possible to
reproduce music with a high sound quality desired by the user.
[0210] In this sense, in the sound processing unit 3, the
interpolation processed signal whose interpolation value has been
finely regulated with respect to each frequency band is produced.
And, an analog signal is further produced by synthesizing such a
plurality of the interpolation processed signals. Therefore, by
allowing the user to appropriately change the sampling function
with respect to each frequency band and in accordance with various
conditions including reproduction environment, sound source, music
tones and so on, it becomes possible to reproduce music with a high
quality desired by the user, in which the frequency characteristics
of the analog signal have been regulated.
[0211] Specifically, in the present invention, since the variable
parameter .alpha. of the sampling function S.sub.N(t) can be
individually changed with respect to each frequency band to perform
interpolation, the interpolation value can be finely regulated with
respect to each frequency band, thereby making it possible to
further finely regulate the frequency characteristics of the analog
signal. Namely, as compared to the case in which the frequency
characteristics are regulated by simply changing the variable
parameter .alpha. of the sampling function S.sub.N(t) so as to
interpolate the discrete data of all frequency bands without
separating such discrete data into each frequency band of the low,
the intermediate and the high-frequency range, the present
invention allows the interpolation value to be finely regulated
with respect to each frequency band, thereby making it possible to
further finely regulate the frequency characteristics of the analog
signal and reproduce music with a high quality desired by the
user.
[0212] Further, in the case of this embodiment, the fundamental
sampling function f(t) is stored in the fundamental term
calculation means 16 in advance, followed by calculating the value
of the fundamental sampling function f(t) while t represents the
distance to the interpolation position t0 from each band-by-band
data d1, d2, d3 and d4 extracted by the data extraction means 15,
and then applying convolution operation to the value of the
fundamental sampling function f(t) corresponding to each
band-by-band data d1, d2, d3 and d4. In this way, the fundamental
interpolation value ya at the interpolation position t0 is
calculated.
[0213] Furthermore, in the sound processing unit 3, the control
sampling function C.sub.o(t) is stored in the control term
calculation means 17 in advance, followed by calculating the value
of the control sampling function c.sub.o(t) while t represents the
distance to the interpolation position t0 from each band-by-band
data d1, d2, d3 and d4 extracted by the data extraction means 15,
and then applying convolution operation to the value of the control
sampling function c.sub.o(t) corresponding to each band-by-band
data d1, d2, d3 and d4. In addition, the result of the convolution
operation of the control sampling function c.sub.o(t) is multiplied
with the variable parameter .alpha. of an arbitrary number set by a
user, thereby obtaining the control interpolation value yb at the
interpolation position t0.
[0214] Also, in the sound processing unit 3, the fundamental
interpolation value ya and the control interpolation value yb thus
obtained are linearly added together so as to calculate the
interpolation value y between the discrete data, thereby making it
possible to obtain an interpolation value y reflecting the value of
the variable parameter .alpha. with which the value of the control
sampling function C.sub.o(t) is multiplied.
[0215] Accordingly, in the sound processing unit 3, the
interpolation value y obtained through the interpolation process by
the sampling function S.sub.N(t) can be easily regulated by simply
changing the value of the variable parameter .alpha., thereby
eliminating the necessity of providing a plurality of circuit
boards with respect to each different sampling function S.sub.N(t),
and thus simplifying the configuration and reducing the cost.
[0216] Further, in the sound processing unit 3, the fundamental
sampling function f(t) and the control sampling function
c.sub.o(t), both of which are of finite support and can be
differentiated for only once in the entire interval, are employed
as the sampling function S.sub.N(t), and the control sampling
function c.sub.o(t) is multiplied with the variable parameter
.alpha., thereby making it possible to drastically reduce the
calculation amount needed for interpolating the discrete data as
compared to the conventional case in which Shannon's sampling
function is used, and prevent aliasing distortion since truncation
errors as observed in the case in which Shannon's sampling function
is used do not occur.
[0217] In the case of this embodiment, the value of the wave shape
of the sampling function S.sub.N(t) is allowed to converge toward 0
in an interval defined by a set of two interpolation positions
located before and after the interpolation position t0 or a
narrower interval. Therefore, only four discrete data including the
two discrete data located before and after the focal position are
used when performing data interpolation and the like using the
sampling function S.sub.N(t), thereby drastically reducing a
processing burden as compared to the case in which Shannon's
sampling function is used.
[0218] Further, in the case of this embodiment, with regard to the
sampling function S.sub.N(t), the fundamental sampling function
f(t) and the control sampling function C.sub.o(t) which varies due
to the value of the variable parameter .alpha. are stored
independently from each other, and individually apply convolution
operation to the discrete data. The result of the convolution
operation of the control sampling function C.sub.o(t) and the
discrete data is multiplied with the variable parameter .alpha.,
and the result of the convolution operation of the fundamental
sampling function S.sub.N(t) and the discrete data is linearly
added to the result thus obtained. In this way, an output signal is
obtained, and because of such configuration, only one control
sampling function C.sub.o(t) is needed, thereby simplifying the
formulas as much as possible and allowing the variable control of
the control sampling function C.sub.o(t) to be carried out
easily.
