Method Of And Apparatus For Signal Processing

Abstract

Method of and apparatus for convolution and correlation of electromagnetic signals by application of two signals to a piezoelectric medium to establish two acoustic waves which are propagated in a fashion such that phase matching and frequency conservation conditions are met whereby parametric coupling occurs.

Description

FIELD OF THE INVENTION

The present invention relates generally to signal processing and more particularly, to a method of and apparatus for obtaining the convolution and correlation of signals. The invention described herein was made in the course of work under a grant or award from the United States Air Force.

BACKGROUND OF THE INVENTION

Mathematically, as explained in detail in Chapter 3 of Bracewell, The Fourier Transform And Its Applications (1965), the correlation of two time functions f(t) and g(t) is defined by

Cr = .intg. f(.tau.) g(.tau.-t)d.tau. (1)

and convolution, in turn, is the time reversed relationship defined by

Cn = .intg. f(.tau.) g(t-.tau.)d.tau. (2)

t, in each equation being representative of time displacement of one function relative to the other. Accordingly, the mathematical evaluation of either operation can be considered as a process whereby first, the two functions are translated in time with respect to one another by a specified amount, t, secondly, the product of the translated functions is taken, and finally, this product is integrated. Quite obviously, the mathematical process can be physically realized if two signals can be made to undergo the three steps of the process, translation, multiplication, and integration.

In a rather complex fashion, the correlation function has been physically realized in a number of instances, one well established application being found in the so-called "correlation radars" wherein the cross-correlation of the transmitted signal with the reflected signal, a time-delayed replica of the transmitted signal, is specifically defined by the equation

Cc = .intg. f(.tau.) f(.tau.-t)d.tau. (3)

The value of t now constituting the time taken by the radar wave in traveling to the target and back. It has been found that the cross-correlation process constitutes a measure of the coherence between the transmitted and received signals and thus has provided far reaching significance in solving a major problem encountered in any radar operation, that of detecting the received signal against a background of noise.

A number of cross-correlation radar receivers have been designed and for the most part employ analog and digital techniques. For example, one well known technique couples the input signal to a digital computer by means of an analog-to-digital converter and the computer is programmed to cross-correlate, point by point, the two signals and to extract them from the noisy background. This requires a sizeable computer memory and a relatively large amount of computer time. Thus in addition to the complexity of such installations, the cross-correlation function is not immediately available, that is, the function is not performed substantially simultaneously, or in other words, in real time.

More commonly, "correlation radars" employ a "matched filter" as mentioned in Chapter 9 of Introduction To Radar Systems, by Skolnik (1962) along with the cross-correlation detectors mentioned hereinabove and as discussed in detail in the "matched filter" issue of IRE Transactions on Information Theory, Volume IT-6 (June, 1960), the matched filter basically constituting a filter designed so that its output is proportional to the "correlation" of the signal with itself. Obvious problems in matched filter design are encountered with complex modulation waveforms such as the noise waveform utilized to preclude electronic countermeasure techniques. Yet other sophisticated modulation waveforms also present problems in matched filter utilization. For example, if as commonly provided, two radar pulses are emitted sequentially by the radar transmitter with different modulation characteristics, two matched filters are obviously necessary for appropriate detection, one filter being matched to the first pulse and the other matched to the second pulse.

In spite of the fact that complexity and other practical difficulties of the type mentioned hereinabove do exist in correlation radars, the convolution and correlation processes are recognized as powerful tools in the processing and analysis of signals and in addition to the mentioned radar utilizations, Lee and Weisner have employed cross-correlation in the characterization of linear systems as reported in their Statistical Theory of Communication, and other have applied cross-correlation to the analysis of brain waves, vibration analysis and any number of applications where the comparision of two signals provides useful data, particularly, if such data can be extracted and presented substantially simultaneously to the investigator.

SUMMARY OF THE PRESENT INVENTION

Generally, it is the objective of the present invention to provide a method of and apparatus for convolution and/or correlation of signals in real time and in a relatively simple fashion through utilization of the nonlinear acoustic interaction of the signals in a piezoelectric medium. In accordance with the invention the three steps of translation, multiplication and integration are achieved by introducing the two signals into the piezoelectric medium in a particular and precisely defined fashion by application of suitable electromagnetic signals thereto. The phase velocities of the two signals which are propagated through the piezoelectric medium in the form of modulated acoustic waves are different thus to achieve the requisite translation step. For example, in one specific case of correlation, the first signal is introduced at one time with a predetermined phase velocity and the second signal is introduced at a later time but with a higher phase velocity so as to overtake the first signal during the period of signal propagation through the medium. In one specific case of convolution, in turn, the two signals are introduced at opposite ends of the medium so as to meet during their propagation therethrough again to provide the translation step in the form of a time reversal as requisite to meet the conditions of the convolution definition.

