Abstract:
There are disclosed speech encoding methods and arrangements, including among others a speech synthesizer that reproduces speech from the encoded speech signals. These methods and arrangements employ a reduced bandwidth encoding of speech for which the bandwidth more nearly than in prior arrangements approaches that of the rate of occurrences of the individual sounds (equivalently, the articulatory movements) of the speech by locating the centroid of the individual sound, for example, by employing the zero crossing of a single (v(L)) representing the timing of individual sounds, which is derived from a φ signal which is itself produced from prescribed linear combination of acoustic feature signals, such as log area parameter signals. Each individual sound is encoded at a rate corresponding to its bandwidth. Accuracy is ensured by generating each individual sound signal from the linear combinations of acoustic feature signals for many times frames including the time frame of the centroid. The bandwidth reduction is associated with the spreading of the encoded signal over many time frames including the time frame of the centroid. The centroid of an individual sound is within a central time frame of an individual sound and occurs when the time-wise variations of the φ linear combination signal are most compressed.

Description:
This application is a continuation of application Ser. No. 484,231, filed Apr. 12, 1983, now abandoned. 
    
    
     BACKGROUND OF THE INVENTION 
     My invention relates to speech processing and, more particularly, to compression of speech patterns. 
     It is generally accepted that a speech signal requires a bandwidth of at least 4 kHz for reasonable intelligibility. In digital speech processing systems such as speech synthesizers, recognizes, or coders, the channel capacity needed for transmission or memory required for storage of the digital elements of the full 4 kHz bandwidth waveform is very large. Many techniques have been devised to reduce the number of digital codes needed to represent a speech signal. Waveform coding such as PCM, DPCM, Delta Modulation or adaptive predictive coding result in natural sounding, high quality speech at bit rates between 16 and 64 kbps. The speech quality obtained from waveform coders, however, degrades as the bit rate is reduced below 16 kbps. 
     An alternative speech coding technique disclosed in U.S. Pat. No. 3,624,302 issued Nov. 30, 1971 to B. S. Atal and assigned to the same assignee utilizes a small number, e.g., 12-16, of slowly varying parameters which may be processed to produce a low distortion replica of a speech pattern. Such parameters, e.g., LPC or log area, generated by linear prediction analysis can be spectrum limited to 50 Hz without significant band limiting distortion. Encoding of the LPC or log area parameters generally requires sampling at a rate of twice the bandwidth and quantizing each resulting frame of LPC or log area parameters. Each frame of a log area parameter, for example, can be quantized using 48 bits. Consequently, 12 log area parameters each having a 50 Hz bandwidth results in a total bit rate of 4800 bits/sec. 
     Further reduction of bandwidth decreases the bit rate but the resulting increase in distortion, interferes with the intelligibility of speech synthesized from the lower bandwidth parameters. It is well known that sounds in speech patterns do not occur at a uniform rate and techniques have been devised to take into account such nonuniform occurrences. U.S. Pat. No. 4,349,700 issued Sept. 14, 1982 to L. R. Rabiner et al and assigned to the same assignee discloses arrangements that permit recognition of speech patterns having diverse sound patterns utilizing dynamic programming. U.S. Pat. No. 4,038,503 issued July 26, 1977 to Moshier discloses a technique for nonlinear warping of time intervals of speech patterns so that the sound features are represented in a more uniform manner. These arrangements, however, require storing and processing acoustic feature signals that are sampled at a rate corresponding to most rapidly changing feature in the pattern. It is an object of the invention to provide an improved speech representation arrangement having reduced digital storage and processing requirements. 
     SUMMARY OF THE INVENTION 
     Sounds or events in human speech are produced at an average rate that varies between 10 and 20 sounds or events per second. Acoustic features, however, are generated at a much higher rate which corresponds to the most rapidly changing features in the pattern, e.g., 50 Hz. It has been observed that such sounds or speech events, e.g., vowel sounds, generally occur at nonuniformly spaced time intervals and that articulatory movements differ widely for various speech sounds. Consequently, a significant degree of compression may be achieved by transforming acoustic feature parameters occurring at a uniform time frame rate, e.g., 50 Hz into short speech event related units representing articulatory movement in individual sounds occurring in the speech pattern located at nonuniformly spaced time intervals at the sound occurrence rate, e.g., 10 Hz. The coding of such speech event units results in higher efficiency i.e., substantially lower bit rate without degradation of the accuracy of the the pattern representation. 
