SIGNAL PROCESSING AND SYNTHESIZING METHOD AND APPARATUS

Abstract: A system to perform non-spectral analysis and synthesis of a complex waveform. The sensor signal (30) is applied to preamplifier (60) and then to logarithmic analog to digital (LAD) convertor (40). The converted signal is differentiated by residue processor (62), from which amplitude (65), residue (66), and the real and complex zeros (64) are extracted. The zeros (64) are applied to periodicity sorting matrix (PSM 45) from which signal periodicity is determined. The outputs of circuits (45, 65, 66) are futher processed by waveform information vector (WIV) format recognition circuitry (67, 68). The recognized signal may be displayed (71) or stored in memory (69) before display (72). Circuit (70) may be used to further recognize the signal.

Description: SIGNAL PROCESSING AND SYNTHESIZING METHOD AND APPARATUS BACKGROUND OF THE INVENTION This invention relates to the processing and syn¬ thesizing of complex signals, and more specifically relates to a novel method and apparatus for processing and identify- ing the components of a complex signal and for synthesizing complex signals in which signal components are identified in terms of discrete locations in a one or more dimensional representation, derived from the measurement and/or genera¬ tion of at least the epoch and damping of the signal compo- nents which make up the complex waveform which is being processed or produced. The analysis and synthesizing of complex waveforms is a well developed art and has application to a large num¬ ber of fields. For example, the analysis of acoustical signals having complex waveforms produced by one or more spaced sources is well known. Similarly, analysis of signal waveforms of electrical signals, seismic signals and other signals is well known with application in speech processing, environmental sensing, biomedical signal analysis, and the like. Equivalent systems are known for the generation of complex waveforms as may be encountered in fields such as music synthesizing, the production of artificial speech, and the like. In presently known acoustical systems,. it is possible to obtain desired information from only simple v/aveforms and from single source objects, such as a single speaker against a low background noise. The effect of fact.ors such as ampli¬ tude, dynamic range, enunciation and sex of the speaker will cause complexity and unacceptable performance in speech analy- s is equipment. Similar problems exist in waveform analysis of signals produced by sources other than the human voice. Those systems which do exist are relatively costly and use substantial input power for their operation due to complex structure and complex processing algorithms. Virtually all existing complex signal analyses sys¬ tems are based on some form of Fourier or spectral analysis or, more generally, on the use of least-squares estimation of polynomial functions. Such methods have a common defi¬ ciency in that during the processing sequence, important information is lost due to the need for a relatively long measurement interval required to estimate the polynomial- coefficients of a Fourier series. Since the measuring in¬ terval must be relatively long, the measurement process loses information related to "epoch" which relates to the time at which a new individual signal within the waveform has begun. Because of this restriction, Fourier type analy- - sis techniques cannot identify multiple source objects which occur simultaneously within the interval of observation or measurement of a complex waveform produced by the multiple objects. If, in a spectral analysis system, the interval for estimation of the polynomial coefficients is reduced in order to improve epoch accuracy, then the accuracy of the mean square estimate of the source function is reduced. Consequently, in the case of Fourier analysis, the spectrum becomes more and more blurred as the sampling window is reduced in time. The difficulties of present systems for analysis of stochastic signals are summarized by a known time-frequency 5 uncertainty which specifies that accuracy in a frequency domain requires low resolution in the time domain and vice- versa. This is described, for example, in the article by D. Gabor entitled "Theory of Communication", Journal of IEEE, Volume 39, Part III, No. 26, November, 1946. The above pro- ° blem is also described by S. M. Kay and S. L. Marple, "Spec¬ trum Analysis - A Modern Perspective", IEEE Proceedings, Volume 69, November, 1981, pp. 1380-1419 and by H. Bremerraan, "Pattern Recognition, Functions and Entropy", IEEE, Transac¬ tions on Biomedical Engineering, Volume BME-15, No. 3, July, 5 1968. It is interesting to note that the human ear has solved the waveform analysis problem, although the opera¬ tion of the ear in this analysis function is not understood. In older theoretical analyses of the operation of the ear, it was assumed that the hearing process employs spectral processing. Thus, an early theoretical model of hearing was made by Von Helmholtz in 1863. The Von Helmholtz model was based on a Fourier or frequency domain signal analysis. Both Von Helmholtz and his successors concentrated on study- ing well-defined and relatively simple signal conditions, especially with only one signal at a time. These simplifi¬ cations have provided a reasonable basis for a theoretical study, but disregard how the ear deals with frequency dis¬ crimination over a wide, logarithmic range, how it responds to transients and its ability to detect and identify sounds over a wide amplitude and dynamic range with near optimum detection sensitivity and how it can discriminate multiple sources spatially and temporally even when they are inter¬ leaved with wide ranges in amplitude. Acoustic sources can also be identified by the ear in spite of background noise and extreme distortion of amplitude and phase. This is the well known "cocktail party effect" in which the human ear can pick out the voice of an unseen speaker from a background of other voices of equal or greater amplitude. The use of Fourier analysis type techniques fails to explain many of the functions of the human ear, including those described above, in terms of a consistent signal processing theory. Signal processing methods and apparatus which are presently available are extremely complex and expensive, even though their functions do not come close to the effi¬ ciency and wide range application of the human ear. The present invention provides signal processing which more nearly approaches the results obtained by the human ear and which is less complex and costly than presently available equipment. BRIEF SUMMARY OF THE INVENTION The present invention provides a novel signal pro¬ cessing method and an equivalent signal generating method for the analysis and generation of complex waveforms which employs a non-spectral analysis approach and can be imple¬ mented with reliable and relatively inexpensive processing circuitry. In accordance with the present invention, the com¬ plex waveform is analyzed by making sequential measurements t either- or both the real and complex zeros of the waveform. The directly measurable parameters at the real and complex zeros of the waveform are the waveform energy level, the epoch or initiation of new wave fronts and derivatives of the waveform. Direction of arrival can also be measured. These parameters are termed "waveform information vectors" and are sometimes termed hereinafter "WIVs". These WIVs are then processed by relatively simple digital or analog cir¬ cuitry in order to derive from the measured information which characterizes and locates each signal source object OMH within the ensemble of arriving waveforms. The primary means of identification is in the formation of patterns in the vector space formed by coordinates of periodicity vs. residue vs. amplitude. This vector space is termed the "Aural Retina" because of its analogy with the ear and the process of hearing. It has been shown that human listeners identify sounds in terms of pitch and timbre. Specifically, pitch is an attribute of periodicities in the time domain, and timbre is an attribute of instantaneous harmonic con¬ tent, or residue, in the frequency domain. This relation¬ ship between pitch and periodicity, and timbre and -residue allows a specific definition of a pattern space within the ear and the hearing process, within which the objects of aural perception are analogous to the objects of visual perception. In other words, objects defined as sets of points in coordinates of periodicity, residue and amplitude of the Aural Retina are analogous to objects perceived in the visual retina in terms of height, width and brightness. TJO accomplish this function, the WIVs are extracted at the instant of each real or complex zero of the waveform and compared with a set of prior patterns so as to derive information regarding epoch and wave shape of the individual source objects which have produced the entire waveform. Fol¬ lowing each subsequent analysis interval, additional informa- tion on the waveform is made available to continuously refine the analysis process. Thus, with the present invention, acoustic sounds may be described by a pattern in two-dimensional space plot¬ ting periodicity (pitch) vs. residue (timbre). Spatial or directional information between sources which produce a given complex waveshape at a sensor are determined by employing spatially directed channels which measure the wave from a given direction. The Aural Retina measurements which are made in the various directions are then compared and the signals of the multiple sources are separated and individually identified. In an analogous manner, the novel process and appar¬ atus of the invention can be employed to synthesize complex waveforms so as to synthesize the human voice or the like with relatively simple equipment. The specific processing circuitry which is employed for a given application depends on the frequency range of the waveform. Thus, for frequency ranges from seismic fre¬ quencies up to ultrasonic frequencies, standard LSI and VLSI techniques and components can be used. In this frequency range, the waveform processing can be used in such appli¬ cations as oil prospecting, underwater submarine detection and tracking, speech instruction and hearing research, auto¬ motive engine tuning and other acoustic analysis, evaluation of musical instruments, bioelectric monitoring, speech recog¬ nition and the like. The invention is also applicable to higher frequency waveforms which might be in the far ultrasonic to radio band and up to 200 MHz for use in radio detection in the broadcast band, interference detection and location in the radio band, and the like. The invention also applies to detection in even higher frequency ranges through 1,000 MHz. , where the circuits are implemented preferably with surface acoustic wave devices for application to spread- spectrum communication systems and the like. THEORETICAL BASIS OF THE INVENTION The theoretical basis for the novel Aural Retina concept of the present invention is now described in connec¬ tion with the processing of an existing complex waveform in contrast to the production of the complex waveform which will be later described. Any complex waveform which is produced by the superimposed responses of a plurality of objects each of which represent a respective source of information can be described mathematically by: where A. - k amplitude coefficient; S, = kth complex frequency (o< i. + j ._# ) / . k = epoch (start) of kth excitation function It is presumed in Equation 1 that t .t * The function f(t) As expressed in Equation (1), the composite wave¬ form f(t) is the sum of a sequence of exponential wavelets of various amplitudes, which occur as response functions of excitations occurring at the various epochs (or instants). This process is schematically illustrated in Figure 1. Thus, Figure 1 schematically illustrates at the left, n excitation sources 20-23 each of which produce a pulse type excitation at some time *£, . Sources 20-23 can have any desired rela- n tive spatial location and any desired size. When the objects are stimulated by the unit impulse excitation impulse ζ (τ£ ) their response signals can have any desired shape, as shown by the different wave shapes above boxes.24-27 wherein the waves are oscillatory waves or critically damped waves, or the like, illustrated by the values A hCK ). The response k K signals of each of objects 20-23 can be generally represen¬ ted as f k (t) - A k hCT k . l k )eV* ( 2 ) where 1. represents the kth location. The outputs of boxes 24-27 are summed in a summing device 28 which produces the output f(t) which is the func¬ tion of Equation 1 above. Note that the complex waveform shown in Figure 1 contains the epochs *" & , Ε , Ε and ^ of 1 3 n the generators 20-23 respectively. From the above, the waveform emitted by each object potentially contains information about the spatial and tem¬ poral patterns of each object. To analyze the function shown OMPI ^* ? W Λ/ I AT O 10^ * in Figure 1, the signal analysis system of the invention has the capability to sort, compare and associate the measurements of epoch, amplitude and response function for each of the sources 20-23 with a high degree of analysis fidelity. By analysis fidelity is meant the amount of recoverable infor¬ mation to the available source information. The signal sources which are involved are normally characterized by arbitrary and unpredictable parameters. Thus, waveforms produced by environmental and biological sensors are at best random, stochastic or transient. For example, human speech and various animal sounds will have highly variable periodic components intermixed with random and transient events. In some cases, many signal sources will coexist in time and space. Because of this randomness and variability, the signal analyzer of the invention must extract information within very small time intervals. Otherwise, the ability to associate the epoch information of objects 20-23 with the corresponding system response of system response blocks 24-27, respectively, is lost. If this information is lost, there is then no way to identify the components of a source. Note that this problem is also related to the ability to detect a sig¬ nal in a background of noise or othe^ signals. From the above, it is apparent that a crucial re- quirement for the analysis system is that the system must identify epoch t as accurately as possible. The epoch 'K, in Equation 1 is that impulse which produces the single response function of a wavelet, where the wavelet can range from an overdamped case in which c< » 1 to the oscillatory case where 0 *< _< 1, where ζ is the real portion of the complex frequency °< +j ». In the oscillatory condition, epoch is the onset of a periodic function at the complex frequency, In a complex signal, the sum of the various wavelets appear- ing at various epochs will cause the various peaks and nulls in the waveform. Therefore, each ripple in the waveform of Figure 1 is a feature which results from either an excitation impulse or an oscillatory response. These features can be represented as real and complex zeros in the time domain as described, for example, in the publication by H. B. Voelcker, "Toward a Uniform Theory of Modulation", Part I: Phase-Envelope Rela¬ tionships, IEEE Proceedings, Volume 54, March, 1966, pp. 340- 353 and Part II, Zero Manipulation, IEEE Proceedings, May, 1966, pp. 735-755. Also see United States Patent 3,510,640 to H. B. Voelcker, entitled "Method and Apparatus for Inter¬ polation and Conversion of Signals Specified by Real and Complex Zeros". In accordance with the invention, means are provided for identifying and measuring the complex zeros in a complex waveform in order to measure both the epoch and the period of the exponential wavelets which make up the complex wave form. Since any individual zero in the complex waveform might be either the onset of a new wavelet or a response from a previous wavelet, means are provided to measure and store the information at each zero so that it can be related to previous and/or subsequent data. Directly measurable parameters at the zero points are energy level A, epoch, and derivatives. The direction of arrival of the energy is also an instantaneous parameter and is determined by comparing instantaneous energy and epoch of spatially-separated