[0219] In addition, in the sound processing unit 3, the amplifier
5a, 5b and 5c is provided with respect to each frequency band and
the sound pressure level is individually amplified by each
amplifier 5a, 5b and 5c, thereby allowing the user to choose to
amplify only the sound pressure level of the frequency band he/she
finds difficult to catch as necessary, and thus making it possible
to reproduce music with a high quality desired by the user.
(5) Other Embodiments
[0220] However, the present invention is not limited to the present
embodiment, and various modifications can be made without departing
from its inventive spirit. For example, although the sampling
function S.sub.N(t) is a piece wise polynomial function of finite
support, which can be differentiated for only once in the entire
interval, the number of times the function can be differentiated
may be set to two or more. Further, in the aforementioned
embodiment, explanation was made about the configuration in which
the analog signal is produced as a synthesized signal by performing
interpolation using the sampling function S.sub.N(t). However, the
present invention is not limited to such configuration, and may
employ a configuration in which a synthesized signal which has been
simply oversampled is produced by performing interpolation using
the sampling function S.sub.N(t), followed by producing the analog
signal by means of an analog-digital converter.
[0221] Further, in the aforementioned embodiment, explanation was
made about the case in which the sampling function S.sub.N(t)
converges toward 0 when t=.+-.2. However, the present invention is
not limited to such case, and the sampling function S.sub.N(t) can
be rendered to converge toward 0 when t=.+-.3 or more. For example,
when the sampling function S.sub.N(t) converges toward 0 when
t=.+-.3, the last six discrete data are extracted by the data
extraction means 15, and the values of the sampling function
S.sub.N(t) are calculated with respect to these six discrete data
by means of the function processing means 14.
[0222] Furthermore, in the aforementioned embodiment, the
fundamental sampling function f(t) and the control sampling
function C.sub.o(t) are stored in the fundamental term calculation
means 16 and the control term calculation means 17 respectively.
The fundamental interpolation value ya and the control
interpolation value yb are then calculated by applying convolution
operation to the band-by-band data d1, d2, d3 and d4 using the
fundamental sampling function f(t) and the control sampling
function c.sub.o(t) respectively, followed by linearly adding the
fundamental interpolation value ya and the control interpolation
value yb so as to obtain the interpolation value y. However, the
present invention is not limited to such configuration. The
sampling function S.sub.N(t) can be obtained by linearly adding the
fundamental sampling function f(t) and the control sampling
function c.sub.o(t) in advance, and stored. In this case, using the
sampling function S.sub.N(t) whose variable parameter .alpha. has
been changed, convolution operation of the band-by-band data d1,
d2, d3 and d4 can be applied so as to directly calculate the
interpolation value y.
[0223] Furthermore, in the aforementioned embodiment, explanation
was made about the case in which the interpolation process is
carried out with respect to the band-by-band regulated signal whose
sound pressure level has been amplified. However, the present
invention is not limited to such case. The predetermined
interpolation process can also be carried out with respect to each
band-by-band signal by rendering an interpolation process unit to
directly receive a band-by-band signal separated by the band
separation means into the predetermined frequency bands, without
amplifying the sound pressure with respect to each frequency
band.
[0224] Furthermore, in the aforementioned embodiment, explanation
was made about the case in which the interpolation process is
carried out after the sound pressure has been amplified. However,
the present invention is not limited to such configuration. As a
matter of fact, the sound pressure level can be amplified after the
interpolation process has been carried out. In this case, the
interpolation process is individually carried out with respect to
the band-by-band regulated signal, and the interpolation processed
signals thus obtained is then individually multiplied with the
sound pressure parameter.
[0225] Furthermore, in the aforementioned embodiment, the
explanation was made about the case in which the sound pressure
level of the frequency band a user finds difficult to catch is
amplified by multiplying the amplification coefficient acting as
the sound pressure parameter. However, the present invention is not
limited to such a configuration. As a matter of fact, the sound
pressure level of the frequency band a user finds easy to catch can
be attenuated by multiplying an attenuation value acting as the
sound pressure parameter. Even in this case, other frequency bands
whose sound pressure levels have not been attenuated can also be
emphasized, thereby making it easy for a user to catch the
frequency band he/she usually finds difficult to catch, thus making
it possible to reproduce a music with a high quality desired by the
user.
[0226] Furthermore, in the aforementioned embodiment, explanation
was made about the case in which the discrete data is separated
into three frequency bands of the low-frequency range, the
mid-frequency range and the high-frequency range. However, the
present invention is not limited to such configuration. The
discrete data can be separated into the two frequency bands of the
low-frequency range and high-frequency range, or even into a
plurality of the frequency bands of four or five including a low
mid-frequency range etc. between the low-frequency range and the
high-frequency range. In this case, the amplifiers and the
band-by-band interpolation units can be provided in accordance with
the number of the frequency bands for separation.
* * * * *