     The invention is directed to speech encoding methods and arrangements adapted to convert signals representative of the acoustic features of the successive time frames of a speech pattern formed at the time frame rate to signals representative of the individual sounds (or equivalently, the articulatory movements producing those sounds) encoded at a lower rate which is their rate of occurrence. While the acoustic feature signals of the successive time frames are formed in a conventional way, the conversion to the lower rate signals comprises linearly combining selected ones of those acoustic feature signals and using those linear combinations for many successive time frames to locate the particular time frames in which occur the sound centroids, or more specifically the zero crossings of the timing signals described hereinafter. For each time frame so located, a signal is generated to represent the individual sound (or equivalently, the articulatory movement) having that centroid. In particular, that signal is generated from the aforesaid linear combinations of acoustic feature signals. Each individual sound signal is encoded at a rate corresponding to its bandwidth. Accuracy is ensured by generating each individual sound signal from the linear combinations of acoustic feature signals rather than the arbitrary smoothing techniques used in the prior art. 
     According to one aspect of the invention a speech pattern is synthesized by storing a prescribed set of speech element signals, combining said speech element signals to form a signal representative of the acoustic features of the uniform duration time frames of a speech pattern, and producing said speech pattern responsive to the set of acoustic feature signals. The prescribed speech element signals are formed by analyzing a speech pattern to generate a set of acoustic feature representative signals such as log area parameter signals at a first rate, e.g., 50 Hz. A sequence of signals representative of the articulatory movements of successive individual sounds in said speech pattern is produced responsive to said sampled acoustic feature signals at a second rate, e.g., 10 Hz and a sequence of digitally coded signals corresponding to the speech event representative signal is formed at the second rate less than said first rate. 
    
    
     DESCRIPTION OF THE DRAWING 
     FIG. 1 depicts a flowchart illustrating the general method of the invention; 
     FIG. 2 depicts a block diagram of a speech pattern coding circuit illustrative of the invention; 
     FIGS. 3-8 depict detailed flowcharts illustrating the operation of the circuit of FIG. 2; 
     FIG. 9 depicts a speech synthesizer illustrative of the invention; 
     FIG. 10 depicts a flow chart illustrating the operation of the circuit of FIG. 9; 
     FIG. 11 shows a waveform illustrating a speech event timing signal obtained in the circuit of FIG. 2; 
     FIG. 12 shows waveforms illustrative of a speech pattern and the speech event feature signals associated therewith; 
     FIGS. 13 and 14 show the principal component factoring and speech event feature signal selection operations of FIG. 4 in greater detail; 
     FIGS. 15 and 16 show the principal component factoring and the feature signal generation operations of FIG. 6 in greater detail; and 
     FIG. 17 shows the sampling rate signal formation operation of FIG. 7 in greater detail. 