sensors. As previously noted, these parameters which are measured at the zeros, are termed waveform information vectors or "WIVs". The derivative or rate-of-change vector is useful after being normalized for absolute signal strength. This is done by dividing the derivative f'(t) of Equation (1) by f(t) to produce the amplitude-independent time derivative of the logarithm of f(t). Thus, v ( t ) = f ' (t) = d[ln f(t)) (3) J f(t) dt OMPI In Equation (3), the function r(t) can be interpreted as the instantaneous ."residue" of the spectral pattern of the signal f(t). Consequently, the function r(t) is frequently hereafter conveniently designated the "residue function". The function r(t) also represents the residue of the responses of pz^ior and present exponential functions in the signal f(t). It is instructive to consider the case where f(t) is a single exponential wavelet having the form In Equation 4, the term oζ is the decay time of the exponen¬ tial wavelet, while the term O is the ringing frequency. Note that these are also the real and complex components of the complex frequency f of Equation (1). By taking the derivative of f(t) of Figure 4 and then dividing it by f(t) of Equation (4), the residue function r(t) is produced as follows: r ( t ) (5) This then reduces simply to : The residue function as represented in Equation 6 can be interpreted in several ways. The objective, in accordance with the present invention, is to identify a function which characterizes the exponential coefficient β< at selected real or complex zeros f(t) or of r(t). The zeros of f'(t) are the same as those of r(t). The advantage of sampling the function r(t) at its zeros is that the function discon¬ tinuities caused by the real zeros in f(t) can be avoided. This process will then lead to extremely simple circuit techniques for extracting the desired information. OMPI_ l ,o A number of methods are possible for obtaining this result and two are described in. the following: In the first method, consider only the real zeros of the function r(t) of Equation (6). It will be seen that when r(t) = 0, then: As before, the imaginary frequency 3 defines the ringing frequency of the single exponential wavelet under considera¬ tion, while oζ defines the real axis frequency and specifies ° the damping or decay time of the exponential. The objective of the electronic system will then be to estimate © and * -^ using the information derived from the zeros of r(t). Both ©^ and ό are first measured as functions of the zeros of r(t) by conventional measurement devices. The residue wave ° form r(t) is then processed to obtain either positive or . negative half cycles, and the period of time of the ringing (assuming that 0 is less than^ ) is then measured. This period is termed T^ . A convenient way to obtain the quan¬ tity &ζ is to measure the period between the leading edge 0 and the peak of the waveform so that The parameter 6" then becomes the definition of residue. When the period T^ described above equals T^/ it corres¬ ponds to the duration of a quarter cycle of a pure sine wave, which then, at any frequency θ , provides the refer¬ ence zero band width IBW or, conversely, the maximum possi¬ ble rise time. Therefore, the measurable parameter T is related to the residue r(t) by Equation (6) above. Note that T^ is derived from the log derivative waveform, which is not variable with signal amplitude, and thereby removes certain practical problems from the system design. OMPI ? A Ti The relationships between T^ and T^ are shown in Figure 2 for values of . In Figure 2, the value ^ is the equivalent of timbre, whereas the quantity 1/T^ is periodicity or per- ceived pitch of the signal for different amounts of residue of in the signal. The diagram of Figure 2 forms the basis of the Aural Retina concept of the invention. Thus, elementary signal functions are instantaneously identified by their point positions within the existence diagram bounded by d = Q for a sine wave signal condition. Note in Figure 2 that no signal can exist to the left of o = o. Between the values of residue from (a criti¬ cally damped line), the signals are oscillatory and will have separable periodicities. A single impulse response would appear in Figure 2 as a single point. Repetitions of impulse responses would produce unique patterns of dots depending upon the interference pattern of the excitation period with the ringing period. In the overdamped region to the right of < =1T74T , single impulses will appear on the zero pulse repetition frequency axis at the measured rise time. Note that rise time is essentially the composite of all of the exponentials appearing at a given impulse epoch. However, a train of periodic pulses appears at a point specified by its rise time T^ and its repetition rate ΥA . Noise pulses will tend to scatter throughout the existence plane of Figure 2, with their density concentrated near the periodicity of the upper band width cutoff of the system. The above method has presupposed that ΥA , the period of the the ringing frequency, can be measured. In this elementary example, measurement of T Δ presents no problem, but in general, the measurement of Ta requires a special measuring system which will be later described. The above describes one type of Aural Retina which can be employed in accordance with the invention and relies on measurement at the real zeros of the function r(t). It is also possible to derive the residue function r(t) at the complex zeros of the function since the complex zeros will correspond to the peak values of f(t). Thus, it will be noticed, from Equation (6), that: From the above, when f(t) = sine βt = 1 (a peak), then r(t) = - ©<• In general then, r(t), when it is sampled at the peaks of f(t) by the measuring equipment, will produce a measure related to the value oi . In employing this type of measurement, the residue provide an instantaneous estimate of the waveform rate of change or instantaneous bandwidth. This method will then define a rectangular existence region instead of the triangular plane existence region of Figure 2. It should be noted that the pattern developed in Figure 2 for the Aural Retina is similar to an existence diagram which was developed by Schouten on the basis' of psycho-acoustic experiments on human subjects as described in the paper by R. Plo p and G. F. Smoorenburg, Editors, "Frequency Analysis and Periodicity Detection in Hearing", Lydon: A. W. Sijthoff, 1970. Thus, there is a correlation between the mathematical analysis above based on availability of waveform information vectors in an exponential waveform and the actual measured response of the ear as shown in Fig¬ ure 2A which is a reproduction of Schouten's existence diagram The diagram of Figure 2, which represents the Aural Retina of the present invention, will have the various in¬ stantaneous WIV data applied, thereto, where the WIV data can be relatively easily measured. It will later be shown how the WIV samples will be processed in order to derive the 14 desired information concerning the source objects of the complex waveform. The term "Aural Retina" has been selected because of the functional similarity between the spatial object analysis of the visual retina and the analysis of source objects in the space defined by the waveform information vectors. This is illustrated in Figures 3a and 3b which schematically illustrates a visual retina and an aural re¬ tina, respectively. In Figure 3a, the visual retina will discern object shapes in a plane formed by a height and a width axis. A third dimension to the visual retina can be represented by the brightness of the object shapes. In the aural retina of the invention, object shapes can be thought of as lying in the plane of the Aural Retina of Figure 2 and related to pitch and timbre, with the third dimension of the aural retina being loudness if the wave form being analyzed is a sound wave. Signal detection in the Aural Retina, as in the eye, is related to two functions: (1) the sensing of an object pattern in terms of an energy threshold; and (2) the selec¬ tion of a specified object pattern from a background of other patterns. In the aural retina of Figure 3b the primary source object patterns are presented in the existence space bounded by residue and periodicity, as in Figure 1 where the patterns represent signal identi ication. Acoustic sounds are similarly described in the ear by pitch and timbre, as shown by the existence diagram in Figure 2A which was plotted on the basis of psycho-acoustic experiments on human subjects. In prior art arrangements in which Fourier analysis type of processing is employed for complex signals, it will be noted that the same signal can be represented by the Aural Retina with lower dimensionality than is possible using the neces¬ sary large number of Fourier coefficients. The lower dimen¬ sionality inherently permits the use of faster and cheaper computer processing for the processing of the signal, as will be described, and requires less memory than does the spectral analysis technique. A significant feature of the invention is that the procedure described above is reversible. Thus, waveforms of arbitrary content can be synthesized by suitably program¬ ming the epochs and other waveform information vectors in the signal generating circuits. BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 is a schematic drawing illustrating a plurality of signal sources and their summed response func¬ tions. Figure 2 schematically illustrates a two-dimensional existence plane in which particular signals can be displayed in accordance with the invention. Figure 2A is a diagram produced by psycho-acoustical experimentation on the performance of the human ear. Figures 3A and 3B compare the characteristics of the visual retina to the Aural Retina of the invention, as shown in Figure 2. Figure 4 schematically illustrates analysis inter¬ vals used for processing a complex waveform in accordance with the invention. Figure 5 is a functional block diagram of a system for carrying out the analysis intervals of Figure 4. Figure 6 is a block diagram of a preferred circuit arrangement constructed in accordance with the invention. Figure 7 is a block diagram of an analog residue processor which can be used in Figure 6 and in connection with the present invention. Figures 8a to 8f show a digital residue processor which can be used in place of the analog system of Figure 7. OMPI Figure 9A schematically illustrates an interleaved pulse train of overdamped wavelets which are to be analyzed. Figure 9B schematically illustrates " a waveform which is to be analyzed which has periodic, excitation with an underda ped response function. Figure 10A schematically illustrates an input signal which is to " be processed. Figure 10B shows the clocked signal which is produced from the signal of Figure 10A. Figure 11 schematically illustrates a logic map of a novel periodicity deinterleaving system for deinterleaving the signal train of Figure 10B. Figure 11A schematically illustrates the reasons for false recognition of a pulse in higher octaves of a plurality of octaves. Figure 12 is a logic map of a periodicity sorting matrix for sorting a plurality of octaves. Figure 13 is a logic diagram for a simplified perio¬ dicity sorting matrix to be used with the circuitry of the present invention. Figure 14 is a block diagram of a quasi-analog processor arrangement made in accordance with the present invention. Figure 15 is a segmented existence diagram useful for describing the outer product of the periodicity and residue which is measured in accordance with the inventio-.i and displayed in an Aural Retina type display. Figure 16 is a block diagram of an aural retina processing and automatic signal recognition circuit which can be produced in accordance with the invention. Figure 17 shows an alternative method for recogniz¬ ing signal patterns which does not require the RAM of Figure 16. Figure 18 schematically illustrates a logic map for a single octave epoch detector circuit. Figure 18a schematically illustrates the manner in which Figure 18 can be extended to a multi-octave system. Figure 19 is a block diagram of a waveform synthe¬ sizer made in accordance with the invention. Figure 20 is a diagram of a zero placement matrix used for the waveform synthesizer of Figure 19. Figure 21 is a timing diagram of the zero placement • matrix of Figure 20. Figure 22 illustrates a method for residue modula- tion for a synthesizer arrangement. Figure 23 is a typical signal waveform to be analyzed Figure 24 shows the spectrum analysis of the signal of Figure 23. Figure 25 is the waveform of Figure 23, along with pulses representative of different aspects of the waveform and the Aural Retina display corresponding to the waveform of Figure 25. Figure 26 shows a second waveform, added to the waveform of Figure 25. Figure 27 shows the spectrum analysis of the combined waveforms of Figure 26. Figure 28 shows the Aural Retina display correspondin to the combined waveforms of Figure 26. 17a DETAILED DESCRIPTION OF THE INVENTION Referring now to the drawings, Figures 1, 2a, 3a and 3b have been previously referred to. A block diagram of a circuit for analyzing WIV data sensed by at least two different sensors is shown in Figure 4. In general, the analysis process of the invention, as shown in Figure 4, employs the storage of each WIV as it is received. The WIV is then compared to prior WIVs. Decisions are then made concerning their meaning and taking action where necessary. The analysis can be carried out in at least five analysis intervals. In Figure 4, there is shown a right sensor 30 and a left sensor 31 each of any desired type, each of which receives waveform energy from one or more energy sources. The sensors 30 and 31 are connected to WIV data measurement circuits 32 and 33, respectively, which will be later des¬ cribed, which are capable of extracting from the received signals, information regarding epoch *V , energy A and resi¬ due R. By suitable manipulation of the data, the direction θ from which the signal came can also be determined. Note that greater numbers of separate sensors can be used to locate a source object- within a solid angle as by employing the trilateration process described in my prior U.S. Patent 3,886,553, entitled "Coordinate Locating Method and System", issued May 27, 1975. However, the direction vector is not always necessary for identifying the source object or its message. Note also that in this measurement, the epoch t is the time at which the signal is received, the energy A is the instantaneous level of the energy and the residue R corresponds to the residue r(t) of Equation (8). The five analysis intervals shown in Figure 4 are defined by the limits of the information available in the collected WIV data. At the instant data is received, the sample at each waveform zero will represent the first in- terval. The angle of arrival of the information may be immediately determined by comparison of amplitude and/or. epoch in the sensors 30 and 31. The information in the first interval from measure¬ ment devices 32 and 33 is processed to develop the spatial WIV information in the processing block 34. The immediately received information can be "flash" information which might develop information regarding the significance of the received signal. Thus, in the first interval, the system can supply rudimentary or flash answers to simple questions regarding the meaning of each WIV event. For example, if the question is: "Is the signal representative of a dangerous condition?", a threshold of amplitude, rate of change or direction can be established to specify some immediate response if danger is detected. Thus, it is not necessary in the first interval to identify the source but only its potential threat. In the second analysis interval, there is provided circuitry for extracting the periodicity ( ^ ) and for com¬ paring epoch of the instantaneous signal to a prior signal. This circuitry is shown in block 35 of Figure 4. If, in the second processing interval, events are observed to have equal time intervals, it can be determined that periodic signal com¬ ponents are present in the ensemble of f(t). Such components may be caused by excitation functions, underdamped system responses, or simply by random occurrences in a stochastic waveform. However, periodic excitation components will be continuously repetitive. The second interval