The second step of multiplication is provided through the well-established mechanism of parametric coupling which briefly provides that if the phases of the signals are matched and simultaneously the principle of frequency conservation is observed, a nonlinear interaction of the acoustic waves results which will induce an electric polarization that is proportional to the product of the two modulation functions of the acoustic waves.

The third step, integration, is readily achieved by known techniques for driving an external circuit with the induced polarization. For example, if microwave frequencies are employed in a fashion such that no spatial variation of the polarization occurs, the induced polarization can be utilized to drive an appropriate mode of a microwave cavity. In the case of convolution, this cavity would be tuned to the sum of the frequencies of the two signals whereas to the contrary, in the case of correlation, the cavity would be tuned to the correlation signal which would constitute the difference frequency in accordance with the frequency conservation principle of parametric interaction, as mentioned hereinabove.

If, as an alternative, the acoustic waves are parametrically coupled so that the induced polarization, D, has a resultant propagation vector, the external circuit can then be arranged, for example in the form of a suitably shaped strip line, to enable coupling to the propagating polarized output electromagnetic signal.

The external output circuit in either the cavity or travelling wave form as described can be reversed in its function, serving as the input for one signal which through appropriate parametric coupling in the piezoelectric medium with a second signal (acoustic) can produce essentially a reserved operation of the convolution/correlation process to produce an output signal, for example, at one end of the piezoelectric medium.

Generally then, the method of signal processing in accordance with the present invention involves the steps of propagating a first acoustic wave through a piezoelectric medium at a predetermined phase velocity, propagating a second acoustic wave through the same medium at a different phase velocity, the two waves being introduced and propagated in a fashion such that the conditions of phase matching and frequency conservation are met to provide a nonlinear parametric interaction whereupon the induced energy can be extracted to provide the output data. The acoustic waves can be of any known type such as volume waves, surface waves, flexural waves, torsional waves, Love waves or the like.

The general characteristics of the described signal processing method involving the nonlinear interaction of acoustic waves in a piezoelectric medium lend themselves to a variety of applications. By way of example, and as will be explained in detail hereinafter, no output will be observed unless the conditions of parametric coupling are met. Because of the frequency conservation conditions, if a known signal is introduced into a piezoelectric medium, a second unknown signal will cause the process to occur only if it, in turn, is of a precisely delineated frequency. Thus, the immediate application of the mechanism to a narrow bandpass filter suggests itself.

Furthermore, because of the requirement for phase matching, regardless of the complexity of the introduced signals, an output will be obtained only when this condition is also met unambigously, thus allowing for example, the precise detection of a reflected radar signal otherwise obscured by attendant noise.

Additionally, with respect to radar systems wherein pulses having different modulation patterns are utilized, the necessity for utilizing a plurality of "matched filters" is obviated since a number of known signals can be supplied through the piezoelectric medium for comparison with the reflected signals, thus simplifying the detection of sophisticated radar signals.

Extrapolating, the possibility of introducing a number of known signals into the piezoelectric medium for comparison with unknown signals leads one to the obvious application of the present method to a pattern recognition scheme wherein, in essence, a number of known patterns can be compared with an incoming unknown pattern so that, through the use of the correlation mechanism, one can establish the unambigous recognition of the unknown signal pattern.

Additionally, if one introduces a number of spaced output circuits along a piezoelectric medium, a series of equivalently-spaced short pulses can be introduced to one end of the medium to provide sampling of the waveform of an unknown signal of longer duration introduced to the opposite end of the medium.

Any number of additional applications will suggest themselves immediately but it is to be observed that, in each case, the relative slow velocity of acoustic waves makes it possible to carry out the convolution or correlation operations in a piezoelectric crystal of very convenient size with signals several microseconds in duration and the results of the operations are immediately available to the investigator. Not only are the results available in real time, but are available through utilization of a relatively simple and inexpensive structure as compared to either the mentioned matched filter or other correlation detection equipment.

BRIEF DESCRIPTION OF THE DRAWINGS

The stated objective of the invention and the manner in which it may be achieved as summarized hereinabove will be more readily understood by reference to the following detailed description of the exemplary structures shown and explained in the accompanying drawings wherein:

FIG. 1 is a diagrammatic perspective view of a structure embodying the present invention for carrying out a convolution operation,

FIG. 2 is a frequency-propagation diagram explanatory of the operation of the FIG. 1 structure.