    
    
     GENERAL DESCRIPTION 
     It is well known in the art to represent a speech pattern by a sequence of acoustic feature signals derived from a linear prediction or other spectral analysis. Log area parameter signals sampled at closely spaced time intervals have been used in speech synthesis to obtain efficient representation of a speech pattern. The closely spaced time intervals or time frames occurring at a uniform rate requires a bandwidth or bit rate sufficient to adequately represent the most rapid changes in the log area parameters of the speech pattern. Consequently, the number of bits per frame and the number of frames per second for coding the parameters are fixed to accommodate such rapid changes in the log area parameters. Alternatively, speech patterns have been represented in terms of their constituent sounds or speech events. As described in the article &#34;Development of a Quantitative Description of Vowel Articulation&#34; by Kenneth Stevens et al appearing in the Journal of the Acoustical Society of America, Vol. 27, No. 3, pp. 484-493, May 1955, and the article &#34;An Electrical Analog of the Vocal Tract&#34;, by K. N. Stevens et al appearing in the Journal of the Acoustical Society of America, Vol. 25, No. 4, pp. 734-742, July 1953, each individual sound such as a vowel sound may be represented as a set of feature parameters corresponding to the articulatory configuration for the sound. The individual sounds or speech events in a speech pattern occur at a rate much lower than the time frame rate, and the bandwidth or bit rate requirements of such sounds are generally much lower than the bandwidth of the rapid changes in the log area or other linear predictive parameters. Other arrangements reduce the speech code bit rate by representing a succession of similar frames by the acoustic features of the first of the similar frames as disclosed in the article &#34;Variable-to-Fixed Rate Conversion of Narrowband LPC Speech,&#34; by E. Blackman, R. Viswanathan, and J. Makhoul published in the Proceedings of the 1977 IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 409-412, and elsewhere. Unlike these other arrangements, the conversion of the sequence of time frame acoustic feature signals into a succession of individual sound articulatory configuration signals according to the invention provides reduced speech code bit rate by concentrating on coding the portions of speech, as described at pages 7 and 11, first paragraphs, containing centroids of signals representing individual sounds or more specifically, where a speech event signal is characterized by minimum spreading, i.e., is relatively compressed, rather than being approximations of the time frame acoustic features signals of the type described in the Blackman et al. reference. In accordance with the invention, log area parameters are transformed into a sequence of individual speech event feature signals φ k  (n) such that the log area parameters are related thereto in accordance with the relationship ##EQU1## The speech event feature signals φ k  (n) illustrated in FIG. 12 are sequential and occur at the speech event rate of the pattern which is substantially lower than the the log area parameter frame rate. Log area parameters are well known in the art and are described in &#34;Digital Processing of Speech Signals&#34; by L. R. Rabiner and R. W. Schafer, Prentice Hall Signal Processing Series, 1978, pp. 444 and elsewhere. In equation (1), each speech event signal φ k  (n) corresponds to the features of the articulatory configuration of an individual sound occurring in the speech pattern, and p is the total number of log area parameters y i  (n) determined by linear prediction analysis. m corresponds to the number of speech events in the pattern, n is the index of samples in the speech pattern at the sampling rate of the log area parameters, φ k  (n) is the kth speech event signal at sampling instant n, and a  ik  is a combining coefficient corresponding to the contribution of the kth speech event function to the ith log area parameter. Equation (1) may be expressed in matrix form as 
     
         Y=AΦ                                                   (2) 
    
     where Y is a pxN matrix whose (i, n) element is y i  (n), A is a pxm matrix whose (i, k) element is a ik , and Φ is an mxN matrix whose (k, n) element is φ k  (n). Since each speech event k occupies only a small segment of the speech pattern, the signal φ k  (n) representative thereof should be non-zero over only a small range of the sampling intervals of the total pattern. Each log area parameter y i  (n) in equation (1) is a linear combination of the speech event functions φ k  (n) and the bandwidth of each y i  (n) parameter is the maximum bandwidth of any one of the speech event functions φ k  (n). It is therefore readily seen that the direct coding of y i  (n) signals will take more bits than the coding of the φ k  (n) sound or switch event signals and the combining coefficient signals a ik  in equation (1). 
     FIG. 1 shows a flow chart illustrative of the general method of the invention. In accordance with the invention, a speech pattern is analyzed to form a sequence of signals representative of log area parameter acoustic feature signals. It is to be understood, however, that LPC, PARCOR or other speech features may be used instead of log area parameters and that log area parameter signals may be formed from LPC or the other speech features as is well known in the art. The instructions for the conversion of LPC to log area parameters are listed in Appendix A hereto in Fortran Language. The feature signals are then converted into a set of speech event or individual sound representative signals that are encoded at a lower bit rate for transmission or storage. 
     With reference to FIG. 1, box 101 is entered in which an electrical signal corresponding to a speech pattern is low pass filtered to remove unwanted higher frequency noise and speech components and the filtered signal is sampled at twice the low pass filtering cutoff frequency. The speech pattern samples are then converted into a sequence of digitally coded signals corresponding to the pattern as per box 110. Since the storage required for the sample signals is too large for most practical applications, they are utilized to generate log area parameter signals as per box 120 by linear prediction techniques well known in the art. The log area parameter signals y i  (n) are produced at a constant sampling rate high enough to accurately represent the fastest expected event in the speech pattern. Typically, a sampling interval between two and five milliseconds is selected. 