adds perio¬ dicity information to the WIV data but only over a range of 19 three instantaneous WIV events, which is the minimum for determining a periodic event. This added information does not usually supply sufficient data to allow identification of a source function so that the response action will be the same as that for the first interval and is identified simply as more "flash" in Figure 4. In the third processing interval, the WIV data, with added periodicity, are averaged over a short time in¬ terval within the processing circuitry 36. The short time interval is chosen to provide a reasonable estimate of the source objects in the waveform received by sensors 30 and 31. This may be regarded as a "snapshot" of the source which allows identification of some aspects of the nature of the source such as who, what, where and when qualities. The fourth analysis interval has circuitry 37 adap¬ ted to examine the successive snapshots from the third inter¬ val to determine variations in time and space in the source objects. This is analogous to successive production of still frames which compose a motion picture film. The effect of the additonal analysis in the fourth analysis interval will supply answers to questions such as: "What are the objects doing?". In the fifth analysis interval, circuitry 38 is provided which permits analysis of syntactic patterns which might answer a question such as: "What are the source ob¬ jects saying?". There can also be succeeding analysis in¬ tervals which will be later discussed. The analysis interval sequence shown in Figure 4 represents a basic procedure for extracting information from any source in accordance with the invention. This procedure can be used to design any desired system for accomplishing the specified results. Thus, the analysis intervals and their circuitry 34-38 can be arranged as necessary depending upon the particular objective of the system. Thus, the cir¬ cuit blocks 32 to 38 can be designed for speech processing, OMPI environmental sensing, biomedical signal analysis and for processing of other related signals. Note that systems em¬ ploying some form of a Fourier analysis or, more generally, a least squares estimation of polynomial functions, cannot use the analysis sequence shown in Figure 4. Figure 5 is a block diagram showing the functional data flow for the system of the invention. The system of Figure 5 employs the same sequence of analysis intervals referred to in Figure 4. Means are provided to first iden- tify WIVs at signal waveform zeros. These zeros can be the real zero crossings, the complex zeros, or both the real and complex zeros. In the most general case, which is given in Figure 5 , there are two sets of WIVs to show the means of determining the direction of arrival at each sampling zero. Thus, there is an Aural Retina for each side of the system and a combined spatial Aural Retina in which left and right WIVs are compared to determine directional parameters. The signals from transducers 30 and 31 in Figure 5 are first sampled and processed by logarithmic analog-to- digital converters 40 and 41, respectively, which convert the received waveforms into logarithmic amplitude-encoded digital data. This is done to allow the sampling of a larger amplitude dynamic range in the instantaneous variations of the waveform than would be possible with standard automatic gain control methods. The log function is also necessary to produce the log derivative from which residue is derived. The peak amplitude, as a digital value, directly forms one element of the WIV space. Digital di ferentiators 42 and 43, respectively, produce the real and complex zeros of the signal as their outputs, which outputs are processed to give the residue vector of the WIV. Thus, in the first analysis interval in Figure 5, there is an amplitude output from the logarithmic analog-to- digital converters 40 and 41 and a residue output from digi- tal differentiators 42 and 43. Information regarding the OMPI W1PO zeros, carrying the epoch information, is also connected to respective periodicity sorting matrices (PSM) 44 and 45, the details of which will be later described. Periodicity sort¬ ing takes place during the second analysis interval of Fig- ures 4 and 5 by comparison of time intervals between zeros in such a way that all periodic components are detected and digitized. Aural Retina circuits 46 and 47 are then provided for the right and left-hand sides of the system, respectively, and constitute circuits for making the first estimates of the waveform content received by transducers 30 and 31, respectively. Since the aural retinas 46 and 47 represent multi¬ dimensional space, if visual display is needed, appropriate displays can be driven by the Aural Retina circuits 46 and 47. The visual interpretation or display of the vectors can be carried out in various ways and the method selected depends on the information which is of interest. It is generally not necessary to observe all vectors simultaneously. In particular, the primary vectors are contained in the exis¬ tence plane bounded by residue and periodicity which are the two parameters present in the main waveform identification information, as shown in Figure 2. This allows the observer to perceive "flash" data quickly. That is, he can understand patterns having particularly important instantaneous content. Also provided in Figure 5 is a spatial aural retina comparison circuit 48 which receives all of the information input to Aural Retina circuits 46 and 47 but makes compari¬ sons between the left transducer vectors and right transducer vectors. Comparison circuit 48 can employ conventional am¬ plitude comparison and/or time-difference direction finding circuits such as those used in radio direction finding appli¬ cations. The perception of amplitude and direction is use¬ ful in certain operational situations but is most helpful in providing a signal object sorting function analogous to the way binaural hearing allows listeners to ignore reverberations and conflicting sounds. Although the Aural Retina circuits 46 and 47 per¬ form signal analysis, the circuits are not employed for making the main decisions about the content of the ensemble. The analogy between the visual and Aural Retinas of Figures 3A and 3B is appropriate at this point. Thus, the Aural Retina should be regarded essentially as the repository of spatial patterns and only subsequent recognition processes can identify the patterns and interpret their meanings. The third analysis interval of Figure 5, like that of Figure 4, concerns the storing and averaging of the rough data of each arriving WIV. This processing is employed to produce a set of smooth WIVs which can be observed visually in selected situations, then stored and retrieved at will. In the third interval display there is provided circuit 50 for WIV storage and averaging to obtain composite fine reso¬ lution data. Suitable microprocessors can be employed for the circuitry 50. A storage CRT can also be used for stor- ing and averaging. Since the patterns are now under the control of the system, "templates" of desired WIVs may be provided to enable automatic recognition of various input signal situations. Thus there may be provided a source of stored signal patterns 51 which can be applied to a suitable comparator 52 which will determine whether the WIVs received in the storage 50 corres¬ pond to predetermined signal patterns of system 51. If a "hit" is determined, the circuit 52 can produce a suitable decision or output related to the signal waveform content which has been processed in the circuitry 50. In the Aural Retina concept, this function is the equivalent of signal detection. Note that unlike the con¬ ventional method of frequency-selective energy detection, no decision is made to reject or to select energy during the process. Thus, when a signal is detected by a recognition OMPI W v IP O decision, it does not necessarily remove the WIV pattern of any other signal. The arbitrary and simultaneous detection by recognition of a wide variety of interleaved signal pat¬ terns can thus be carried on and the adaptive selection processes are easily implemented. In the fourth interval- of Figure 5 there is provided circuitry for comparing smoothed vectors, shown as circuitry 53. In"this circuitry 53, assemblies of smoothed WIVs which contain certain common features are compared and variation 0 patterns are identified. For example, this process might recognize diphthongs (pitch or formant variation) in speech. Circuitry 54 can be provided to produce outputs related to decisions on variable patterns. Circuitry 53 can also be employed to drive a display which could, for example, be a strip chart. Relatively few signal sources other than human speech will require more than three or four of the process¬ ing intervals shown in Figure 5. Other steps, however, are possible and, for example, a fifth processing interval can w be employed which contains circuitry 55 for normalization for automatic recognition of a voice and for speech process¬ ing. Circuitry 55 could also be used, for example, for sonar target recognition if desired. A stored template for a specific pattern variation is shown by the circuitry 56 5 and can be connected to the block 54 for automatic recogni¬ tion of a predetermined pattern variation. Figure 5 demonstrates the broad aspects of the Aural Retina concept and shows that there will be many com¬ mon features among any number of specific applications of 0 the concept. Any desired circuits can be employed to carry out the various functions disclosed in Figure 5. A specific Aural Retina arrangement which can be used in Figure 5 is shown in Figure 6 in block diagram form for the channel of Figure 5 which extends from the signal 5 sensor 30. The circuitry extending from signal sensor 31 of OMPI 24 Figure 5 will be essentially identical to that which will be described in connection with Figure 6. The object of the system of Figure 6 is to carry out the computations indicated by Equations (8) and (9). The general procedure carried out by the block diagram of Figure 6 will be to convert signal ' waveform into a uni-polar logarithmic form from which amplitude, residue and epoch are obtained. It may be necessary, in certain applications, such as in processing seismic signals used in geophysics, to analyze both positive and negative polarities. This would require a dual LAD. Outputs of the dual LADs would be pro¬ cessed identically and then merged, where appropriate, into the PSM for periodicity analysis. Thereafter, periodicities are measured and associated with the WIV data in a short- term storage device. This interim storage permits the accu¬ mulation of recurring data patterns which characterize indi¬ vidual signals. Thereafter, periodically, these patterns are scanned into a microprocessor-controlled storage where smoothing, display and automatic signal recognition are performed. This process accomplishes the functions for the first three processing intervals of Figure 5. Subsequent processing in four or more intervals would be performed primarily in conventionally designed computer algorithms. In Figure 6, components identical to those of Fig¬ ure 5 have been given identical identifying numerals. It will be seen that the sensor signal 30 is first applied to a preamplifier 60 and then to the logarithmic analog-to-digital converter 40. A conventional clock 61 is connected to conver¬ ter 40, residue -processor 62, periodicity sorting matrix 45 and epoch frame circuitry 63. After amplification and digi¬ tal conversion, the residue processor 62, which is a part of the digital dif erentiator 42 of Figure 5, extracts and encodes amplitude and residue information, as well as the real and complex zeros which contain the epoch data. The zero information and amplitude information is applied to OMPI ι wι?o t_ 25 circuits 64 and 65, respectively, and the residue information is applied to circuit 66. The zero information of circuitry 64 is then applied to the periodicity sorting matrix 45 and the output of circuits 45, 66 and 65 is applied to a WIV format circuit 67. Note that the periodicity sorting matrix 45 has analyzed the zeros and sorted the periodic sequences to identify their arrival times. An outer product matrix circuit 68 receives the WIV format information from circuit 67 and the epoch frame infor- mation from circuit 63 and operates to assemble the WIVs for instantaneous identification. The outer product matrix cir¬ cuit 68 then transfers each recognition event to a temporary storage circuit 69 where averaging and interpolation of the outer product matrix can be performed. Automatic recogni- tion of selected source objects can also be accomplished at this level in the automatic source object recognition cir¬ cuit 70. The output of outer product matrix circuit 68 is also applied to the visual Aural Retina display circuit 71 and the information from interpolation and averaging circuit 69 is also output to the Aural Retina display 72 which pro¬ duces the smoothed information. In general, the signal processing functions of the blocks shown in Figure 6 could be performed by analog methods. That is, they could operate directly on signal waveform, as shown in Figure 7. Referring to Figure 7 which shows an analog residue processor, it is seen that the signal f(t) is connected to a unidirectional logarithmic amplifier 80, the outpu of which is connected to a differentiator 81 which has an appropriate RC time constant circuit. The output of differentiator 81 is the log derivative of f(t) which con¬ tains the desired residue function r(t). Since this constant occurs only at the peaks of f(t), it is necessary to gate out the log derivatives at only these instants by selecting the peaks of f(t). This is done by differentiating the function f(t) in differentiator 82 and then detecting the OMPI zero crossings in the conventional zero crossing detector circuit 83. These zero crossings are then used to operate the gate 84 and the gate 85 in order to gate- the residue function and the log of the amplitude, respectively, into the subsequent processing circuit only at the complex zeros. A zero crossing detector 86 is also connected to the output of the log amplifier 80 in order to apply the output log f(t) only at the time there is a real zero. Note that real zeros are detected from the edges of the log f(t) signal. Also note that the peaks in the signal correspond to the first-order complex zeros and are used for further analysis. While the analog circuity of Figure 7 is relatively simple in structure, the logarithmic amplifier 80 and differ¬ entiator 82 and the peak detector circuitry are costly. Moreover, a digital processing circuit would lead directly to the output form needed for subsequent processing by a digital microcomputer used for pattern recognition. A logarithmic analog-to-digital converter which shows an overall block diagram which shows the paths of the • various digital timing waveforms as they relate to the vari¬ ous system functions; a detailed logic design diagram for the three basic blocks or PC boards of the present operating system; and timing waveforms showing how the various func¬ tions are performed in digital processing. Figure 8a shows the various timing control lines derived from the base clock 90. There are three basic con¬ trol areas separated by dotted lines: (1) the LAD sampling switch 91; (2) the digital differentiator and data encoding circuits 92; and (3) the PSM data input and readout 93. A timing divider 94 produces a set of timing pulse trains which are used to derive the proper durations for the control signals. The LAD switch pulse put out by timing logic circuit 95 is designed so that its period coincides with the basic shift register clock within the PSM 93. The switch pulse width is chosen to be as small as is consistent OMPI 27 with the RC charge and discharge requirements of resistor 96 and capacitor 97 of the switching circuit. The LAD sampling switch circuit 91 has a signal input thereto which is the signal f(t). This signal is applied to preamplifier 800 and to an appropriate LAD switch circuit 801 which is connected through the RC circuit 96-97 to the comparator 802. The output of the comparator 802 is then connected to one input of gate 803 and to one input of a real zero select circuit 804, as will be described. The other input to real zero select circuit 804 is derived from the