FIG. 3 is a view similar to FIG. 1 diagrammatically depicting a structure arranged to perform a correlation operation,

FIG. 4 is a frequency-propagation diagram similar to FIG. 2 explanatory of the principles of the FIG. 3 structure,

FIG. 5 is a diagrammatic perspective view of a structure arranged to enable output coupling of a traveling wave,

FIG. 6 is a frequency-propagation diagram similar to FIGS. 1 and 3 explanatory of the operation of the FIG. 5 structure,

FIG. 7 is a diagrammatic side elevational view of a structure enabling sampling of the waveform of an acoustic wave,

FIG. 8 illustrates a structure employing the convolution mechanism as a bandpass filter,

FIG. 9 is a diagram illustrating the bandpass characteristics of the FIG. 8 filter,

FIG. 10 is a block diagram illustrating application of the invention to a radar system, and

FIG. 11 is another block diagram illustrating the invention as applied to a pattern recognition system.

DETAILED DESCRIPTION OF THE EXEMPLARY EMBODIMENTS OF THE INVENTION

The method of signal processing can be specifically utilized to carry out a convolution operation in the manner diagrammatically illustrated in the FIG. 1 structure where two input electromagnetic signals, which may constitute modulated microwave frequency signals, are applied through suitable transducers diagrammatically indicated at 10 and 12 to opposite ends of a piezoelectric crystal 14 so as to generate two oppositely propagating fast shear acoustic waves indicated at A.sub.1 and A.sub.2 along what may be denominated the X-axis of the crystal. It will be immediately obvious that the opposite propagation of the two acoustic waves A.sub.1, A.sub.2 provides signal translation, requisite as a first step in the evaluation of the convolution equation (2).

In order to carry out the second evaluation step, that of multiplication, the frequency and phase relationships of the two acoustic waves A.sub.1 and A.sub.2 are chosen so that the conditions for parametric coupling, phase matching (k.sub.1 + k.sub.2 = k.sub.p) where k, the propagation vector, is equal to the frequency, .omega., divided by the acoustic velocity, v, and frequency conservation (.omega..sub.1 + .omega..sub.2 = .omega..sub.p) are met in the manner explained in detail in Chapter 5 of W.H. Louisell, Coupled Mode and Parametric Electronics, 1960. More particularly, with reference to the frequency-propagation diagram of FIG. 2, for the convolution process, the first acoustic wave A.sub.1, constitutes a forward traveling wave (k.sub.s) with a frequency, .omega..sub.s, whereas the second acoustic wave A.sub.2 is a backward traveling wave (-k.sub.s) at the same frequency, .omega..sub.s. Even though the phase velocities of the two waves as represented by the angles of the vectors of the waves A.sub.1 and A.sub.2 in FIG. 2 have the same absolute value, they are "different" in the sence that one is negative and the other positive so that the required translation occurs. Introducing these values into the parametric equation for phase matching we have, k.sub.s + (-k.sub.s) = o and, in turn, .omega..sub.s + .omega..sub.s = 2 .omega..sub.s provides the specific values of frequency conservation. Since k.sub.p = o, there is no spatial variation in the output electric displacement or polarization, D, of the parametrically-combined waves (i.e., it has zero velocity) and it has a frequency which is the sum of the input wave frequencies, that is, .omega..sub.p = 2 .omega..sub.s, as shown in FIG. 2.

The mentioned multiplication function is obtained through the nonlinear interaction of the acoustic waves, A.sub.1 and A.sub.2, so that the displacement or polarization, D, is proportional to the product of the strain amplitudes, S.sub.1 and S.sub.2, of the amplitude modulated acoustic waves and is directed along the Z-axis of the crystal throughout its entire volume as indicated by the arrows D in FIG. 1. This result stems from the well established effect that the polarization or displacement, D, is a function of both the electric field, E, and the strain, S, and in simplified (non-tensor) notation can be represented by the following equation

D = B(S.sub.1 + S.sub.2) + C(E.sub.1 + E.sub.2) + F(E.sub.1 + E.sub.2).sup.2 + G(E.sub.1 + E.sub.2)(S.sub.1 + S.sub.2)+ (K/2)(S.sub.1 + S.sub.2).sup.2 (4)

wherein B, C, F, G and K are constants E.sub.1 and E.sub.2 are the electric fields and S.sub.1 and S.sub.2 the strain amplitudes of the two acoustic waves A.sub.1 and A.sub.2. The first two terms will be recognized as linear, the third as the electro-optic coefficient which relates to the change of dielectric constant with electric field, and the fourth as the photoelastic constant which relates to the change in dielectric with strain. The fifth term, which is that critical to the operation of the present invention, is related to the change in the velocity of sound with electric field as explained in detail in Piezoelectric Crystals And Their Applications To Ultrasonics by W.P. Manson, 1950 (page 463). In the case under consideration here E.sub.1 and E.sub.2 are zero, so that only the fifth term is of interest and the foregoing equation can be reduced to the simple phenomenological equation

D = KS.sub.1 S.sub.2 (5)

we see that, D, is proportional to the product of the strain amplitudes S.sub.1 and S.sub.2 and in the case, for example, of fast shear acoutic waves propagating along the X-axis of lithium niobate, the constant, K, has a value of 10 coulombs/meter.sup.2 so that detectable electric polarization, D, is provided with input strain amplitudes of the order of 10.sup..sup.-6 (1 watt/cm..sup.2).

