U.S. patent application number 15/997375 was filed with the patent office on 2019-05-02 for phase inversion filter for correcting low frequency phase distortion in a loudspeaker system.
This patent application is currently assigned to Meyer Sound Laboratories, Incorporated. The applicant listed for this patent is Meyer Sound Laboratories, Incorporated. Invention is credited to John D. Meyer, Perrin Meyer.
Application Number | 20190132676 15/997375 |
Document ID | / |
Family ID | 62235517 |
Filed Date | 2019-05-02 |
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United States Patent
Application |
20190132676 |
Kind Code |
A1 |
Meyer; Perrin ; et
al. |
May 2, 2019 |
Phase Inversion Filter for Correcting Low Frequency Phase
Distortion in a Loudspeaker System
Abstract
A filter for correcting phase distortion produced at low
frequencies in a loudspeaker system is created by inverting the
phase response of the determined complex-valued frequency response
of a loudspeaker system. The inverted phase response is obtained by
taking the complex conjugate of the phase response. The impulse
response for the inverted phase response is obtained by means of an
inverse Fourier transform of the inverted phase response. The
impulse response provides a linear phase FIR filter having a long
filter length. The linear phase FIR filter is applied to the audio
signal input to the loudspeaker system. Prior to inverting the
phase response, the determined complex-valued frequency response of
a loudspeaker system can be subjected to high frequency blanking
and polynomial smoothing. Also, the linear phase FIR filter can be
subjected to a window function prior to applying the filter to the
audio signal.
Inventors: |
Meyer; Perrin; (Albany,
CA) ; Meyer; John D.; (Berkeley, CA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Meyer Sound Laboratories, Incorporated |
Berkeley |
CA |
US |
|
|
Assignee: |
Meyer Sound Laboratories,
Incorporated
Berkeley
CA
|
Family ID: |
62235517 |
Appl. No.: |
15/997375 |
Filed: |
June 4, 2018 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
14525898 |
Oct 28, 2014 |
9992573 |
|
|
15997375 |
|
|
|
|
61896899 |
Oct 29, 2013 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
H04R 3/14 20130101; H04R
3/12 20130101; H04R 3/04 20130101 |
International
Class: |
H04R 3/04 20060101
H04R003/04 |
Claims
1. A method of creating a filter for correcting phase distortion
produced at low frequencies in a loudspeaker system having a
transducer driven by a piston with mass, comprising: a. obtaining
the complex-valued frequency response of the loudspeaker system,
said frequency response including a magnitude component (the
magnitude response) and a phase component (the phase response) and
having a number of data points for producing a relatively high
resolution representation of the frequency response of the
loudspeaker system, b. inverting the phase response obtained in
step (a) by taking the complex conjugate of the phase response to
produce an inverted phase response, c. obtaining the impulse
response for the inverted phase response by means of an inverse
Fourier transform of the inverted phase response, wherein said
impulse response is a FIR filter having a long filter length
characterized by a series of RR coefficients, and d. applying the
FIR filter o the audio signal input to the loudspeaker system for
which the frequency response was obtained in step (a).
2. The method of claim 1 wherein the complex-valued frequency
response of the loudspeaker system is measured under free-field
conditions.
3. The method of claim 1 wherein the phase of the complex-valued
frequency response of the loudspeaker system is set to zero above a
high frequency cut-off point to create a high frequency blanked
phase trace, and wherein said cut-off point is located at a
frequency below which the obtained phase response of the
loudspeaker system begins to continuously move away from zero
degrees.
4. The method of claim 3 wherein a second stage smoothing function
is applied to the phase response prior to inverting the phase
response, thereby creating a smooth polynomial approximation of the
high frequency blanked phase response.
5. The method of claim 4 wherein said second stage smoothing
function is a least-square smoothing spline algorithm applied to
the high frequency blanked phase response.
6. The method of claim 1 wherein a second stage smoothing function
is applied to the phase response prior to inverting the phase
response, thereby creating a smooth polynomial approximation of the
phase response.