     After the log area parameter signals are stored, the times of occurrence of the successive speech events, i.e., individual sounds, in the pattern are detected and signals representativve of the event timing are generated and stored as per box 130. This is done by partitioning the pattern into prescribed smaller segments, e.g., 0.25 second intervals. For each successive interval having a beginning frame n b  and an ending frame n e , a matrix of log area parameter signals is formed corresponding to the log area parameters y i  (n) of the segment. The redundancy in the matrix is reduced by factoring out the first four principal components so that each log area parameter signal of a time frame n is represented as ##EQU2## and conversely, the principal components u m  (n) of the time frame is determined from the log area parameters of the frame as ##EQU3## The first four principal components may be obtained by methods well known in the art such as described in the article &#34;An Efficient Linear Prediction Vocoder&#34; by M. R. Sambur appearing in the Bell System Technical Journal Vol. 54, No. 10, pp. 1693-1723, December 1975. The resulting u m  (n) functions may be linearly combined to define the desired speech event signals representing the articulatory features of individual sounds as ##EQU4## by selecting coefficients b km  such that each φ k  (n) are most compact in time. In this way, the speech pattern is represented by a sequence of successive compact (minimum spreading) speech event feature signals φ k  (n) each of which can be efficiently coded. In order to obtain the shapes and locations of the speech event signals, a distance measure ##EQU5## is minimized to choose the optimum φ(n) and its location is obtained from a speech event timing signal ##EQU6## In terms of equations 5, 6, and 7, a speech event signal φ k  (n) with minimum spreading is centered at each negative zero crossing of v(L). 
     Subsequent to the generation of the v(L) signals in box 130, box 140 is entered and the speech event signals φ k  (n) are accurately determined using the process of box 130 with the speech event occurrence signals from the negative going zero crossings of v(L). Having generated the sequence of speech event representative signals, the combining coefficients a ik  in equations (1) and (2) may be generated by minimizing the mean-squared error between each log area parameter signal y i  (n) and the same log area parameter signal constructed from the individual sound features applicable to time frame n ##EQU7## where M is the total number of speech events within the range of index n over which the sum is performed. The partial derivatives of E with respect to the coefficients a ik  are set equal to zero and the coefficients a ik  that minimize the mean square error E are obtained from the set of simultaneous linear equations ##EQU8## 
     DETAILED DESCRIPTION 
     FIG. 2 shows a speech coding arrangement that includes electroacoustic transducer 201, filter and sampler circuit 203, analog to digital converter 205, and speech sample store 210 which cooperate to convert a speech pattern into a stored sequence of digital codes representative of the pattern. Central processor 275 may comprise a microprocessor such as the Motorola type MC68000 controlled by permanently stored instructions in read only memories (ROM) 215, 220, 225, 230 and 235. Processor 275 is adapted to direct the operations of arithmetic processor 280, and stores 210, 240, 245, 250, 255 and 260 so that the digital codes from store 210 are compressed into a compact set of speech event feature signals. The speech event feature signals are then supplied to utilization device 285 via input output interface 265. The utilization device may be a digital communication facility or a storage arrangement for delayed transmission or a store associated with a speech synthesizer. The Motorola MC68000 integrated circuit is described in the publication MC68000 16 Bit Microprocessor User&#39;s Manual, second edition, Motorola, Inc., 1980 and arithmetic processor 280 may comprise the TRW type MPY-16HJ integrated circuit. 
     Referring to FIG. 2, a speech pattern is applied to electroacoustic transducer 201 and the electrical signal therefrom is supplied to low pass filter and sampler circuit 203 which is operative to limit the upper end of the signal bandwidth to 3.5 KHz and to sample the filtered signal at an 8 KHz rate. Analog to digital converter 205 converts the sampled signal from filter and sampler 203 into a sequence of digital codes, each representative of the magnitude of a signal sample. The resulting digital codes are sequentially stored in speech sample store 210. 