In order to carry out the third step of the process, integration, the product of the two strain amplitudes, S.sub.1 and S.sub.2, are summed as the two signals S.sub.1 and S.sub.2 are translated relative to one another. If one chooses to operate at microwave frequencies and D has no spatial variation as explained hereinabove the output resonant circuit can constitute a microwave cavity 16 coupled to an output waveguide 18. As explained by Harrington in Chapter 8 of Time-Harmonic Electromagnetic Fields (1961). The output power, P, radiated into a coupled wave guide, is given by

P = [2.omega..sub.s .beta.Q.sub.o /(1 + .beta.).sup.2 ][.intg.D.sub.2 .omega..sub.s .sup.. E.sub.i dV].sup.2 (6)

where .beta. is the coupling of the cavity to the guide, Q.sub.o, the unloaded Q of the cavity, D, the driving polarization, E.sub.i, the normalized mode amplitude, and the integration is performed over the volume, V, of the cavity. In the present instance, the spatial variation of E.sub.i and transverse variations of D can be neglected to first order and subtitution of equation (5) into equation (6) under such conditions yields the result ##SPC1##

where L is the length of the crystal.

It, in turn, one transforms variables so that .tau. = t - x/v,f(t) = S.sub.1 (o,t), g(t) = S.sub.2 (L,t - L/v), and v is the acoustic velocity, the equation can be rewritten as ##SPC2##

which can be immediately recognized as the convolution of the amplitude modulation functions, S.sub.1 and S.sub.2, of the acoustic waves.

Whereas in FIG. 1, the acoustic waves A.sub.1, A.sub.2 are propagated as a result of the introduction of input signals to the opposite ends of the crystal 14, and the output signal is extracted through the cavity 16, the process can obviously be reversed so long as the conditions for parametric coupling are retained. Thus, an input electromagnetic signal at a frequency 2.omega..sub.s and propagation vector of zero can be introduced through the cavity 16 into the crystal 14 and a second input signal at frequency .omega..sub.s and propagation vector, + k.sub.s can be introduced to one end of the crystal, to provide an output signal at this same end of the crystal resultant from a backward wave of frequency .omega..sub.s (2 .omega..sub.s - .omega..sub.s - .omega..sub.s) and propagation vector -k.sub.s (o - k.sub.s = -k.sub.s) in accordance with the frequency conservation and phase matching conditions requisite for the parametric coupling.

In the described cases, the acoustic waves have travelled in opposite directions to provide the translation necessary for acoustic interaction. As an alternative, translation can occur if two acoustic waves travel in the same direction but at different velocities. The result is a correlation operation as depicted in FIG. 3. More particularly, two input electromagnetic signals are introduced to the same end of a piezoelectric crystal 20 through suitable transducers 22, 24 such that one traveling acoustic wave, A.sub.4, is propagated in the form of a shear wave with a predetermined acoustic velocity and a second wave A.sub.3 is launched at a delayed time but in the form of a longitudinal wave having a slightly greater velocity as can be seen by the vector angles in FIG. 4 so that during the transit of the crystal 20, the second wave A.sub.3 overtakes the first wave A.sub.4 to provide the translation function requisite for either convolution or correlation. More particularly, the transducer 22 for the acoustic shear wave A.sub.4 can, in a conventional fashion, take the form of a crystal disposed between two electrodes across which the one signal is applied to one end of the piezoelectric crystal, this transducer crystal being oriented so that the requisite shear wave A.sub.4 is generated. In turn, the second transducer 24 can be stacked adjacent the first transducer between two electrodes to which the second signal can be applied, this transducer crystal being oriented so as to generate the desired longitudinal wave A.sub.3 at the higher velocity.