7. The method of claim 6 wherein said second stage smoothing
function is a least-square smoothing spline algorithm applied to
the phase response.
8. The method of claim 1 wherein a window function is applied to
the FIR filter obtained in step (c) of claim 1 to remove audible
distortions produced by the FIR filter.
9. The method of claim 8 wherein a Kaiser window is applied to said
FIR filter.
10. The method of claim 8 wherein pre-correction is iteratively
applied to said window function to remove side effects, wherein the
side effects are a low frequency attenuation in the magnitude
response of the FIR filter.
11. The method of claim 1 wherein said FIR filter is modified such
that it is a symmetric filter.
12. The method of claim 1 wherein the length of said FIR filter is
between 5,000 and 50,000 points.
13. A method of creating digital filter for correcting phase
distortion produced at low frequencies in a loudspeaker system
having a transducer driven by a piston with mass, comprising: a,
obtaining the complex-valued frequency response of the loudspeaker
system, said frequency response including a magnitude component
(the magnitude response) and a phase component (the phase
response), and having a number of data points for producing a
relatively high resolution representation of the frequency response
of the loudspeaker system, b. inverting the phase response obtained
in step (a) by taking the complex conjugate of the phase response
to produce an inverted phase response, c. obtaining the impulse
response for the inverted phase response by means of an inverse
Fourier transform of the inverted phase response, wherein said
impulse response is a FIR filter having a long filter length that
depends on a love frequency cut-off that is selected and is
characterized by a series of FIR coefficients, d. applying a
symmetric window function to the symmetric linear phase FIR filter
to force the FIR coefficients to decay to zero by the end of the
FIR filter length, e. adding pre-correction to the windowed
symmetric linear phase FIR filter to correct for magnitude
attenuation introduced by step (d) at low frequencies, and f.
applying the pre-corrected windowed FIR filter to the audio signal
input to the loudspeaker system for which the frequency response
was obtained in step (a).
14. The method of claim 13 wherein in step (a) the complex-valued
frequency response of the loudspeaker system is measured under
free-field conditions.
15. The method of claim 13 wherein a second stage smoothing
function is applied to the phase response prior to inverting the
phase response, thereby creating a smooth polynomial approximation
of the phase response.
16. The method of claim 15 wherein said second stage smoothing
function is a least-square smoothing spline algorithm applied to
the phase response.
17. The method of claim 16 wherein, prior to applying a smoothing
function, the phase response is interpolated on a logarithmic
frequency scale so that the information per octave is constant
across the operating range of the loudspeaker system.
18. A filter for correcting phase distortion produced at low
frequencies in a loudspeaker system, said filter being created in
accordance with the method of claim 1, wherein the filter is
applied to the audio signal in real time.
19. A filter for correcting phase distortion produced at low
frequencies in a loudspeaker system said filter being created in
accordance with the method of claim 1, wherein the filter is
applied to the audio signal off-line and placed on a storage medium
prior to playback through the loudspeaker system.
20. A filter for correcting phase distortion produced at low
frequencies in a loudspeaker system, said filter being created in
accordance with the method of claim 13, wherein the filter is
applied to the audio signal off-line and placed on a storage medium
prior to playback through the loud speaker system.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application is a continuation of prior U.S. application
Ser. No. 14/525,898 filed Oct. 28, 2014, which claims the benefit
of U.S. Provisional Patent Application No. 61/896,899 filed Oct.
29, 2013.
BACKGROUND OF INVENTION
[0002] The present invention generally relates to systems and
methods for correcting the frequency response of loudspeaker
systems and more particularly relates to correcting phase
distortion produced at low frequencies in a loudspeaker system.
[0003] In many cases loudspeakers are perceived as having a
particular tonal quality or sound, which is the result of the
non-linear distortion in the loudspeaker's frequency response. One
such example is a loudspeaker designed to impart a distinct sound
to a guitar amplifier. In this case, non-linear distortion adds
harmonic content or warmth, and diminished response at high
frequencies prevents the guitar from sounding harsh. However, a
loudspeaker meant to reproduce different sounds ideally should be
linear and have a flat magnitude and phase response over its entire
frequency range. Such an ideal loudspeaker can accurately reproduce
any kind of audio signal without noticeable tonal effects.