     Subsequent to the storage of the sampled-speech pattern codes in store 210, central processor 275 causes the instructions stored in log area parameter program store 215 to be transferred to the random access memory associated with the central processor. The flow chart of FIG. 3 illustrates the sequence of operations performed by the controller responsive to the instructions from store 215 and the instruction sequence is listed in FORTRAN language form in Appendix A. 
     Referring to FIG. 3, box 305 is initially entered and frame count index n is reset to 1. The speech samples of the current frame are then transferred from store 210 to arithmetic processor 280 via central processor 275 under as per box 310. The occurrence of an end of speech sample signal is checked in decision box 315. Until the detection of the end of speech pattern signal, control is passed to box 325 and an LPC analysis is performed for the frame in processors 275 and 280. The LPC parameter signals of the current frame are then converted to log area parameter signals y i  (k) as per box 330 and the log area parameter signals are stored in log area parameter store 240 (box 335). The frame count is incremented by one in box 345 and the speech samples of the next frame are read (box 310). When the end of speech pattern signal occurs, control is passed to box 320 and a signal corresponding to the number of frames in the pattern is stored in processor 275. 
     Central processor 275 is operative after the log area parameter storing operation is completed to transfer the stored instructions of ROM 220 into its random access memory. The instruction codes from store 220 correspond to the operations illustrated in the flow chart of FIGS. 4 and 5 and are listed in FORTRAN Language form in Appendix B. These instruction codes are effective to generate a signal v(L) from which the occurrences of the speech events in the speech pattern may be detected and located. 
     Referring to FIG. 4, the frame count of the log area parameters is initially reset in processor 275 as per box 403 and the log area parameters y i  (n) for an initial time interval n 1  to n 2  of the speech pattern are transferred from log area parameter store 240 to processor 275 (box 410). After determining whether the end of the speech pattern has been reached in decision box 415, box 420 is entered and the redundancy of the log area parameter signals is removed by factoring out the first four principal components u i  (n), i=1, . . . ,4 as aforementioned. The principal component factoring operations of box 420 are shown in greater detail in FIG. 13. Referring to FIG. 13, a log area parameter correlation matrix Ax(i,j) is formed for i and j ranging from 1 to np (box 1301), an eigenvector rotation matrix is generated by singular value decomposition of matrix Ax(i,j) for i and j ranging from 1 to 16 (box 1305), and the principal component signals u i  (n) are formed over the interval from n b  to n e  for i=1, 2, 3, 4 from the log area parameter signals and the results of the eigenvector rotation matrix (box 1310). 
     The log area parameters of the current time interval are then represented by ##EQU9## from which a set of signals ##EQU10## are to be obtained. The u i  (n) signals over the interval may be combined through use of parameters b i , i=1, . . . , 4, in box 425 so that a set of signals ##EQU11## is produced such that φ k  is most compact over the range n 1  to n 2 . This is accomplished through use of the θ(L) function of equation 6. The combining of the u i  (n) signals of box 425 is shown in greater detail in FIG. 14 in which the principal component signals u i  (n) from box 420 are weighted to form signals wu i  (n)=u i  (n)(n-63) in box 1401. A correlation matrix of the weighted principal component signals Bx(i,j) is generated for i and j ranging from 1 to 4 (box 1405) and an eigenvector rotation matrix is generated by singular value decomposition of correlation matrix Bx(i,j) for i and j ranging from 1 to 4 (box 1410). The principal component signals u k  (n) are combined with the results of the eigenvector rotation matrix of box 1410 for n ranging from n b  to n e  in box 1415 to form the articulatory configuration signals which are the speech event signals of box 425 of FIG. 4. A signal v(L) representative of the speech event timing of the speech pattern is then formed in accordance with equation 7 in box 430 and the v(L) signal is stored in timing parameter store 245. Frame counter n is incremented by a constant value, e.g., 5, on the basis of how close adjacent speech event signals φ k  (n) are expected to occur (box 435) and box 410 is reentered to generate the φ k  (n) and v(L) signals for the next time interval of the speech pattern. 
     When the end of the speech pattern is detected in decision box 415, the frame count of the speech pattern is stored (box 440) and the generation of the speech event timing parameter signal for the speech pattern is completed. FIG. 11 illustrates the speech event timing parameter signal for the an utterance exemplary message. Each negative going zero crossing in FIG. 11 corresponds to the centroid of a speech event feature signal φ k  (n). 