With additional reference to FIG. 4, the multiplication function resultant from the nonlinear interaction of the parametrically coupled waves A.sub.3 and A.sub.4 will be readily understood. The acoustic wave A.sub.4 first launched in time in the form of an acoustic shear wave has a frequency, .omega..sub.4, and a propagation vector, k.sub.4, while the second acoustic wave A.sub.3 launched subsequently in time at a greater velocity in the form of a longitudinal acoustic wave has a frequency .omega..sub.3 and a propagation vector k.sub.3. When the second launched wave A.sub.3 overtakes the first launched wave A.sub.4, the conditions requisite for parametric coupling are established so that (k.sub.3 - k.sub.4) is equated to zero so that the resultant electric polarization, D, has no spatial variation (zero velocity) and, in turn, is at the difference frequency (.omega..sub.3 - .omega..sub.4), to which a resonant cavity 26 or other power extracting mechanism can be coupled to provide the final step of integration. In this instance, since no time reversal occurs, the output signal represents the correlation function of the strain amplitudes S.sub.3 and S.sub.4 of the acoustic waves. 0 In both the FIG. 1 convolution structure and the FIG. 3 correlation unit, the propagation vector k.sub.p of the output wave was zero, thus enabling coupling to a resonant cavity 16 or 26. However, it is to be expressly understood that the conditions for parametric coupling, .omega..sub.1 = .omega..sub.2 = .omega..sub.p, and k.sub.1 + k.sub.2 = k.sub.p in no wise require that k.sub.p = o. If k.sub.p .noteq. o, spatial variation of the output signal output does occur, but only a change in the output coupling mechanism is requisite to match the finite velocity of such signal. For example, if as shown in FIG. 5 and explained through the frequency propagation diagram of FIG. 6, one signal S.sub.5 is introduced at one end of a piezoelectric crystal 11 at frequency .omega..sub.5 and propagation vector, k.sub.5, and a second signal S.sub.6 at frequency .omega..sub.6, and propagation vector, -k.sub.6, is introduced to the opposite end of the crystal 11, a convolution of the signals S.sub.5 and S.sub.6 will provide an output, D, whose output frequency is the sum of .omega..sub.5 and .omega..sub.6 and whose propagation vector is k.sub.5 - k.sub.6. If, as shown in the FIG. 6 diagram, k.sub.5 and k.sub.6 have different values, k.sub.5 - k.sub.6 .noteq. o, the output polarization, D, will shift along the length of the crystal 11 at a predetermined velocity. To enable output coupling then, instead of a resonant cavity, a folded strip line 13 is formed on the crystal 11 with dimensions such that it is matched to the velocity of D.

The foregoing discussions of the method of signal processing have been limited to the convolution of correlation of two input signals to provide a third output signal but it is obvious that the inventive concept is not so limited. If for example, the amplitude modulation pattern of a complex wave of known frequency is to be analyzed, such signal S.sub.7 can be introduced at one end of a crystal 15 as shown in FIG. 7 and a plurality of short pulses as indicated at S.sub.8, S.sub.9, S.sub.10, S.sub.11 at the same frequency can be introduced at the opposite end of the crystal at predetermined intervals corresponding to the spacing between output electrodes 17 along the crystal. When parametric coupling occurs with the pulses S.sub.8, S.sub.9, S.sub.10, S.sub.11 adjacent the respective electrodes 17, as shown in FIG. 7, the individual output signals will constitute the products of the individual pulse signal amplitudes and the amplitude of the analyzed signal at each particular position, in accordance with the general convolution principles discussed hereinabove, thus providing a sampled analysis of the waveform of the signal 7.

By way of specific example, the convolution operation discussed in general terms hereinabove with respect to FIGS. 1 and 2, has been carried out at microwave frequencies with the structure shown in FIG. 8. A piezoelectric crystal 14 having the precise configuration shown in FIG. 1 and an overall length of approximately 3.5 cm. is housed within walls of suitable conducting material defining the microwave cavity 16, one wall of the cavity being provided with an adjustment screw 28 to enable fine tuning. To opposite ends of the piezoelectric crystal, the input signals which constitute microwave signals each having a frequency of 1,440MHz and modulated by a rectangular pulse are delivered through coaxial cables 23, 25 to opposite ends of the crystal 14, the center conductors of the coaxial cables being disposed against the opposite ends of the crystal at the positions of the transducers 10, 12 illustrated in FIG. 1 and the outer cable conductors being, in turn, connected to the conducting cavity defining walls, thus to generate electric fields which launch acoustic shear waves of identical frequency but precisely opposite phase propagation vectors in the manner explained in connection with FIGS. 1 and 2. In accordance with such explanation, an electric polarization D is generated in the crystal 14 at a frequency of 2,880 MHz and is delivered through a suitable coupling aperture to an output wave guide 18. Specifically, the acoustic power injected was approximately 2 watts/cm..sup.2 which corresponds to a strain amplitude of 2 .times. 10.sup..sup.-6 (the Q of this particular resonator is 300 and the value of .beta. is 0.2), and at the peak output power level of -70 dBm the signal-to-noise ratio was 20 dB which value is in good agreement with the theoretical considerations of the convolution operation discussed hereinabove with respect to FIGS. 1 and 2.