[0004] Highly linear and accurate loudspeakers are often desired
for particular applications, such as studio monitors used in film
post production, CD mastering, and the like. Any non-linearity in a
studio monitor will distort the audio output, a particularly
undesirable result in a studio listening environment where
decisions are made about the audio mix, microphone placement, et
cetera, based on the audio output produced by the monitor.
[0005] A limitation in achieving accurate sound reproduction from
studio monitors, and other full range loudspeakers, is phase
distortion introduced at low frequencies. A medium or large scale
studio monitor setup consists of 2-way or 3-way loudspeakers, where
low frequencies (100-1000 Hz) are typically produced by a 12 inch
cone moving coil transducer. To reproduce very low frequencies
(<100 Hz) at loud levels, the system will also include a
subwoofer, which typically consists of one or two 18 inch cone
moving coil transducers. (In both cases, the cone material is
usually made of paper, but could be fabricated of other materials
such as carbon fiber or plastic.) Because the physics of all moving
coil transducers are fundamentally similar--all are classical
mass-spring systems--they act as high-pass systems. This
low-frequency roll-off in the magnitude response also results in a
phase shift or phase lag.
[0006] Due to this phenomenon, filters are often used to attain a
flat magnitude response by boosting the low frequencies. The
filters most often used for this purpose are 2.sup.nd order
biquadratic filters, or multiple biquads, cascaded together. While
multiple biquads can be used to flatten the low frequency magnitude
response of a loudspeaker, the resulting phase response is neither
flat nor zero. With such filters, the cost for a flat low frequency
magnitude response is low frequency phase distortion.
[0007] Headphones represent one way to overcome these physical
limitations. Because they are worn close to the ears, they don't
need substantial acoustic power to produce high sound pressure
levels. As a result, the transducer (also a moving coil) can be
very lightweight, which allows for a flatter magnitude response,
and the transducer motion can be relatively small, which improves
linearity. As a result, professional headphones are usually very
linear and have a very flat frequency response. However, headphones
do not provide an accurate stereo image and prevent easy
interaction among studio professionals.
[0008] The present invention provides a filter that can correct the
low frequency phase distortion inherent in loudspeakers with cone
moving coil transducers. The filter of the invention also has a
flat magnitude response. Thus, an almost ideal frequency
response--flat in magnitude and zero in phase can be produced
across a loudspeaker's entire operating frequency range. While it
is contemplated that the filter created in accordance with the
invention would be implemented as a digital filter, it is not
intended that the invention be limited to digital
implementations.
SUMMARY OF INVENTION
[0009] The invention is directed to a method of creating a filter,
most suitably a digital filter, which corrects low frequency phase
distortion in a loudspeaker system with a transducer driven by a
piston. The invention is further directed to a phase inversion
filter created by such a method. In a first step of the method, the
frequency response of the loudspeaker system is measured or
obtained from mathematical models. The system frequency response is
a complex-valued transfer function that includes magnitude and
phase components at each frequency, called the magnitude response
and the phase response, respectively. The frequencies (data points
on the frequency scale) must be spaced close enough that the
frequency response is a relatively high resolution representation
of the loudspeaker system.
[0010] The high frequency cut-off can then be selected, above which
the phase response of the loudspeaker system is substantially zero
and below which it continuously moves away from zero. In order to
reduce measurement noise at high frequencies, the phase response is
set to zero, or blanked, above this cut-off.
[0011] To further reduce noise, the phase response can be smoothed.
It may be advantageous to interpolate the phase response on a
logarithmic frequency scale so that the information per octave is
constant across the operating range of the system. A smoothing
function can be fit to the phase, creating a polynomial
approximation of the phase response.