LAD sv/itch pulse and the other input to gate 803 is derived directly from the fast clock output of timing divider 94. A control logic circuit 805 receives inputs from the divide by two output of timing divider 94; from the divide by 64 output of timing logic circuit 95 and from the fast clock output of timing divider 94. The control logic out¬ puts of circuit 805 are then connected to data counter 810, which also receives the output of gate 803, to complex zero select logic circuit 811 and to the latch 812. The outputs of data counter 810 are applied to subtract circuit 813 and to latch 812 as shown and the subtract circuit outputs of circuit 813 are applied to residue latch 814 and amplitude latch 815. The output of complex zero select logic 811 is applied to the zero mode combination select circuit 816 and the various circuits are interconnected with one another, as shown. The output of residue latch 814 consists of the residue function, while the output of amplitude latch 815 is the log amplitude output function. The PSM data input and readout section 93 consists of a readout scan select logic circuit 820 which receives outputs from the fast clock read¬ out scan clock and shift clock, respectively, and its eight output leads (typically) are connected to the periodicity sorting matrix 45. The periodicity sorting matrix 45 has an output connected to counter 821 which, in turn, operates latch 822 which puts out data related to digital periodicity - " gWEAi OMPI ^SNATlC in the input signal. An interrogate pulse logic control circuit 826 is provided and receives an input from the shift clock and from the zero mode combination select circuit 816 and produces an output to the periodicity sorting matrix 45. The waveforms of Figure 8b illustrate the operation of the LAD 91. The waveform f(t) is the output of the pre¬ amplifier 800 which feeds the switch 801 controlled by the switch pulse. At each switch pulse the electronic switch circuit (typically a CMOS semiconductor chip such as the CD4066) is closed, causing the capacitor 97 to charge to the level E of the signal f(t) at that instant. When the switch pulse is removed, the capacitor 97 discharges through the resistor 96. The discharge voltage appears at the input of the amplitude comparator 802 (an LM311 chip). Comparator 802, which was turned ON by the charge voltage, remains ON until the discharge falls below the threshold level E . The threshold E is usually selected to be as close to zero as possible so as to achieve a large amplitude dynamic range. The duration of the comparator pulse is given by T = RC logE/E , where RC is the time constant. For maximum dynamic range, Emax/'ET,-, the value of RC is selected so that ' T is less than the period of the switch pulse. Also shown in Figure 8b is a "cleaned" comparator pulse output where the switch pulse is used to cancel out its own contribution to the width of the comparator signal, and to eliminate spurious transients. From there, the com¬ parator pulse as shown in Figure 8b is used to gate fast clock pulses into the data counter 801. The cleaned pulse is also sent to the real zero select logic 804, which detects when the shift clock interval within which the waveform f(t) goes from negative to positive, this clocked zero pulse is illustrated in waveform (f) of Figure 8(b). The gated pulses of waveform (e) of Figure 8b are sent to the data counter 810, which converts the sequence of pulses in each sample into a binary number. Under the sequence of operations determined by the control logic for each sample period, shown in Figure 8(e), these sample num¬ bers representing the logarithm of the waveform's instanta- neous amplitude are subtracted, compared, latched (stored), and cleared. In the subtract operation, the stored two's complement number, B, of the previous sample is added to the "present" number, A, in the binary counter 810. This opera¬ tion is equivalent to a discrete derivative of the logarithm of the waveform f(t), and thus represents the log derivative. Occurring simultaneously with this subtraction operation is the comparison decision which determines whether the present number, A, is greater than or less than the previous number, B. This decision is detected by sensing the condition of the "sign bit" output of subtract circuit 813 of the two's complement difference. If there is a change in the sequence of decisions, it indicates the occurrence of a complex zero in the form of a null or a peak. This peak/null decision is then converted, by circuit 811 to a clocked pulse for analysis in the PSM. Various combinations of real and complex zeros can be selected for experimental situations in signal analy¬ sis. Following the subtract operation, there is a con¬ trol pulse from logic circuit 805 which decrements the coun- ter data of counter 810 by two and inverts it so as to pro¬ duce the two's complement number, which is then latched in latch 812 and cleared from the counter in preparation for the next, sampling interval. Although the subtraction occurs on every sample interval, the result is stored in the latch register on only those samples for which a zero has been detected. This sample represents the instantaneous residue function f(e<)- In a similar manner, the log amplitude information (before two's complement) can be stored at peak complex zeros. These time-coincident samples of amplitude and residue now compose two of the waveform information vectors or "WIVs". (As described earlier, the amplitude samples can be compared to derive a direction-related vector. Note that each sample interval corresponds to the main shift clock interval which controls the delay shift registers of the Periodicity Sorting Matrix 45. Figure 8a shows the lines carrying the timing signals and the func¬ tional blocks associated with the PSM 93. The PSM requires the shift clock timing signal to control its delay shift registers, a readout scan select signal to control the se¬ quence of reading out the detected periodicities, and a means for digitally encoding the periodicity measurements as they are read out of the PSM. The interrogate pulse logic 826 accepts the zeros from the digitial differentiator cir¬ cuit and assures timing for correct input to the PSM shift register. It should also be noted that there is a block which allows selection of any desired combination of the waveform zeros as follows: real peak null real + peak real + null peak + null real + peak + null In the above, the term (+) is defined as a logical OR. The ability to make this selection is desirable in obtaining optimum processing for various types of input signals. For example, at present it appears that the best analysis of human speech would use the real + peak mode. It can be seen from Figure 8a that the binary data of the periodicity measurements is stored in latch 822 so ' that it can be processed according to the methods previously described for the Aural Retina. Figure 8c shows a detailed circuit diagram of an operable LAD circuit 91. This circuit carries the necessary component identification, and carries out the functions of the amplifier 800, switch 801 and comparator 802 described in Figure 8a. The component pin members are also shown. An LM326 precision voltage regulator 803 to supply H;12 volts to the LM387 feedback inverting amplifier 831 is provided. The CD4066 switch 832 is controlled by the positive switch pulse derived from the 2N3904 transistor amplifier 833.- Amplifier 833 is needed to convert the 5 volt TTL logic level to the 15 volt level for proper switching of switch 832. A low pass filter 833 is used to help isolate switching effects from the preamplifier 831. The discharge time constant RC of resistor 96 and capacitor 97 is chosen at 10K ohms and 220 pf to accommodate the desired dynamic range. The output of the switched wave¬ form is isolated from the comparator 802 by using a 2SK43 field effect transistor source follower with high input resistance and low output resistance. The LM311 comparator 802 triggers positive and recovers when the signal falls below the threshold adjusted by the variable resistor 840. Bypass capacitors are used to reduce triggering on stray noise and to stabilize the triggering action. The SN7408 gate is used to buffer the comparator from the various sub- sequent load functions. The feedback input amplifier 831 contains an offset voltage balance adjustment. Also, there are 7.5 volt zener diode regulators in the volt supply "rails". This is needed to reduce the total voltage supply to the CD4066 to within the manufacturers' 15 volt limit. Returning to Figure 8a, there is next described the logic which is used to generate the timing signals needed to drive the PSM 93 and the digital differentiator 92. This circuitry is given in detail in Figure 8d, and the waveforms seen at various points in the timing sequence are shown in Figure 8e. The master clock 90 is an oscillator using an SN74LS04 hex inverter with capability for a 2:1 frequency adjustment at 2 MHz. The output is labeled "Fast Clock" and is used directly in subsequent logic. From here, the clock rate is divided by two in successive steps labeled A, B, C, D and E, in Figure 8e. The waveforms, are obtained from the two SN7493 integrated circuits M_ and M_. At point "E" the waveform is again divided by two in two channels so as to obtain a two-phase clock. The E clock is thus inverted before driving divide circuits Mb(A), from which the main PSM shift clock is derived. The uninverted E clock is divided by M Λ (B). This set of waveforms now allows forma- 6 tion of some required control signals. The LAD switching pulse is derived by AND gates M and M... (pins 8, 9, 10), which perform AND on waveforms B, C, D, E and G of Figure 8e. The inverted output is shown in curve (i) of Figure 8e. The scan pulse gate J of Figure 8e is derived from M (pins 4, 5, 6), which performs AND on waveform H and the shift clock. The J signal then performs AND on the A clock signal such that 24 pulses occur per each shift clock interval through AND gate M (pins 11, 12, 13), as in Figure 8(a). The cleaning pulse is generated by the D flip-flip M and AND gate M (pins 8, 9, 10) of Figure 8d. The pur¬ pose of this circuit is to widen the switch pulse slightly so that undesired switching transient effects can be removed from the comparator output. The D flip-flop provides one delayed fast clock pulse that is combined with the switch pulse to give the waveform shown in curve (p) of Figure 8e. The readout scan clock must next be switched into discrete channels to provide a sequential readout shift clock to be used in the PSM 45. This is accomplished by the counter M which generates a 3-bit sequential binary code. This code is demultiplexed by M g (74138) so as to produce a pulse with a duration of one shift clock interval which cycles over the eight octave channels. This switch gate thus selects the OMPI ^ \ 33 proper PSM channel to receive the readout scan clock pulses using the inverters M and M 1 > and AND gates M 1 _ and M-... This sequence is illustrated in curves (q) and (r) of Figure - 8e. The selected readout scan clocks for octaves 8 and 7 are chosen to illustrate the beginning of the eight-octave scan cycle which proceeds from 8, 7, 6...2, 1; then recycles to 8, etc. This allows the periodicity data to be scanned in order, from the lowest to highest frequencies. Digital encoding of the recognized periodicity sample is provided by the binary counter M and M 1T . This counter accumulates the number of readout scan pulses for each eight-octave scan cycle. When a periodicity recognition pulse occurs, as il¬ lustrated in curve (s) of Figure 8e, the serial data pulse corresponding to the recognition channel gates out the bi- nary number into an eight-bit parallel bus. The example of Figure 8e shows a periodicity recognition at channel 36 with the corresponding binary number in curve (t) of Figure 8e. It should be noted that this method of data read¬ out was chosen for certain practical system considerations. Several alternative methods can be devised, as will be ap¬ parent to skilled binary logic designers. As shown in Figure 8a, the control signals for the digital differentiator section 92 are also derived from the timing logic circuit 95. This control logic is detailed in the circuit diagram of Figure 8f. The control signals in Figure 8f are formed through the logical sequences produced by AND gates contained in U n , M_, M_ and by the inverters of 2 5 7 M . They are three successive pulse signals, shown in curves (j)» (k) and (1) of Figure 8e and designated Subtract, Com- plement and Latch/Clear. The gated clock pulses (see curve (e) in Figure 8b), which are produced by the AND gates M (11, 12, 13) and M (8, 9, 10), are fed to the eight-bit up-down counter M^ and M . The total count is always reached prior to the end of the control pulse timing cycle. During the counting cycle OMPI the counter outputs are passed through the exclusive OR gates M and M.. to the eight-bit binary adders M, g and M g These adders are also connected to the eight-bi t latches M 10 and M„, which contain the two's complement result of the previous count cycle. Thus, the eight-bit output of the adders presents the continuous difference o -the counting cycle with the- previous frame count. At the end of the count cycle the difference remains static. The control pulse sequence proceeds frm this point. The first control pulse is the "Subtract" pulse, which trans¬ fers the frame difference into the storage latched M„ and 6 M . The subtract pulse also clocks the J-K flip-flop and causes its state to change, depending on the presence or absence of a sign bit in the latch M.. . This decision de- termines whether the present count A is greater than or less than the previous count B. Using this data, the two dual D-type flip-flops and AND gates produce pulses corresponding to the complex zeros of the signal waveform, as will be described later. The second control pulse, the "Complement", has two effects: it decrements the up-down counter by one bit, and it then causes the exclusive OR gates to invert, or comple¬ ment, the binary number from the counter. This is the two's complement number which the Latch pulse (the third in the sequence) causes to be stored in the latches M and of Figure 8f. The latch pulse also activates a one-shot multi¬ vibrator M which produces a very short pulse of about 125 nanoseconds in width. This pulse, being slightly delayed, then clears the counters in readiness for the next counting cycle. The purpose of the delay is to assure that the num¬ ber is stored before it is cleared. The real zero instant is selected by using the cleaning pulse 5(p) to clock the D-flip-flop pair M with JL the LAD comparator output feeding the D input. This circuit selects only the positive transitions of the signal envelope 35 as it crosses-the real zero axis. Its duration is only one shift clock interval. An illustration of the zero selection process derived from the waveform samples is shown in Figure 8b. In this timing diagram are seen the comparator pulse. (c), the cleaned comparator pulse (d) and the gated fast clock pulses used to encode the data (e). As the waveform f(t) crosses the zero axis, the LAD comparator is triggered and remains H (High) until the waveform falls below zero. This zero crossing thus produces a pulse having a width of one shift clock period (f). As the waveform increases in amplitude, the decision A > B continues H until sample pulse #4. Since the comparator width (digital amplitude) of #4 is less than #3, the sign bit decision A < B goes H, causing a transition in the J-K flip-flop. The illustration in Figure 8b shows the resulting pulse in waveform (g) , which identi ies the peak of waveform f(t). Note that the decision is necessarily delayed by two shift clock intervals, but this is a constant which is accounted for in subsequent processing. Note that the null mode, which detects " the transi¬ tion to A > B will occur at both the real positive zero and at any null in the waveform. Thus, if only the null zero is desired in subsequent processing, it will be necessary to combine the separate real zero detection with the real zero portion of the null mode detection such that the real zero is cancelled. The periodicity sorting matrix 45 of the preceding description is the circuit which recognizes and sorts all periodic elements of the signal ensemble simultaneously. The signal ensemble which is