Further in accord with such considerations, it will be intuitively obvious from the discussion of the requisite conditions of parametric interaction that any variations in frequency of the input signals will cause a sharp reduction in the output signal as represented by the electrical polarization, D. More particularly, with reference to FIG. 9 wherein the output amplitude, D, is plotted against the variable frequency f.sub.2 of one signal in relationship to another signal of designated frequency, f.sub.1 the output response curve having the general form of the function of sin x/x where, x = .pi.[(f.sub.1 /v.sub.1)-(f.sub.2 /v.sub.2)] L and L is the crystal length, includes but one major central response lobe whose width is indicative of the narrow bandpass of the structure. For example, in the case of the crystal described in connection with FIG. 8 whose overall length, L, was 3.5 cm., the operating passband at the signal frequency of 1,440 MHz is no more than approximately 100KHz. Thus it is apparent that this structure can be used as an excellent bandpass filter and that such passband can readily be narrowed by the simple process of lengthening the crystal. Furthermore, it is apparent that an electronically tunable filter is provided, it being merely necessary to vary f, to tune the filter.

In addition, since the convolution and correlation functions merely constitute time reversed operations of one another, as explained hereinabove, a structure such as shown in FIG. 8 can be readily converted from the performance of the convolution operation to performance of a correlation operation by the simple time reversal of one of the input signals. This statement can be more readily explained by way of specific example in the form of a pulse-compression radar system illustrated in block diagram in in FIG. 10. As shown, a pulse generator 30 is arranged to supply a frequency-swept pulse P to a frequency modulator 32 that modulates the carrier wave from a radar transmitter 34 so that a frequency-swept pulse is delivered to the radiating antenna 36, the frequency of the pulse P increasing with time. The reflected signal received by a receiving antenna 38 from the object to be detected is delivered to a mixer 40 in a conventional fashion wherein the return signal is mixed with the output of a local oscillator 42 for delivery to a conventional intermediate frequency amplifier 44 whereupon the reflected signal is delivered in the form of a pulse P.sub.1 whose frequency increases with time to one end of a piezoelectric crystal 46 which may be, for example, precisely of the type shown in FIG. 8 and whose theory of operation was described in connection with FIGS. 1 and 2.

A frequency-swept reference pulse P.sub.2 is delivered to the opposite end of the crystal 46 and in order to enable the correlation operation to proceed, the time reversal necessary to enable such operation is achieved by passing the same pulse P from the pulse generator 30 to a pulse inverter 48 so that the reference pulse P.sub.2 delivered to the opposite end of the crystal 46 has a frequency which decreases with time, thus constituting a mirror frequency image of the shape of the reflected pulse P.sub.1. However, since the reflected singal pulse P.sub.1 is delivered to the right end of the crystal 46 and the reference pulse P.sub.2 is delivered to the left end and so are propagated in opposite directions, the corresponding acoustic signal wave forms S.sub.t, S.sub.r are identical, thus enabling correlation when phase coherence of the two occurs. To provide time correspondence between the two signals S.sub.t, S.sub.r propagated through the crystal 46, the reference pulse P.sub.2 may be passed through a conventional variable delay line 50 so that both the reference signal and the return reflected signal will be propagated through the crystal simultaneously to provide the phase matching conditions of parametric coupling. The crystal output in the form of the electric polarization D is delivered through a suitable wave guide for detection and ultimate display, for example, on a scope for visual indication of the target position in a conventional fashion forming no part of the present invention.

Several points should be observed in operation of the described radar system utilizing the principles of the present invention. In the first place, the duration of the transmitted pulse can be relatively long since the acoustic velocity through the crystal 46 is relatively slow (v = 3 .times. 10.sup.5 cm./sec.), thus allowing processing of a signal 10 microseconds duration in a crystal but a few centimeters in length. The longer pulse duration, in turn, allows more energy to be transmitted in each pulse thus ultimately improving object detection, without the requirement that the individual pulse amplitude be at an excessive level. In order to obtain good range resolution, however, short pulses are requisite and various techniques such as described in U.S. Pat. No. 2,624,876 have been utilized to provide "pulse compression."

In the present case, an output signal appears in the crystal only when phase coherence of the transmitted and reflected signals, S.sub.t and S.sub.r, exists and because of the short time duration of such coherence, the output signal resultant from signals S.sub.t and S.sub.r having a pulse duration of 10 microseconds constitutes a narrow output spike approximating 10 nanoseconds, thus representing a pulse compression factor of approximately 1,000.