[0012] This phase response can then be inverted by taking its
complex conjugate. It is converted to a Finite Impulse Response
(FIR) filter by an inverse Fourier transform. This impulse response
in the time domain can then be modified to be symmetric, so that
the coefficients with the largest values are in the center of the
filter. The resulting FIR filter will be substantially linear
phase.
[0013] Next, a symmetric window function can be applied to the FIR
so that its coefficients decay to zero at both ends of the filter.
Then, to correct the effects caused by the windowing operation,
filters can be added to restore the frequency response to a flat
response. The magnitude and phase responses can then be corrected
down to a low frequency cut-off that is based on the operating
range of the loudspeaker system, as determined from the system
frequency response. The corrected, windowed, symmetric,
substantially linear phase FIR filter can then be applied to the
audio signal before being reproduced by the loudspeaker system. The
loudspeaker system will have a flat frequency response and a phase
response that is zero down to the low-frequency cut-off.
[0014] The method of the invention can be practiced without
necessarily performing all of the foregoing steps. For example,
after the frequency response of the of the loudspeaker system is
determined, it can be decided whether further processing is
required before inverting the phase and producing a FIR filter.
Also, it is contemplated that the method might be practiced without
applying a windowing function to the FIR filter.
BRIEF DESCRIPTION OF THE DRAWINGS
[0015] FIG. 1 is a block diagram of loudspeaker system using a
phase inversion filter in accordance with the invention.
[0016] FIG. 2 is a block diagram illustrating steps for creating a
phase inversion filter in accordance with the invention.
[0017] FIG. 3 provides graphs showing the measured anechoic
frequency response of an exemplary three way loudspeaker system.
The magnitude response is plotted on the top graph of FIG. 3 and
the phase response is plotted on the bottom graph.
[0018] FIG. 4 is a phase versus frequency graph showing the effect
of high frequency blanking above a frequency cutoff of 1.3 kHz.
[0019] FIGS. 5A and 5B are phase versus frequency graphs showing
the effect of phase unwrapping and of polynomial smoothing on the
unwrapped phase trace. The unwrapped, high frequency blanked phase
is shown in FIG. 5A and the smooth polynomial approximation is
shown in FIG. 5B.
[0020] FIG. 6 is a graph showing the impulse response obtained from
the polynomial approximation of the phase. A detail of the center
of the filter is shown in the full graph, while the inset shows the
full length of the filter.
[0021] FIG. 7 are graphs showing the effect of the windowing
function on magnitude (top graph) and phase (bottom graph) of the
system frequency response. The raw system response is shown for
comparison. The windowing function alone ("Window only") produces a
magnitude drop below 30 Hz, which is corrected by a pre-distortion
filter ("Window+correction") down to 24 Hz.
[0022] FIG. 8 compares the raw system response to the response
obtained using the PIF Filter and method.
DETAILED DESCRIPTION
[0023] The present invention is directed to a filter and a method
of creating a filter that compensates for low frequency phase
distortion produced by loudspeaker systems, such as those used as
studio monitors. The filter of the invention utilizes a unique
phase inversion technique and will be referred to herein as a phase
inversion filter, or PIF. Use of a PIF in a loudspeaker system is
generally illustrated in FIG. 1 wherein a loudspeaker system,
denoted by the numeral 11, is comprised of a two-way loudspeaker 13
driven by an audio signal input 15 through a PIF 17 and cross-over
19. The presence of the PIF in the signal input path for the audio
input of the loudspeaker will result in a flat frequency response
and a phase response that is zero down to the low frequency cut-off
for the loudspeaker. The PIF is most practically a digital filter
which could be applied to the audio content either in real time or
offline; if the latter, the processed audio would be stored on a
storage medium prior to playback. It will be appreciated that,
while for illustrative purposes the PIE and cross-over are shown in
a particular order and as discreet functional blocks, they could be
implemented in a single functional block or in a different
order.
[0024] Unlike conventional filter design for loudspeakers, the PIF
is based on the theory of moving coil loudspeakers in general and a
physical characterization of the loudspeaker system in particular.