applied to the periodicity sorting matrix can in general consist of various mixtures of random or periodic excitation of overdamped and underdamped wavelets. When considering the category of periodic signals, there are two basic situations: 36 (1) Two or more interleaved unsynchronized pulse trains of which at least one is periodic (wavelets are over¬ damped) ; or (2) A periodic excitation with oscillatory response functions (wavelets are underdamped). These two signal conditions are shown in Figures 9A and 9B, respectively. Figure 9A shows two interleaved pulse trains having the periods T and T_, respectively. Figure 9B shows a waveform which is typical, for example, of voiced speech where the repetition rate defines the voice pitch. The ringing wavelet responses are known as formants. The essential problem of measuring the individual repetition periods of the waveforms of Figures 9A and 9B can be seen from the Figures. It is apparent that no method which is based solely on measuring successive time intervals of zero crossings or peaks could succeed at sorting interleaved signal sources. However, in accordance with the present invention, a novel periodicity sorting matrix, schematically illustrated in Figure 11, is provided which accomplishes this function. The arrangement shown in Figure 11 is based on the continuous analysis of a signal for its periodic components as it propagates through a tapped delay line. An array of logic gates is connected in such a way that whenever a sig¬ nal pulse arrives at the input, there is a simultaneous com¬ parison with all previous pulses in the delay line. This occurs in such a way that the event of two equal time spacings can be recognized. This event is defined here as a periodi¬ city. Periodicities do not have to occur in a contiguous sequence as do pulses in a pulse train. For example, a series of randomly spaced pulses will occasionally produce three pulses having equal intervals. In the purely random series, these false periodicity detections would be distri¬ buted over the range of recognition gates with equal proba¬ bility. The statistical frequency of the false recognition 37 would depend on the pulse density of the ensemble. When the distribution is not completely random, but is, centered near a particular repetition rate, as in a "jittered" pulse train, the number of responses is largest at the gate corresponding to the average pulse repetition frequency surrounded by a- Gaussian-type distribution of responses. The spread of this distribution will depend on the sigπal-to-noise ratio. Figure 11 shows schematically the topological rela¬ tionship of an array of AND gates and a delay shift register. Figure 11 is a "logic map" of the circuit arrangement. The - illustrative circuit of Figure 11 contains twelve AND gates each schematically illustrated by a respective one of hori¬ zontal lines 100-111. Each of the AND gates 100-111 is connected to the schematically illustrated -tapped shift register delay line 112 which has 25 positions. The gates 100-111 are connected to the various positions of the shift register at the points represented by diagonal slashes along the length of the horizontal lines representing the gates 100-111. The signal coming into the shift register 112 is the signal derived, for example, from an output- of the zero select logic 811 of the digital residue processor of Figure 8a. This signal is connected to a log A-D converter 113, digital differentiator 114 and zero select logic 811. Thus, the input signal which might have the form shown in Figure 10A will be converted to the signal shown in Figure 10B. Note in Figure 10B the interleaved pulses of pulse train A and of pulse train B are labeled separately as A and B , n n' respectively. A shift clock 113 timing diagram is schematically illustrated at the lower portion of Figure 11 with a matrix which schematically illustrates the manner in which pulses A and B enter the shift register and then propagate down the shift register delay line 112. The AND gate connections shown in Figure 11 are arranged sequentially and respond to OMPI any periodic event which occurs within a 2:1 range. Alter¬ nating pairs of connections of the center tap of each peri¬ odicity gate 100-111 are needed to assure recognition of all possible combinations of intervals between the sequential pulse pairs. These combinations are a result of the 24 discrete clock time intervals of the shift register delay line 112. For convenience in describing the system, the time scale of the signal is shown quantized into the same 24 units as those of the tapped shift register delay line. The two pulse trains A and B shown in Figure 10B are also shown timed to the same scale as that of the shift clock 113 and have periods of 6 and 10 time units, respec¬ tively. When the first pulse of wave train A, labeled pulse A , enters the delay line 112, there are no other pulses, so there is no recognition. Similarly, when pulses B.. , B and A enter sequentially, there is no recognition of any peri¬ odicity and they continue through the system. When pulse B arrives at time unit 15, however, pulses B„ at time unit 8 and B at time unit 1 are in the system and three simulta¬ neous pulses are produced, thereby producing a recognition response for pulse train B having a period of seven time units. In a similar manner, when pulse A arrives, there will be another recognition from the ten unit gate. With subsequent operation, each pulse train is continuously de- interleaved in the discrete channels of periodicity recog¬ nition register 115. In the circuit of Figure 11, it is extremely impor¬ tant to use the 2:1 relationship of submultiples in order to provide a logical inhibit function to prevent false response of the system. Thus, it is necessary to eliminate false responses at submultiples of the true periodicity under the assumption that it is desirable to recognize periodicities over a range greater than one octave. The key to removing these false responses is the 2:1 relationship referred to above. 39 NOT TO BE TAKEN INTO CONSIDERATION FOR THE PURPOSES OF INTERNATIONAL PROCESSING (See Section 309(c) (iii) of the Administrative Instructions) OMH WIPQ intersections marked by diagonal hatch lines. The first AND gate lines represent and are labeled the "1st octave" of sig¬ nal pulses; the 2nd octave of AND gate lines are connected and labeled as shown; and the 3rd octave which are the lower eight AND gates are also labeled. A periodicity recognition register 121 corresponding to the periodicity recognition register 115 of Figure 11 is connected to the outputs of the twenty-four AND gates. The dispersive delay line 120 of Figure 12 has a non-uniform delay characteristic wherein the relative delays at each step are indicated by the spacing of the taps. The time between units 0 to 16, which have the highest time reso¬ lution, corresponds to the time quantization of the highest expected periodicity of the signal. In units 18-32 the relative delay is two time units; in the delay units 36-64 it is four time units. The octave relationship of the gates is contiguous so that there is a continuous periodicity re¬ cognition capability over a three octave periodicity range. The submultiple inhibit function referred to previ¬ ously is accomplished by feeding back the output of each gate to the delay line increment in which the recognition occurs. This feedback is labeled "Recognition Inhibit Sig¬ nals" in Figure 12. Thus, the propagation of a submultiple signal pulse is terminated before it enters the lower perio¬ dicity recognition octaves. It was previously noted that in the arrangement of Figure 12, the distance between delay line taps is propor¬ tional to the delay time. Thus, designing a suitable system for the necessary seven or eight octaves of an acoustic signal environment, in a practical situation, requires means for reducing the physical distance along the delay line per delay unit as the delay increases. An arrangement for re¬ ducing this spacing is shown in the digital circuit diagram of Figure 13 which carries out the functions previously described in the logic maps of Figures 11 and 12. Figure 13 shows how the logic map of Figure 12 can. be translated into conventional circuit design. This dia¬ gram presents all the essential features of an operable system and, except for the base module octave, are identical in construction. Each octave is provided with respective storage shift registers 140, 141 and 142 for octaves 1, 2 and 3, respectively. Only four elements of the shift regis¬ ters, rather than eight elements, as shown in Figure 12, are shown in Figure 13 for purposes of simplicity. Of course, any number of elements can be used, depending on the desired resolution. The storage shift registers 140, 141 and 142 func¬ tion as the register 121 of Figure 12 and produce an output in response to the detection of a periodicity "hit". This output could take any desired form, such as an electronic output control signal produced during the serial readout of all contents of the register. The output can also take the form of an LED output for each location within the storage shift registers. Each element of each storage shift register is provided with a three-input AND gate shown as the AND gates 150-161 which have their outputs connected to the A, B, C and D inputs of the storage shift registers 140, 141 and 142 in the manner shown. The clocked pulse signal input such as the input signal of Figure 10B is then applied to a clocked shift register having ' sections 170 and 171 in the first oc¬ tave and sections 172 and 173 in octaves 2 and 3, respectively. Similar clocked shift register sections will be provided for each of the other octaves. Thus, as many octaves as desired can be employed in order to cover as large a frequency range as is desired for the signal analysis function. The shift register elements are clocked by a clock 180 which runs at the same rate as is used to clock the signal pulse train. (This circuit is referred to as the Data Shift Clock in Figure 8a). The delay time for each OMPI successive octave is increased by a factor of 2 by dividing the clock rate of clock 180 by 2 for each successive octave. Thus, 2:1 divide circuits 181, 182 and so on are provided to reduce the clock rate input by 2 to each successive shift register 172, 173 and so on. In order to ensure transfer of data between octave delay lines, an extra shift register element, denoted T is inserted in each octave delay line 171, 172 and 173 to take care of the quantized time position of the period of the pulse pairs, which occurs when the analog periodic signal is sampled by the shift clock. The signal from the T element of each clock shift x register is connected to transfer OR gates 190, 191 and 192, respectively, in octaves 1, 2 and 3, respectively. The other input to the OR gates 190, 191 and 192 is the signal from the previous delay element To 0 , T1..-_s and Tl... for OR gates 190, 191 and 192, respectively, so that the signal pulse can always be transferred to the input element of the next shift register of the next octave. The first input for each of the AND gates 150-153 is an input from a T position of the clock shift register 170. A second inut to AND gates 150-153 is taken from clock shift register positions T T , T_ and T 0 , respectively. 5 6 7 8 Similarly, the second input of AND gate 154-157 is taken from shift register positions T τ ιπ» τ , a ^d T of clock shift register 172. The second input to AND gates 158-161 is taken from positions T. , T , T._ and T,_ of register 173. The third 13 14 15 16 input for gates 154-161 consists of the output of OR gates 200-207, respectively. The third input of AND gates 150-153 is shown as the output of OR gate 210, the T or T output of shift register 171, the output of OR gate 211 and the output of position T or T of shift register 171, respec¬ tively. *gU E ^ OMPI ^ IPO * The arrangement described above will produce a periodicity output in one of the storage shift register positions for storage shift registers 140, 141 and 142 in the manner shown by the diagonal slashes previously dis¬ cussed in Figures 11 and 12. Because of the discrete nature of the periodicity sampling, an interrogation gate 220 is provided to double the width of the interrogation pulse in all octaves below the base module. Thus, the first input to each of AND gates 10 154-161 consists of the output of OR gate 220, the inputs of which are connected to clock shift register positions T and T , respectively. Figure 13 shows the digital circuit means by which detected periodicities can be stored and transferred to a I 5 subsequent display and/or automatic processing stage. Thus, the outputs of the recognition gates 150-161 are sent to the preset inputs of the storage shift registers 140, 141 and 142. The storage shift register records the event of a periodicity in its storage element, after which the inhibit 20 function described in connection with Figure 12 operates to remove the pulse from its associated delay shift register element. Thus, in Figure 13, each of clock shift registers T , T 6 , T ? , T g of 171, and each of the registers of 172 and 173 receives a clear inhibit connection from the output of 25 AND gate 150-161, respectively. For an example of the operation of the circuit of Figure 13, assume that a periodicity triplet exists in regis¬ ter locations T_. T_ and T_. The event is recorded in regis- U O o ter D . The pulse in T is then cleared by the inhibit pulse 30 wwhhiicclh appears at the T clear input of the shift register 171. Each storage shift register 140, 141 and 142 is provided with an extra delay element labeled X. This addi¬ tional element is used to store data which is to be shifted 35 into the next register if a serial readout of the data is desired. As stated previously, the data stored at each storage register can also be observed directly by connecting each storage element to a light emitting diode. Alternately or simultaneously, data can be transferred out in serial form by standard shift register methods. If desired, the data in the storage shift registers can be decoded in binary numeric form to identify directly the recorded element. Any other form of data readout can be selected as desired by the designer of a system. Periodicity sorting matrices per se are known but are substantially more complex than the novel arrangement shown in Figure 13. A known configuration is described in my publication entitled "PRF Signal Analyzer" , IBM Technical Disclosure Bulletin, Volume 10, No. 11, April, 1968, p. 1781. That system employs a different form of octave submultiple inhibit and is inferior in performance and is more complex than the system of Figure 13 and requires many more delay elements and logic components. This is especially true when the periodicity sorting system requires more than three or four octaves. A significant feature of the circuit of Figure 13 is that it can use as man octaves as are desired, with the number limited only by the time response speed of the logic element. Thus, circuits employing eight octaves have been successfully operated and with resolution of 24 increments. The periodicity sorting matrix of Figure 13 could be carried out in a variety of circuit techniques. Thus, the delay function can be performed by devices such as analog tapped delay lines, cascaded one-shot multivibrators, charge- coupled delay integrated circuits, digital shift registers and surface acoustic wave devices. However, for signal pro¬ cessing in lower frequency ranges, as employed in seismic systems and normal audio/acoustic frequency ranges, the digi¬ tal shift register arrangement of Figure 13 is the preferred circuit arrangement. OMPI The general features of a system using analog or quasi-analog methods which can employ charge. coupled delay devices or surface acoustic wave devices is schematically illustrated in Figure 14 which shows, a circuit for carrying out the first and second analysis intervals of Figures 5 and 6. While the function of the circuit of Figure 14 can be carried out by an all digital processing system, the system is simplified by employing an analog or quasi-analog system to provide the information needed for the Aural Retina cir- cuit. More specifically, as shown in Figure 14, the signal f(t) to be analyzed is applied to a suitable delay line such as the dispersive delay line 200 which has n taps T -T . This produces a discrete sampled