Additionally, it will be obvious that in view of the explained operation of the convolution mechanism that the output in the form of the electric polarization D is proportional to the product of the strain amplitudes of the signals propagated through the crystal that, in effect, a substantial amplification is derived, thus allowing the entire system to operate at relatively lower power levels to obtain the same amplitude of output signals.

Finally, because of the rapid dimunition in output as represented by the electric polarization D with variance in the coherence of the reference and reflected signals, a very high signal-to-noise ratio, as mentioned herein-above, is achieved so that ambiguity in target signals is removed and indirectly, the effects of countermeansure "jamming" techniques are rendered less effective in obscuring a target detected by this radar installation.

In view of the mentioned fact that the acoustic waves travel at a relatively slow velocity of approximately 3 .times. 10.sup.5 cm./sec., a piezoelectric crystal of reasonable dimensions can be utilized to enable the comparison of a number of known signal patterns having individual waveform characteristics with incoming unknown signals thus to enable the realization of a simple yet practical method of pattern recognition. By way of example, there exist 26 letters in the English alphabet and each of these can be presented in the form of distinct electrical signals which can be sequentially delivered as reference signals to a piezoelectric crystal whose length is no greater than five inches. This follows from the fact that distinctive electrical signals can have a time duration of no more than 1 microsecond and at an average acoustic velocity of 3 .times. 10.sup..sup.-5 cm./sec., a sequence of 26 sequential signals can exist simultaneously within a crystal of this length. With reference to FIG. 11, these reference signals can be suitably shaped and continuously recycled from a reference unit 70 so as to constitute a sequential reference input to one end of a piezoelectric crystal as indicated at 72 in FIG. 11 for comparison, in accordance with the basic theory discussed hereinabove, with an unknown input signal which can be derived from an optical scanner 74 whose output resultant from scanning of a particular visual letter display is converted, for example, by a converter 76 in the manner described in U. S. Pat. No. 3,453,494 to provide distinct electrical pulses which can, in turn, be inverted by an inverter 78 in the fashion discussed hereinabove in connection with the description of the radar system shown in FIG. 10 thus to provide the time reversal requisite for correlation. The inverted signal is delivered to the opposite end of the crystal 72 and the output resultant from the electrical polarization, D, existent when coherence between the input signal and one of the 26 reference signals exists can be suitably displayed. Since the reference singals are delivered in time sequence, the precise timing of the output signal will provide immediate identification of the unknown "letter" of the alphabet. The output data is accordingly precise and unambiguous since the mechanism provides a high signal-to-noise ratio, as discussed hereinabove.

While but a few applications of the convolution and correlation signal processing method have been described, immediate application to many other correlation techniques will be apparent and can be carried out with relatively simple and inexpensive units. Furthermore, the acoustic waves can take varied forms, as mentioned hereinabove, which are convenient for each particular application. Accordingly, the foregoing explanation of the invention and its application to several specific utilizations is to be considered as purely exemplary and not in a limiting sense and the actual scope of the invention is to be indicated only by reference to the appended claims.

Claims

What is claimed is:

1. The method of signal processing in a piezoelectric medium which comprises the steps of

propagating a first modulated acoustic wave through the medium at a predetermined phase velocity and propagation vector,

propagating a second modulated acoustic wave through the medium at a different phase velocity and propagation vector whereby translation of the acoustic waves occurs,

said waves being propagated in a fashion such that phase matching and frequency conservation conditions are simultaneously met during the wave propagation through the medium whereby parametric coupling results, thus to provide the modulation product of the modulated wave energy, and

extracting the wave energy of the modulation product to provide the output signal.

2. The method of claim 1 wherein

the step of propagating the first acoustic wave is carried out by propagating the first wave in one direction through the piezo-electric medium, and

the step of propagating the second acoustic wave is carried out by propagating the second wave in the opposite direction through the piezoelectric medium.

3. The method of claim 2 wherein,

the propagation vectors of said first and second acoustic waves are equal but opposite whereby the parametric coupling produces an output wave with no spatial variation.

4. The method of claim 2 wherein,

the propagation vectors of said first and second acoustic waves are of different values whereby the parametric coupling produces an output wave of finite velocity.

5. The method of claim 1 which comprises the steps preceding the wave propagating steps of

generating said first and second acoustic waves by application of modulated electromagnetic signals to the piezoelectric medium.

6. The method of claim 5 wherein

the step of generating the first acoustic wave is carried out by applying a modulated electromagnetic signal to one end of the piezoelectric medium, and

the step of generating the second acoustic wave is carried out by applying a modulated electromagnetic signal to the opposite end of the piezoelectric medium.

7. The method of claim 6 which comprises

varying the frequencies of the electromagnetic signals so that one constitutes the frequency mirror image of the other.