In accordance with the invention, a linear-phase, symmetric finite
impulse response (FIR) filter is created that compensates for the
system's inherent high-pass phase response.
[0025] The method of creating a phase inversion filter in
accordance with the invention involves an ideal mathematical
inversion and the manipulation of the initial mathematical model to
obtain a usable filter design. The objective is to create a system
response that has a flat magnitude response and a phase response
that is zero over the system's operating range. The simplest way to
create such an ideal system response is to calculate the inverse of
the system's complete frequency response. Although formally
correct, such a filter is useless in practice since it is almost
certain to be unstable at 0 Hz (or DC): this instability would
create auditory artifacts that would unduly compromise system
performance.
[0026] For a real loudspeaker system with a finite bandwidth, which
does not reproduce 0 Hz, the PIF filter must be limited to the
operating bandwidth of the loudspeaker system. In this way, an
ideal inversion can be realized over the operating bandwidth. For
example, the PIF can be constructed to invert phase down to a low
frequency cut-off of about 30 Hz. Thus, the filter compromises by
enforcing a flat magnitude response at the price of letting the
phase response return to the natural high-pass shape that is
characteristic of mass-spring systems.
[0027] As is well understood in filter theory, the low frequency
cut-off is constrained mathematically by the filter length: the
lowest correctable frequency has a period roughly equivalent to the
filter length. The filter length also determines the throughput
latency of the filter, which is crucial if the filter is to be
applied in real-time. For example, a symmetric FIR filter with
20,000 points (sometimes referred to as "taps") and a sampling rate
of 100 kHz has a latency of 100 ms and can correct down to 5 Hz.
The latency can be reduced by using a shorter filter, but this will
raise the lowest possible cut-off frequency. In general, the PIF
must be relatively long (16,000 points is typical), much longer
than typically used in the professional audio industry. Depending
on the frequency response of the system being corrected, a usable
range of filter lengths is about 5,000 to 50,000 points. Filter
lengths of 5,000 and 50,000 points have, respectively, a latency of
25 ms and 250 ms and a low frequency cut-off of approximately 20
and 2 Hz.
[0028] Steps for creating a PIF in accordance with the method of
the invention are generally illustrated in FIG. 2. The starting
point is to determine the frequency response of the loudspeaker
system (block 100). After determining the initial frequency
response, a need for further processing of the initial frequency
response is assessed (block 102). The phase response can be further
processed in several ways to improve the ability of the PIF filter
to generalize to all spaces. The further processing can include
assessing the need to apply high frequency cut-off and the need for
polynomial smoothing (blocks 104 and 106). A high cut-off can be
applied by applying high frequency blanking (block 108) and
smoothing can be through polynomial smoothing techniques (block
110). The phase of determined frequency response, whether further
processed or not, is then inverted (block 112) and the
corresponding FIR filter is computed by an inverse Fourier
transform (block 114). The need to apply a windowing function to
the corresponding FIR filter is then assessed (block 116). The FIR
filter can be processed by a windowing function (block 118),
although any magnitude effects this produces must be corrected for
(blocks 120, 124). In the last step, the resulting PIF is applied
to the input audio signal and reproduced by the loudspeaker system
(block 126).
[0029] The aspects of foregoing steps are now described in greater
detail. The frequency response of the loudspeaker system can either
be a single loudspeaker, for example, a loudspeaker having a 12
inch cone driver and a one inch compression driver, or a
loudspeaker as described above plus a subwoofer with a crossover.
The PIF method ideally requires that the loudspeaker or loudspeaker
system have a flat magnitude response. However, it is understood
that the PIF method can compensate for a non-flat magnitude as
well.
[0030] Typically, the measurement of the loudspeaker or loudspeaker
system is made under free field conditions, such as in an anechoic
chamber or outdoors away from all objects. If the measurement is
not free field, the PIF method will also invert the phase response
contributed by the acoustic environment, creating a system valid
only for that one environment. Such a measurement can be taken by a
dual-channel FFT analyzer such as the SIM 3 audio analyzer,
manufactured by Meyer Sound Laboratories, Incorporated of Berkeley,
Calif. However, any measurement of the free-field frequency
response will suffice as long as it has sufficient signal to noise
and frequency resolution (greater than 24th octave).