waveform of f(t) along the length of the delay line which has an increasing delay per unit length. Each tap of delay line 200 is connected to a respective circuit such as one of circuits 201-204 which converts the stored function f(t) to log f(t) in a known manner. The output signal log f(t) for the function in each of the taps is then connected to a suitable subtraction cir- cuit 205 which is arranged to subtract the output of each log converted delay tap value from the value of the preceding delay tap. This produces a discrete derivative of log f(t) which is the function r(t) = d[log f(t)]/dt which is the "residue" previously described. The residue function r(t) is then applied to respec¬ tive threshold detectors .206 provided for each delay cell which operate to determine the epoch of selected waveform features such as peaks or zeros. At the instants correspond¬ ing to those features, the values of r(t) or residue are gated into the Aural Retina circuit 207 via the residue gates 208. Simultaneously, the outputs of threshold detectors 206 are applied to the periodicity sorting matrix 209 which may be identical to the circuit of Figure 13. The output of PSM 209 is also applied to the input of the Aural Retina circuit 207. The Aural Retina circuit 207 then has inputs dealing with periodicity of the waveforms, residue and ampli¬ tude so that it now has the information needed to produce the necessary waveform recognition patterns. • Note that the general arrangement shown in Figure 14 can be carried out with charge-coupled delay or surface acoustic wave device technology. There are significant advantages in the arrange¬ ment of Figure 14 because the arrangement eliminates the need for intermediate storage, addressing, averaging and parameter association logic which are needed in an all digi¬ tal configuration. There is next considered the manner in. which the outer product matrix 68 of Figure 6 can be implemented in- order to carry out the third processing interval described in Figure 5 in which the WIVs are assembled in a vector space in which the signal patterns can be recognized. One method by which this can be accomplished is disclosed in my United States Patent 3,886,553, entitled "Coordinate Locating Method and System", issued May 27, 1975. The method disclosed in that patent is intended primarily for locating emitters in geographic coordinates by recognizing the time difference patterns of received radiation. However, the circuits can be used for any arbitrary coordinate system. The following describes a novel method and circuit for identifying waveform patterns using the two-dimensional space of residue «< versus periodicity "£. In general, the waveform information vectors which comprise a four-dimen¬ sional space made up of residue, periodicity, direction and amplitude can also be used. In the novel arrangement of the invention, the residue data which is derived from the peak-sample log deri¬ vative output of register 98 of Figure 8 is first converted to a time difference analog. The periodicity readout of the periodicity sorting matrix of Figure 13 is also converted to a time difference analog by means of the serial readout mode v/ι?o described in connection with Figure 13. Periodicity and residue then form the coordinates of a rectangular Aural Retina existence space, as was described in Figure 2. This plane can be segmented into an array of rectangles bounded by reference points, as illustrated in Figure 15. The reference points in Figure * 15 are designated by the numerals 00-03; 10-13; 20-23; and 30-33. Each of these reference points can be represented as points in time as a function of the continuous time variables o and T. Each point, therefore, defines a unique relative time delay pat¬ tern. By arranging a means to recognize the time delay pattern between the two input variables θ( and T, it is pos¬ sible to locate corresponding points in the existence dia¬ gram. Since each point or set of points represents a wave form shape, the ability to locate these points is equivalent to identifying the signal. Figure 16 shows a circuit in block diagram form which is designed to accomplish the above function and con¬ stitutes the outer product matrix circuit 68 of Figure 6. The circuit of Figure 16 attends to the outer product mani¬ pulation of the WIVs which have been measured in the wave form. In Figure 16, the two time-difference encoded para¬ meters for periodicity P and residue « are fed to respec¬ tive shift register tapped delay lines 300 and 301. A third identical register 302 is also provided. Each of registers 300-302 consists of conventional flip-flops. Registers 300 and 301 have four taps each labeled 3, 2, 1 and 0, respec¬ tively. Each of these taps is connected to a respective AND gate each of which is schematically illustrated by one of the horizontal lines which are numbered 01 to 33. Each of these AND gates corresponds to a position in the existence diagram of Figure 15. Each of the gates has three inputs, with the third input coming from the last tap of delay line 302 shown as the line 304 in Figure 16. OMPI A reference delay circuit is also provided in Fig¬ ure 16 to allow for recognition of all points in a plane. For each delay line, there is provided clocked countdown systems 305, 306 and 307 which allow the input time delay pulse to be shifted through each delay line with higher resolution than is given by the relatively coarse division of the discrete delay line taps for delay lines 300-302. This countdown method allows a fine-grain interpolation of the pattern location by comparing the relative values of responses of adjacent reference points as is disclosed in my previously referred to Patent 3,886,553. The operation of the circuit of Figure 16 is as follows At any instant, a signal's location in the plane of Figure 15 corresponds to a particular AND gate 01 to 33 which is activated by the outputs of three coincident delay line taps. Only one gate can be activated at a time and then produces an output pulse. The array of- gates is then connected to a conventional logical priority encoder 310a which converts the position of the activated gate into a binary code number at lines A A , A and A . This number exists for the duration of the gate pulse. The encoded recognition pulse then addresses a random access memory 310. For each recognition event a count will be added to the memory at the location specified by the gate address. After each readout scan, the random access memory 310 is cleared and the cycle begins again. The scan recognition cycle thus retains epoch information for all events within the resolution of the period of the highest-frequency signal. Two functions that can be accomplished in processing the contents of the random access memory 310 are: (1) scanning out the composite Aural Retina exis¬ tence plane for examination of its contents which constitutes a "learning" process, and (2) performing automatic recognition of preselected patterns as a result of the examination of the memory contents. OMPI / ?Λ.- 49 The readout of memory 310 is controlled through a suitable microprocessor 311 which sequentially addresses all elements of the memory 310. The accumulated count at each address can then be compared with adjacent reference points and, by means of a suitable interpolation algorithm such as that described in my aforementioned patent 3,886,553, the pattern point can be computed to the resolution allowed by the original time measurement. These high resolution points then compose the pattern of the existence diagram as repre- sented in a single periodicity sorting matrix octave readout scan cycle. By accumulating in an adder these interpolated patterns in the microprocessor memory over a suitable inte¬ gration period, a complete snapshot or picture of the Aural Retina signal pattern is obtained. That is, the adder adds each new recognition event from the 0PM to the number of hits already stored in the RAM. It then creates a "histogram" of pattern responses in the storage interval. After each such interval, the accumulated patterns may be read out into a display or into temporary storage for subsequent analysis in the fourth processing interval which tests for variable patterns, as was described in connection with Figure 5. The readout scan conversion process can be used for identifying patterns which correspond to specific signal waveforms and their individual source objects. It is, in effect, a learning process. By testing and recognizing the pattern coordinates produced by various signal source ob¬ jects, a set of "templates" can be created to test for the presence of desired incoming signal patterns. A template of this kind is shown in Figure 16 as the block 320. The tem- plate will in fact consist, for example, of a read only memory encoded in a sequence of addresses corresponding to preselected waveforms. In order to test for a specific pattern, the addresses of the templates or read only memory 320 are applied to the random access memory address bus in 50 the readout mode after each periodicity sorting matrix read¬ out octave scan cycle. If the tested pattern is present in the random access memory 310, the test will produce an event which may be recorded in a suitable recognition response counter 321. After a predetermined number of recorded events in a particular template test pattern, a threshold comparator 322 can be activated to indicate the presence of the source object in the signal ensemble. This information may then be used to activate further analysis systems or control devices. Figure 17 shows an alternate circuit to that of Figure 16 for the Aural Retina processing and automatic - signal recognition which does not require the random access memory 310. Referring to Figure 17, there is schematically illustrated the shift register delay lines 305, 306 and 307 of Figure 16 and there is also shown the AND gates 00 to 33. Each of the time reference inputs from register 307 is pro¬ vided wi h pattern select switches 350 which can be alter¬ nately opened or closed, as desired, either manually or remotely, in order to preselect one or more patterns which can be recognized. The output of gates 00 to 33 is then connected to a suitable response summing circuit 351 which, in turn, operates a counter 352 to accumulate the number of responses, and the threshold circuit 353. Circuit 353 will then produce an appropriate recognition signal when the desired signal is present, as selected by switches 350 in an ensemble of mixed input signals. That is, a valid signal recognition signal will be produced only when a predeter¬ mined number of responses has occurred. There have be n described methods of scan conver¬ sion and pattern recognition in two dimensions, as shown in Figure 15. The same methods can be applied to the recogni¬ tion of signal source objects in the four-dimensional WIV space, as described by the generalized system of Figure 5. This is accomplished by expanding the outer product matrix of Figure 16 into four dimensions through the use of two 51 additional tapped delay shift registers containing the am¬ plitude and direction input data in time encoded form. Additional recognition AND gates will be required for the process, as specified by the product of the number of dis¬ crete elements in each vector. The number of gates can thus become impractically large for satisfactory pattern discri¬ mination. However, an interpolation process such as that described in my prior U.S. patent 3,886,553, can be employed to improve resolution by about 100:1 while using relatively few gates. In this way, the four-dimensional periodicity sorting matrix can be implemented economically. The outer product function described previously can be performed using microprocessor methods. However, due to the large number of multiplications and comparisons on the array of reference points that must be performed at each clock data interval, the computer processing approach be¬ comes difficult and requires substantial computing speed and power. The scan conversion processor and the waveform recognizing system allow identification and location of the set of source objects in the signal environment as has been described in connection with Figure 16. They, therefore, comprise the means for achieving the objectives of the third analysis interval of Figure 5. In terms of information con- tent, the data rate has been compressed. With this lower data rate, the use of conventional microprocessing methods becomes appropriate, so that the requirements of the remain¬ ing processing intervals for determining pattern changes and their meanings can best be accomplished by computer algorithms It will be noted that the concepts of the present invention are generally valid to any signal processing ar¬ rangement regardless of frequency range. The only limita¬ tions on the circuitry are derived from response speeds of the individual devices used. While acoustic processes have been emphasized for application of the invention, it will be 52 apparent tha -the invention is applicable to higher frequency applications than those in the acoustic range. There is next described in Figure 18 a novel process and circuit for detecting epoch or onset of a timed series of events. Thus, in Figure 18, the signal pulse train input is applied to a suitable tapped delay register 400. The taps of register 400 are connected to three input AND gates which are each represented by a horizontal line leading to taps A through H of recognition register 401. The outputs of the recognition register 401 are then connected to a NOR gate 402 and the output of NOR gate 402 is connected to one input of AND gate 403. The other input of gate 403 is taken from the 0 delay element of delay register 400. The operation of the system of Figure 18 is as follows: The criterion for epoch is the event of the pre¬ sence of an interrogate pulse in the 0 element of delay register 400 without a corresponding periodicity recognition. The NOR gate 402 produces a low output whenever a periodicity recognition is recorded in the recognition register 401. At the same time, the event of a periodicity recognition requires that a pulse logic level H must exist in the 0 delay tap of register 400. However, an epoch is defined as the event of no recognition when an interrogation pulse or the output pulse of tap 0 occurs. This event can occur either when an aperiodic pulse is received or during the first two pulses of a periodic sequence. The logic events from the AND gate 403 are tabulated as follows: Delay NOR Gate Epoch Gate 1 402 4 L L L Not Possible L H L No Signal H L L Periodicity Recognitio H H H Epoch Detection The above table shows that epoch is identified by the logic H when an unrecognized interrogation exists. Note that an epoch detection event is coincident with the arrival time of each pulse, regardless of the length of delay required for detection of its associated periodicity. The epoch detection method described in relation to Figure 18 is extended to include a multi-octave system in Figure 18a. Referring to Figure 18a, the clocked pulse train input is applied to each of n octave circuits schema¬ tically shown as three circuits 410, 421 and 422. Each octave 420, 421 and 422 has an OR gate 423, 424 and 425, respectively, instead of the NOR gate 402 of Figure 18. OR gates 422, 423 and 424 each operate to detect periodicity within its range. A multiple input NOR gate 426 is attached to all of the octave OR gates 423 to 425. When a signal appears in delay circuit 427, but when no periodi¬ city recognition is detected in any of the octaves, then the Gloal Epoch Gate assumes a logic H. This indicates an epoch event as previously described for the single octave of Figure 18. From this point, the use of the epoch information obtained in Figure IB determines how it must be processed. The epoch data can be separated into two groups: (1) onsets of periodic sequences specified by pulse pairs; (2) arrivals of random events specified by single pulses. Although the above might seem to offer a fairly obvious distinction, the mere presence of two epoch pulses does not necessarily indicate which type of event has oc¬ curred (one periodic onset or two random events). This can be resolved by arranging the means for associating the epoch pulses with the periodic recognition data. Thus, if any pulse pair is associated with a subsequent periodicity mea¬ surement, the epoch event must be an onset; if