8. The method of claim 6 which comprises the additional steps of, generating a swept-frequency pulse to provide one signal and, inverting the pulse to form the mirror-image signal.

9. The method of claim 1 wherein

the step of propagating the first acoustic wave is carried out by propagating the first wave through the piezoelectric medium in a predetermined direction at a predetermined phase velocity, and

the step of propagating the second acoustic wave is carried out by propagating the second wave through the piezoelectric medium in the same direction but at a different phase velocity than that of the first acoustic wave.

10. The method of claim 9 which comprises the steps of,

generating a shear acoustic wave by application of one electromagnetic signal to the piezoelectric medium at a given time, and

generating a longitudinal acoustic wave by application of another electro-magnetic signal to the piezoelectric medium at a later time.

11. The method of claim 1 wherein,

the energy extraction step is achieved by coupling to an external circuit tuned to the combined frequencies of the parametrically-coupled acoustic waves.

12. The method of claim 1 which comprises the steps preceding the wave propagating steps of

generating the first acoustic wave directly by coupling electromagnetic energy to the piezoelectric medium, and

generating the second acoustic wave indirectly by coupling electromagnetic energy to the medium in a fashion such that an electrical polarization exists which parametrically couples with the first acoustic wave to generate the second acoustic wave.

13. The method of claim 1 wherein,

said first acoustic wave has an unknown modulation pattern, and

said second acoustic wave has a known modulation pattern consisting of a series of short pulses spaced at predetermined intervals and which comprises the additional step of coupling electromagnetic signals generated by parametric coupling of the waves from the medium at intervals equivalent to the predetermined pulse intervals of said second acoustic wave.

14. The method of claim 1 which comprises the steps preceding the wave propagation steps of

generating said first acoustic wave with a modulation pattern consisting of a finite determined sequence of separate and distinctly shaped signals, all of which simultaneously exist in the piezoelectric medium, and

generating said second acoustic wave with a modulation pattern consisting of unknown signals corresponding to one of the finite sequence of signals of said first wave.

15. The method of claim 1 which comprises the steps preceding the wave propagation steps of

generating said first acoustic wave by applying an electromagnetic signal of unknown frequency to the piezoelectric medium,

generating said second acoustic wave by applying an electromagnetic signal of known but variable frequency to the piezoelectric medium, and

varying the frequency of said variable signal until the conditions for parametric coupling are established.

16. The method of claim 1 which comprises the steps of,

generating a pulse-modulated electromagnetic signal,

applying such signal to the piezoelectric medium at a controlled but variable time to generate said first acoustic wave transmitting said pulse-modulated signal,

receiving a pulse-modulated signal constituting a reflected version of the transmitted signal and applying said reflected signal to the piezoelectric medium to generate said second acoustic wave whereby parametric coupling occurs if phase coherence of the two signals exists in the medium.

17. The method of claim 16 wherein,

said pulse-modulated electromagnetic signal is frequency-modulated, and which comprises the additional step of inverting one of the signals applied to the medium to generate said first and second acoustic waves.

18. Signal processing apparatus which comprises

a piezoelectric medium,

a pair of transducers adjacent said medium to permit coupling of electromagnetic signals into said piezoelectric medium whereby acoustic waves are propagated therethrough,

means for applying modulated signals to said transducers in a manner such that different phase velocities of the acoustic waves exist within said piezoelectric medium and wave translation occurs so that the conditions of parametric coupling, phase matching and frequency conservation exist during propagation of the acoustic waves through the medium, thus to provide the modulation product of the modulated wave energy, and

external circuit means for coupling the product modulation wave energy generated by the parametric interaction of the modulated acoustic waves.

19. Signal processing apparatus according to claim 18 wherein,

said external circuit means constitutes a resonant cavity encompassing said piezoelectric medium.

20. Signal processing apparatus according to claim 18 wherein,

said external circuit means constitutes a folded strip line adjacent said piezoelectric medium.

21. Signal processing apparatus according to claim 18 wherein,

said transducers are disposed at opposite ends of said piezoelectric medium wherefore the acoustic waves propagate in opposite directions.

22. Signal processing apparatus according to claim 18 wherein,

said transducers are disposed at the same end of said piezoelectric medium.

23. Signal processing apparatus according to claim 18 which comprises,

means for varying the frequency of one of the applied electromagnetic signals.

24. Signal processing apparatus according to claim 18 which comprises,

means for pulse modulating one of the applied electromagnetic signals.

25. Signal processing apparatus according to claim 24 which comprises,

means for frequency modulating each pulse of the pulse modulated signals.

26. Signal processing apparatus according to claim 18 which comprises,

means for modulating one of the applied electromagnetic signals to provide a sequence of patterns, each having a predetermined distinct shape.