[0031] FIG. 3 shows an anechoic frequency response, measured with
SIM, of an exemplary three way system manufactured by Meyer Sound.
The system consists of an Acheron Designer, an X400 Subwoofer, and
a Galileo 408 that uses 2.sup.nd order elliptical high-pass and
low-pass filters to create the crossover between the Acheron
Designer and the subwoofer. The Acheron Designer is a two way
studio monitor that has a 4 inch diaphragm compression driver for
the high frequencies and a 12 inch paper cone moving coil
loudspeaker for the low frequencies. The X400 suhwoofer has a
single 18 inch woofer. The combined system has a flat magnitude
frequency response and a phase response that deviates from zero
below 1.3 kHz.
[0032] Theoretically, the PIF could correct the phase over the
entire operating bandwidth of the loudspeaker system, but there are
practical reasons to avoid correcting the phase at higher
frequencies. The small high frequency fluctuations in the phase
trace at the bottom of FIG. 3 are effectively measurement noise.
This is because no space is perfectly anechoic: at a minimum, the
space used to measure the frequency response contains a microphone
and a loudspeaker, if not also positioners and other equipment. All
these objects reflect sound, particularly the high frequencies that
have wavelengths comparable to the size of those objects. These
ripples are different at each position, so correcting them at one
measurement location makes them worse at another. Also, high
frequency ripple also varies with temperature and humidity, which
change over the course of hours. For these reasons, the PIF method
may include an upper cut-off frequency above which the phase
response is set to zero, or blanked, as represented by block 108 in
FIG. 2. The result of high frequency blanking is shown in the phase
response trace reproduced in FIG. 4, where the high frequency
cut-off is at 1.3 kHz.
[0033] The PIF method may also include polynomial smoothing as a
way to reduce noise in the phase response (blocks 106 and 110 of
FIG. 2). Depending on the initial frequency resolution of the
frequency response, the phase trace may need to be resampled so
that the frequencies are logarithmically spaced. Logarithmic
spacing allows standard curve-fitting routines, such as
least-squared cubic splines, to provide consistent smoothing over
all octaves and to prevent the smoothing polynomial from
oscillating and creating a potentially unstable or distorted FIR
filter. Before a smoothing algorithm can be applied, however, the
phase must be unwrapped. Unwrapping removes the discontinuities
when the phase changes from 180 to -180 (or vice versa) by adding
or subtracting 360 degrees; this results in a curve which is
continuous (in the mathematical sense) and has a continuous
derivative. If the derivative is not continuous, the smoothing
algorithm would produce a poor approximation of the phase with
additional noise. In the example of FIG. 4, phase wraps can be seen
at 24 Hz and 90 Hz, The unwrapped phase can be seen in FIG. 5A.
[0034] The unwrapped phase trace can then be smoothed to produce a
smooth polynomial approximation to the phase. There are many ways
to perform smoothing: the approximation shown in FIG. 5B was
computed with a least-squares spline algorithm. Smoothing removes
small magnitude, high order acoustic phenomena. This creates a PIF
that only corrects for the large scale effects caused by the
general physical principles already described, not for the
small-scale, local effects that are valid at only one frequency o
only one position. As with frequency blanking, this removes
artifacts in the frequency response measurement caused by acoustic
reflections and diffractions.
[0035] The smooth phase approximation is inverted (block 112 in
FIG. 2) by taking the complex conjugate of the complex
representation of the phase. This is equivalent to multiplying by
-1, or to reflecting the phase trace around the x-axis at 0
degrees.