not, then it OMPI & is random. For example, the onset epoch will always be followed, by a sequence of periodic pulses (at least one) having periodicity equal to the spacing of the pulse pair. The specific logic needed to. implement this arrangement will be apparent to those skilled in the art. As previously described, the novel process of the invention can be employed for waveform synthesization, as well as for waveform processing and detection. It is pos¬ sible to synthesize the function f(t) of Equation (1) once the Ak, , sk. and "T- " k, parameters are g°iven. In terms of the Aural Retina, s is defined loosely by β( as a function of residue, and by Ε as a function of the periodicity of the ringing frequency if o< is less than critical damping. Thus, by supplying residue and amplitude at each zero, defined by epoch * U. , it is possible to synthesize an approximation of any proposed waveform. Basically then, synthesis is equi¬ valent to defining the responses of the set of hypothetical source objects which creates the complex waveform. Spatial information is carried in the differences of Ak. and t*k which are inherent in physical locations of sources relative to the position of the receiver or source. This would then allow synthesis, for example, of stereophonic sound. As in the Aural Retina signal analyzer, however, the synthesizer method is applicable to synthesis of random excitation sig- nals, as well as periodic signals. In synthesizing a signal, the structure of the sig¬ nal must first be known and this can be provided by a suit¬ able composer program or the like. The program will specify the desired placement of zeros in time (epoch, periodicity and duration), along with residue, amplitude and direction (the WIV) at each zero. In the case of voice response sys¬ tems, for example, where a computer produces speech infor¬ mation, the synthesizer program would contain the WIV and zero pattern data representing a specified speech vocabulary. In the band width - compressed speech system known as the 55 "vocoder", the composer program would be specified by the encoded speech data which has been transmitted through a communications channel. Another application for the syn¬ thesizer might be to reproduce music, voice or facsimile data which has been stored in a computer data storage device which could be transportable. To carry out the synthesis operation, there is provided a synthesis matrix which contains the means to place waveform zeros, both real and complex, periodic or aperiodic, in a desired sequence according to the defined epochs and durations of the postulated source objects. Further, as each zero is placed in sequence, it is modulated by the WIV Information (residue, amplitude and direction) which is associated with the source object, as is determined by the composer program. It should also be noted that the degree of waveform fidelity can be controlled by regulating the resolution of the residue, amplitude and time periodicity components. For example, by eliminating the residue and amplitude vectors, a representation of clipped speech can be generated for those communication applications where only intelligibility is important. Following the synthesis matrix function, an appropriate spectrum shaping filter can be used to reduce the effects of sampling and non-linear processing. A block diagram of a novel waveform synthesizer made in accordance with the above features of the present invention is shown in Figure 19. The object of the system of Figure 19 is to reverse the Aural Retina operation previ¬ ously described. Thus, the periodicities are locations in time produced by the zero placement matrix 500 of Figure 19 which physically is the reverse of the periodicity sorting matrix previously described. As shown in Figure 19, zeros are produced in the block 502 under the influence of the composer program 501, and are applied to the zero placement matrix 500 in terms of epoch, periodicity and duration. The zero placement matrix 56 500 converts ^ information on epoch, periodicity and duration into a suitable set of pulses representing the zeros which define the zero crossings, peaks and nulls of the waveform. The residue vector of composer program 501 is applied to the residue processing block 503 and the residue vector informa¬ tion generated in block 503 is applied to the residue modu¬ lator 504. Residue modulator 504 and its subsequent functions 505 to 510 perform the necessary operations for synthesis at each zero, including: a) integration to obtain log f(t); b) taking its anti-log to produce f(t); and c) multiplying f(t) by A to obtain appropriate amplitude at each complex zero and to define the real zeros, where A=0. As each pulse exits from the zero pulse placement matrix 500, the pulse output of modulator 504 is "modulated" in width by the residue function in modulator ' 504. The wave form output of modulator 504 then is a square wave approxi¬ mation of the waveform f(t) which is desired to be produced. The square wave approximation output of modulator 504 is then appropriately divided into two or more channels which allow the insertion of amplitude and time delay infor¬ mation containing, for example, stereophonic information about the source objects. Thus, the signals, after division, are applied to integrators 505 and 506. They are, there¬ after, passed through anti-log circuits 507 and 508, respec¬ tively, to perform the inverse log derivative operation previously described. The output of each of circuits 507 and 508 is then modulated in amplitude by modulators 509 and 510, respectively so that: (1) relative amplitudes A of source object expon- entials are according to the waveform requirements, and (2) relative differences in amplitude between chan- nels are according to the required acoustic propagation laws. OMPI • Amplitude modulation circuits 509 and 510 are con¬ trolled by relative amplitude outputs of direction monitor¬ ing circuit 511 which is controlled by the composer program 501. .Direction circuit 511 also has time delay outputs for both signal channels, labeled right and left channels, which are applied to time delay circuits 512 and 513, respectively. This provides the necessary time delays required by acoustic propagation of the signal. The outputs of time delay cir¬ cuits 512 and 513 are then applied to appropriate filters 514 and 515, respectively, which are essentially band pass filters which remove d.c. components and high frequency sampling components. The outputs of these two filters then define the left waveform and right waveform of the synthe¬ sized signals. The absolute amplitude of the signals can be appropriately controlled in the absolute amplitude control block 517 which is connected, as shown, to direction circuit 511. It will be apparent that many variations are avail¬ able of the system shown in Figure 19. For example, if only positive or negative zeros are used, the waveform becomes a rectified signal. In many cases, the distortion produced might be tolerable. Also, the stereophonic effect disclosed in Figure 19 is often unnecessary. Figures 20 and 21 schematically illustrate a zero placement matrix circuit which could be used as circuit 500 in Figure 19. An examination of Figures 20 and 21 shows the similarity between the zero placement matrix and the pulse sorting matrix previously described in connection with Fig¬ ure 13. However, in the zero placement matrix of Figure 20, each periodicity combination for each quantized pitch fre¬ quency is represented by a separate line instead of using OR gates as in the periodicity sorting matrix of Figure 13. This allows the programmer or composer to select pitches which are intermediate between the quantized increments. ^ * Z o Referring to Figure 20, there is shown an example of a zero placement matrix which can produce six discrete periodicities or pitches per octave. In Figure 20, each of the horizontal lines, represents an inverse of the AND gates used in the PSM. Each of the inverse AND gates, has three outputs which are connected to the "preset" input of selected shift registers 530, 531 and 532. The connection is sche¬ matically represented by a slash-line, which represents a suitable means of connection such as a resistor, diode or direct wire connection. A shift clock 533 times the operation of each shift register with the timing divided by two for each subsequent register as by the countdown circuits 534 and 535. Note that the shift registers operate in the reverse direction from those previously described for the periodicity sorting matrix. Clock transition gates 536 and 537 interconnect the delay lines 530, 531 and 532. Each of the inverse AND gate inputs is connected to respective line address decoders 540, 541 and 542 for the three octaves shown in Figure 20. Decoders 540, 541 and 542 are used to select the desired periodicity pulse group by connecting to the various delay line taps as shown. Suit¬ able line addresses are produced by the composer program, depending upon the input information to the system. The function of the line address decoders 540, 541 and 542 can be carried out in several ways. As a first pos¬ sibility, the conventional line decoder using binary address numbers to select a line may be employed. In another embodi¬ ment, a shift register containing a bit at the selected line can be employed. One desirable feature of using a shift register for the function is that it can address several lines in parallel, simultaneously, while the demultiplexer can do only one at a time. In the system described above in Figure 20, it will be seen that there are six discrete periodicities or pitches A, B, C, D, E and F per octave. The base octave has two possible combinations for A, C and E, while other octaves, due to clock countdown, have three for A, C and E, with two each for B, D and F. In general, this is 5n/2 lines per octave for all but the base octave and 3n/2 for the base octave. The delay line taps 0-6. supply the "center pulse" of the three-pulse group which defines a periodicity. The base octave is the only octave in which the center pulse requires its own set of shift register delay taps. For example, notice that taps 7-12 not only provide the 3rd pulses of the base octave, but also the center pulses of the second octave. Likewise, taps 13-18 provide the 3rd pulses of the 2nd octave, and the center pulses of the 3rd octave. Two important requirements for the synthesizer are shown in Figure 20. The first is that AND gates 536 and 537 are used to inhibit the upper octave clock from shifting the data pulse from the lower octave until the full lower clock period has been com¬ pleted. Without this feature, the periodicity would lose a clock increment for each octave over the correct pulse period. The second is that the entry of the zero, pulse into the selected periodicity line must be clocked on the leading edge of the clock pulse of the octave in which it is being inserted. This Is shown in the labeled "line enable" con¬ trol in the line address decoder in Figure 20. The operation of the zero placement matrix of Figure 20 can be further understood from the timing diagram of Fig¬ ure 21. Figure 21 shows the correct clock timing pulse trains for addressing the lines, as well as the transition inhibit for clock pulses when the signal pulse is transferred from a lower to an upper octave. In Figure 21, a selected pulse is shown in line B of the third octave of Figure 20. 60 The pulses are- injected at the spacings in the shift regis¬ ter at B B and B . The shift. clock transitions are shown between octaves. These pulses represent the desired periodic zeros and then propagate step-by-step through the shift register chain to create the specified output. As a further illustration, another line in Figure 21 is shown as addressed at A A„ and A 0 simultaneously with the B Q , B.. , B„ Q pulse. This shows that the system can produce a set of interleaved zeros which would specify a complex waveform. Although Figure 21 shows the shift register element select by means of "Preset" inputs, it will be apparent that it can also be done by direct connection to the "D" input. Also, the form of the line itself can consist of direct wiring or any desired kind of logic address method. Although the block diagram of Figure 19 shows sep¬ arate functional blocks 504 for residue modulation and 509 and 510 for amplitude modulation, it is possible to combine the operations for a simpler circuit construction. Thus, there is described hereafter a method for inserting residue information based on the idea that the period between the real zero and the first peak is T/4. In terms of the damped exponential concept of the Aural Retina existence diagram of Figure 2, this T/4 period for rise time represents a residue of zero. As residue increases toward infinity, the rise time approaches zero. Thus, by means of a one shot multivibrator, it is possible to create a period of T/4 for each periodicity which represents the sine wave or zero residue condition. Then by decreasing the multivibrator period as a function of residue amplitude, it is possible to generate a signal con¬ taining the required residue at each zero. A schematic arrangement employing one shot multi¬ vibrator 600 in this way is shown in Figure 22. The multi- vibrator 600 of Figure 22 has a residue input connected to the line including resistor 601 and has a variable input pulse repetition frequency weighting time constant deter¬ mined by the RC circuit including resistor 602 and capacitor 603. An input from this circuit is applied to the multi- vibrator pulse trigger input while the residue signal is connected to the reset input. The output of the one shot multivibrator 600 then consists of the residue modulated pulse as indicated schematically below device 600. In operation, the basic T/4 width of the one shot or a sine wave at a given periodicity is defined by the existence diagram and is controlled by the PRF weighting time constant. The composer program can control this weight¬ ing by varying the resistor and/or the capacitor in any suitable manner. The residue signal resets the one shot according to the magnitude of the specified residue. For example, for a sine wave condition, period T can be set to T/4. .The period T can be made T/8 for critically damped exponentials and approximately equal to zero for wide band overdamped exponentials. The output signal of the multivibrator 600 is then integrated so that the spectrum has, for example, a 6 db per octave roll-off. The anti-logarithmic function can then be performed by various well known techniques using, for example, operational amplifiers or digitally controlled attenuators. The next step In the processing sequence is to assign amplitude levels to each pulse according to the com¬ poser program of Figure 19. This can be done by conventional amplitude modulation methods such as diode bridges, digitally controlled attentuators or gain controlled amplifiers. The zero pulse matrix part of the synthesis system can be carried out with digital techniques, whereas the later portions of the circuit can employ analog signal processing. It is, however, possible, .if desired, to employ all digital methods. These could be especially useful in the modulation and anti-log functions which require non-linear operations on the signal. 62 To demonstrate the advantages of the invention, there is next described a comparison of waveform analysis by the novel invention as compared to spectrum analysis tech¬ niques, and to explain and illustrate the ways by which the Aural Retina and Fourier analysis each obtain similar infor¬ mation for identifying a signal. It will also be shown how the Aural Retina can obtain this information (a) faster than is practical with spectrum analysis, (b) with fewer dimensions (less data processing) and (c) in the presence of overlapping signals by using epoch information which is lost in spectral processing. Moreover, there will be shown how processing functions which are equivalent to correlation and deconvolu- tion can be accomplished. Figure 23 shows a simple periodic series of damped sinusoids, which represent an elementary form of signal. In this example, the ringing frequency is 1,000 Hz, and the repetition frequency of each ringing impulse is 200 Hz. In terms of voice processing, this would represent a pitch of 200 Hz and a formant of 1,000 Hz. The Fourier transform is the conventional method of processing this kind of signal for the purpose of identifying these parameters. The Fourier method is successful if the signal exists unchanged during a specific time interval for the required measurements to be made within a specified precision. This is due to the pre¬ viously described, well-known, time-frequency inequality Λt ^f . 