[0036] A FIR filter, or a time domain impulse response, is then
created by taking the inverse Fourier transform of the inverted
phase. (FIG. 2, block 114) Because this filter corrects an
arbitrary phase response, the FIR filter is not necessarily causal
or symmetric. It is made into a linear phase filter, which is both
causal and symmetric, by placing the peak value in the center of
the filter, as shown in FIG. 6.
[0037] A linear phase FIR filter has now been produced. In order to
remove audible distortions, particularly if the filter is to be
used in real time, the FIR filter coefficients must decay to zero
at both ends. This condition is enforced by applying a symmetric
window function to the FIR coefficients. (FIG. 2, block 118.) The
window can be a Kaiser window, which is a common windowing filter
that contains a sidelobe attenuation parameter. In the case of
high-fidelity audio, which has a dynamic range of 100 dB, the
sidelobe attenuation can be chosen to be 100 dB. However, any
symmetric bell shaped windowing function could be used, such as
Hanning or Hamming windows, as long as its side lobe attenuation is
acceptable.
[0038] As seen in FIG. 7, the above-described windowing has the
undesirable side effect of changing the magnitude response of the
PIF filter in a low frequency attenuation of the magnitude
response. A small number of filters can be used to correct this,
either by fitting them iteratively using acoustic measurements of
the system under test, iteratively using a computational approach,
or mathematically with a fitting algorithm such as a least-squared
method. While the filters used to produce the effects shown in FIG.
7 are 2.sup.nd order biquad IIR. filters, other kinds of filters
could be used as well. This is done until the low frequency region
of the frequency response is flat to within some desired criterion
and down to some low frequency cut-off point. The example in FIG. 7
has magnitude flat to within +/-2 dB and down to 23 Hz, and a phase
of zero down to 40 Hz.
[0039] FIG. 8 illustrates the effects that a PIF filter created in
accordance with the method of the invention has on the system
response of the selected loudspeaker system. The low frequency
phase response of the original system had its first phase wrap at
100 Hz: the PIF system's first wrap is at 30 Hz, considerably
lower. The magnitude trace is practically identical over the entire
operating range. Note that the slight magnitude difference below 30
Hz, and the slightly negative phase at 40 Hz could be improved with
further iterations of the window correction step.
[0040] It should be noted that the mathematical operations in this
method could be performed in a different order and still produce a
functional PIF. Many of the operations used are linear, and as a
result commutative: one skilled in the art could rearrange them
appropriately. In order to clearly explain the invention, however,
this method describes them in a fixed sequence.
[0041] The PIF filter is now complete, and can be applied to an
audio signal either off line or in real time. Applying it in
real-time can be a challenge, because this filter is much longer
than most FIR filters used in the professional audio industry. A
real time processing algorithm developed by Meyer Sound called
SCaRF (Spectral Convolution and Real-time Filtering) convolves
real-time signals with very long FIR filters. The basic idea behind
SCaRF is the observation that CPU architectures cannot compute long
FIR filters efficiently because of how their memory is structured.
Memory in modern CPUs consists of a large amount of slow main
memory and a small amount of fast cache memory, or random access
memory. The cache memory is too small to implement long FIRs in
real-time, and the main memory is too slow. However, the cache
architecture is naturally suited to the butterfly patterns in the
Fast Fourier Transform (FFT): modern CPUs can attain almost peak
DSP throughput when calculating FFTs, even with long lengths. SCaRF
takes advantage of this to perform real-time filtering in the
frequency domain. First, the FFT of the PIF and the input audio
samples are taken. Since convolution of an FIR filter in the time
domain is equivalent to multiplication in the frequency domain, the
FFT of the PIF is multiplied by the FFT of the audio samples. The
inverse Fourier transform is performed to obtain an audio stream
that is now filtered by the PIF.
[0042] The complete system is now ready: the PIF filter is applied
to the loudspeaker system in real time using the FFT-based SCaRF
algorithm, and the resulting frequency response is flat in both
frequency and phase.
[0043] While the invention has been described in considerable
detail n the forgoing specification and accompanying drawings, it
is not intended that the invention be limited to such detail,
except as necessitated by the following claims.
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