1* This restriction is unrealistic in practical applications where the signal waveform is time-limited, variable and composed of multiple sources. We can develop an illustration of the problem of this time-frequency limitation by showing how the Fourier spectrum evolves as a function of the time of onset (epoch) of the signal waveform in Figure 23. Thus, the spectral envelope taken at intervals relative to the onset, t are shown in Figure 24. For convenience in later comparison with Aural Retina, these spectral sampling intervals will 63 correspond to- he waveform peaks, although, in general, spectral sampling windows are entirely arbitrary with re¬ spect to the waveform. At t in Figure 24, the spectral envelope corres- ponds to the rise time of the exponential from onset to the first peak. In effect, this can be defined as the bandwidth of the signal. Note that the "bandwidth" has only an empiri¬ cal definition with respect to rise time. Thus, the spectrum is that of a pulse whose peak is defined by the 1,000 Hz ring- ing frequency (or pole) of the exponential. it is "flat" from 0 Hz to the point where it begins to "roll off" at 1,000 Hz. At the second positive peak at time t„ in Figure 23, a complete cycle of one millisecond has occurred, and the spectral energy begins to center around the ringing frequency. Using the .At ^if inequality, the bandwidth around the peak is Af=l/Δt=l/lxl0~ 3 =l,000 Hz. Similarly, at the third and fourth samples in Figure 24, the envelope grows sharper around the ringing peak, with bandwidths of 500 and 330 Hz, respectively. Then, at the beginning of the second impulse response, the spectrum begins a new function. The repetition of the impulse occurs at 1/200 Hz=5 milliseconds from t and causes "ripples" In the formerly smooth spectral envelope. Peaks of these ripples occur at 200 Hz intervals. As the number of spectral sample intervals increases, the widths of the impulse repetition rate ripples become sharper in accordance with the Δ t At inequality. Thus, at the end of the second response repe¬ tition the spectral resolution «Δ.f is l/10msec=100 Hz. Finally, after four repetitions the resolution is 25 Hz. It is apparent that to be able to measure either the ringing frequency or repetition rate to a certain pre¬ cision, one must "wait" a specified interval. But more importantly, the spectrum envelope mμst be obtained before the parameters can be estimated. This requires computation of the Fourier , transform within the specified interval if "real time" operation is desired. This transformation is a well-known consumer of computing power in spite of the many improvements in the FFT algorithm. A similar analysis of the Aural Retina can be des¬ cribed for the signal illustrated in Figure 23. In this case, the procedure is to extract a set of measurements at each zero (real or complex), which are independent. This independence is an essential feature which distinguishes the Aural Retina from all forms of "least square" polynomial approximation methods, of which the Fourier transform is only one. Figure 25 shows the time sequence of the samples taken at each peak. At each peak, the residue (or instan¬ taneous bandwidth) and amplitude are measured simultaneously. These are the basic measurements on the waveform. From them, by comparing amplitude and time between two spatially separate transducer channels, there is derived a third in¬ stantaneous vector: direction (θ). Also, using the Periodi¬ city Sorting Matrix, the zero samples can be established to identify periodicities, randomness and epochs of time series. In the example of Figure 25, the "residue" vector is a measure of the instantaneous bandwidth. In effect, it is the centroid of the spectral distribution corresponding to the time interval between real and complex zeros or nor¬ malized rise time. It is also an estimate of the ringing frequency of the system, and is thus a "predictor" function. The amplitude vector, as extracted in the Aural Retina system, is a logarithmic function of amplitude at each peak. Direc¬ tion would be a function of the spatial position of the signal source. The sequence of measurements on periodicity is a function of the means by which this parameter is measured. It takes three equally-spaced zeros to detect one periodic event. Thus, as shown in Figure 25, the first two zeros 65 related to the' ringing response periodicity are not recog¬ nized as periodic. They are an indication of the onset of a time series and are defined as the epoch event having zero- periodicity. 5 When the third ringing zero arrives, it is identi¬ fied as periodic at the 1,000 Hz rate. Then, when the second impulse function is received, the process begins again because the periodicity of the impulse repetition rate has not yet been identified. Finally, when- the third impulse arrives, 10 we have identified the repetition rate of the impulses. The pattern then becomes a pair of pairs forming the epoch, fol¬ lowed by a pair of repetition periodicities and a series con¬ taining the ringing periodicities. When comparing the set of measurements derived from 15 the waveform of Figure 23 by the spectrum patterns of Figure 24 with those derived by the Aural Retina (Figure 25), it is seen that with the Aural Retina: (1) the ringing frequency is estimated directly from a simple waveform measurement, the resi- 2.0 due, rather than from a complex analysis of the pattern of a- spectral envelope; (2) the repetition frequency is measured explicitly at the exact instant that such information is available, rather than from an estimate of the 25 ripple spacing on the spectral envelope, or by another complex conversion of the spectrum into a "cepstrum" or an "autocorrelation" pattern; (3) since the vector measurements taken at each waveform zero are independent, they can be 30 treated by statistical procedures to accomplish optimum detection processes that are usually associated with frequency domain techniques. Although certain basic advantages of Aural Retina over Fourier processing can be seen in the processing of this 35 simple waveform, the most significant advantage is found when 66 the signal source contains two or more overlapping time ser¬ ies. To illustrate this situation, Figure 26 shows another single damped sinusoid added to the series of Figure 23. The problem now is to estimate the description of both sig- nals, including their exact instants of onset (epoch). Using Fourier analysis, we now have two spectral patterns which are superimposed during the existence of the two signals. The left-handmost curve of Figure 27 illus¬ trates the spectral pattern of the second damped sinusoid wavelet, which has a ringing period of 4 msec, producing a spectral peak at 250 Hz. The resultant spectrum, at any time after the onset of signal 2, t , is the sum of both spectra. The middle curve of Figure 27 shows the effect of superimposed spectral envelopes. The envelope of the spec¬ tral pattern at the end of the ringing of Signal #2 shows two peaks: one at 250 Hz, and the other at 2,000 Hz. How¬ ever, the effects of the repetition harmonic ripples on the 250 Hz signal pattern cause interference in selecting the true peak of the 1,000 Hz signal. At the end of the series of five impulses, the repetition harmonic ripple pattern completely displaces the true maximum of the 1,000 Hz signal; this is shown at the right of Figure 27. Also notice that there is no indication of the epoch of the 250 Hz signal. In effect, the spectral patterns have either obscured or eliminated the ability to sort the two signals. Since the example of Figure 27 is based on the simplest kind of signal, it is apparent that the complexity of processing becomes much worse when typical real-world signals are used. To illustrate how the Aural Retina solves the pro¬ blem of sorting the two signals, refer to Figure 26. The figure shows the use of the Periodicity Sorting Matrix's de- interleaving process to sort individual samples by analyzing their time domain relationships. After the waveform analyzer extracts the real and complex zeros with their associated measurements of amplitude and residue, the PSM identifies the epochs and periodicities of both signals. As shown in Figure 26, the combined real and complex zeros are sorted ■ one-by-one, so that the two signals, S and S 0 form two iden- tifiable sets of measurements. Although residue (related to the rate-of-change) can be measured at both real and complex zeros, the amplitude Is measured only at peaks. The time sequence plot in Figure 26 shows the instants at which the periodicities of the two signals are identified. Thus, the onset of the wavelet S is identified in the midst of the zeros of the ringing and repetition of sequence S . Although the two signals S and S„ of Figure 26 can be identified by using only the periodicity and temporal relationships, a more complete description of the signals can be obtained by using the residue and amplitude para¬ meters in the form of either a two or a three dimensional space. This is shown in Figure 28. The primary recognition space uses the periodicity vs. residue parameters. Since patterns in this plane are Independent of absolute amplitude, automatic identification is greatly facilitated. In general, the amplitude parameter is needed for describing a signal only as a secondary sorting parameter " (and for possible later synthesis). Figure 28 illustrates the description of Signals 1 and 2 in the Aural Retina recognition space, in which the parameter vectors of Figure 26 are combined so as to show the cluster patterns which identify each signal. For con- venience, each of these patterns is shown as an accumulation over the set corresponding to the duration of each impulse response of Signal #1. The patterns are analogous in func¬ tion to the sequences of spectrograms in Figure 27. Each point in the space represents an accumulation of events. • If the parameters are invariant, the point position is un¬ changed and represents all events over the time of observa¬ tion. Thus, we can derive an additional descriptive dimen¬ sion by summing the events at each point location, as in a multivariate histogram. The above illustration demonstrates the statistical, attributes of the novel signal processing method. With this approach, one can achieve the objectives of signal identifi¬ cation and detection on a basis of classical statistical theory. Furthermore, it now becomes possible to electroni¬ cally duplicate many psychoacoustic phenomena of the ear; for example, the ear's ability to sort overlapped signal sources, as in the "cocktail party effect" and apply the . results to apparatus used in automatic voice recognition equipment. Also, the invention allows high intelligibility of "clipped speech" in terms of the fact that periodicity analysis of the real and complex-zeros contains the major components of speech information, and excludes the residue vector, which contains only the "timbre" quality of the speech sound. From a comparison of the two processing methods, it is seen that, aside from the inherent difficulties Fourier methods ha.e handling overlapping time-limited signals, there are definite differences in the complexity of pro- cessing the signals. The spectral pattern is a two-dimen¬ sional construction, but the same information is contained in the Aural Retina in the form of a small set of point measurements. For example, a damped sinusoid is represented by a pair of points in the periodicity/residue plane, while the Fourier domain requires a line of points whose shape characterizes the ringing peak and the "Q". The reduction in dimensionality is equivalent to a reduction in informa¬ tion needed to describe the signal. Thus, the invention permits lower data rates, lower costs, lower power consump- tion and lower system complexity. 69 Since ' the identifying features of the Aural Retina method are independent of signal amplitude, the effects of large signal amplitudes do not Inherently mask the lower amplitudes. Nor is there a need to maintain a constant amplitude to be able to "recognize" a spectral pattern, as is required by Fourier analysis. Moreover, in the Aural Retina, signal recognition is made relatively easy by simply setting up a "template" which accepts only the specified set of points characterizing the desired signal. Although the present invention has been described in connection with preferred embodiments thereof, many vari¬ ations and modifications will now become apparent to those skilled in the art. It is preferred, therefore, that " the present invention be limited not by the specific disclosure herein, but only by the appended claims.

Claims: WHAT IS CLAIMED IS: 1. The process of analyzing a signal waveform f(t) comprising the steps of applying said complex signal f(t) to a logarithmic converter to produce an amplitude output re¬ lated to log (f)t; applying said output related to log (f)t to a differentiator means to produce an output related to a residue function, d[log f(t)]/dt; producing a zero related output signal which is related to at least each one of either the real zeros or complex zeros in said residue function when said function is either zero or a peak or null value; apply- ing said zero related output signal to periodicity sorting means to determine signal periodicities; and inspecting said residue function dflog f(t)]/dt and said amplitude output related to log (f)t at the instants of said signal periodi¬ cities in an at least two-dimensional existence plane wherein each set of one or more discrete points in said existence plane represents a particular waveform. 2. The process of analyzing a signal waveform f(t) comprising the steps of applying said signal f(t) to a lo¬ garithmic converter to produce an amplitude output related to log (f)t; applying said output related to log (f)t to a . differentiator means to produce an output related to a resi¬ due function, d[log f(t)]/dt; and output means for producing a given flash output related to a predetermined value of said residue function. 3. The process of claim 1 which includes a- second signal waveform input f (t) and means identical to the means described for processing of f(t) for processing f (t); and comparison means for comparing said two-dimensional existence planes produced by processing of said waveforms f(t) and f (t) for determining relative relationships of said signals. 71 4. The process of claim 3, wherein said signals f(t) and ff.. ((tt)) aarree rreecceeiived in first and second spatially related signal channels. 5. The process of claim 1 which further includes the step of normalizing said residue function by dividing by f(t). 6. The process of claim 1, wherein said complex waveform f(t) is the result of individual signal sources and f t) -jr A^ 8 * *-^ K=l wherein A = k amplitude coefficient; S k = k complex frequency (β k + 3 ^ k ) • • . = epoch (start) of k excitation function. 7. The process of analyzing a complex waveform f(t) - A sk(t--ϊk) K=l & wherein A amplitude coefficient; S = k complex frequency (»<, + j β ) *jj. = epoch (start) of k excitation function; said process comprising the steps of determining at least two waveform information vectors (WIVs) of the waveform infor¬ mation vectors of epoch t , energy A, residue R or direction θ of arrival of said waveform, wherein said waveform infor¬ mation vectors are measured at the instant at least one of f(t) or d[f(t)]/dt is zero, and determining the existence of a given immediate flash information characteristic in said waveform by comparison of said at least two WIVs to prede- termined values. 8. The process of claim 7, which includes the further step of determining a periodicity in said at least three WIVs. 72 9. The process of claim 8 which includes the fur¬ ther step of comparing said WIVs to subsequently produced WIVs. 10. The process of claim 8 which includes the further step of comparing said WIVs to a predetermined pattern. OMPI

Inventors: BATES JOHN K JR, BATES, JOHN, K., JR.
Applicants: AURETINA PATENT MANAGEMENT, AURETINA PATENT MANAGEMENT CORP.
Application year: 1984
Main classification: G06F15
IPC codes: G06F17, G06G7, G06J1, G10L11