     Referring to FIG. 5, box 501 is entered in which speech event index I is reset to zero and frame index n is again reset to one. After indices I and n are initialized, the successive frames of speech event timing parameter signal are read from store 245 (box 505) and zero crossings therein are detected in processor 275 as per box 510. Whenever a zero crossing is found, the speech event index I is incremented (box 515) and the speech event location frame is stored in speech event location store 250 (box 520). The frame index n is then incremented in box 525 and a check is made for the end of the speech pattern frames in box 530. Until the end of speech pattern frames signal is detected, box 505 is reentered from box 530 after each iteration to detect the subsequent speech event location frames of the pattern. 
     Upon detection of end of the speech pattern signal in box 530, central processor 275 addresses speech event feature signal generation program store 225 and causes its contents to be transferred to the processor. Central processor 275 and arithmetic processor 280 are thereby adapted to form a sequence of speech event feature signals φ k  (n) responsive to the log area parameter signals in store 240 and the speech event location signals in store 250. The speech event feature signal generation program instructions listed in FORTRAN Language in Appendix C hereto are illustrated in the flow chart of FIG. 6. 
     Initially, location index I is set to one as per box 601 and the locations of the speech events in store 250 are transferred to central processor 275 (box 605). As per box 610, the limit frames for a prescribed number of speech event locations, e.g., 5, are determined. The log area parameters for the speech pattern interval defined by the limit frames are read from store 240 and are placed in a section of the memory of central processor 275 (box 615). The redundancy in the log area parameters is removed by factoring out the number of principal components therein corresponding to the number of prescribed number of events (box 620). FIG. 15 shows the factoring out of the 5 principal component signals in greater detail. In FIG. 15, a log area parameter correlation matrix Ax(i,j) is formed from the log area parameter signals for i and j ranging from 1 to np (box 1501), and an eigenvector rotation matrix is generated by singular value decomposition of matrix Ax (box 1505), and the 5 principal component signals u(n,j) are produced from the log area parameter signals and the results of the eigenvector rotation matrix (box 1510). Immediately thereafter, the speech event feature signal φ L  (n) for the current location L is generated. 
     As aforementioned, the distance signal θ(L) of equation 6 is minimized to determine the optimum φ(n) signal and to find the time frame in which it is centered. The minimization of equation (6) to determine φ L  (n) is accomplished by forming the derivative ##EQU12## where ##EQU13## m is preset to the prescribed number of speech events, i.e., individual sounds, and r can be either 1, 2, . . . , or m. The derivative of equation (13) is set equal to zero to determine the minimum and ##EQU14## is obtained. From equation (14) ##EQU15## so that equation (15) can be changed to ##EQU16## φ(n) in equation (17) can be replaced by the right side of equation 14. Thus, ##EQU17## where ##EQU18## Rearranging equation (18) yields ##EQU19## Since u i  (n) is the principal component of matrix Y, ##EQU20## equation (20) can be simplified to ##EQU21## Equation (22) can be expressed in matrix notation as 
     
         Rb=λb                                               (24) 
    
     where 
     
         λ=θ(L)                                        (25) 
    
     Equation 25 has exactly m solutions and the solution which minimizes θ(L) is the one for which λ is minimum. The coefficients b 1 , b 2 , . . . , b m  for which λ=θ(L) attains its minimum value results in the optimum speech event feature signal φ L  (n). The optimum speech event feature signal corresponds to a controlled time spreading function having its centroid at the detected time of occurrence formed in accordance with the instructions set forth in Appendix C. 
     In FIG. 6, the speech event feature signal φ L  (n) is generated in box 625 and is stored in store 255. The forming of signal φ(n) of box 625 is shown in greater detail in FIG. 16 wherein the principal component signals u i  (n) from box 620 are weighted to form signals wu i  (n)=u i  (n)(n-1) in box 1601. A correlation matrix of the weighted principal component signals Bx(i,j) is generated for i and j ranging from 1 to 5 (box 1605) and an eigenvector rotation matrix is generated by singular value decomposition of correlation matrix Bx(i,j) for i and j ranging from 1 to 5 (box 1610). The principal component signals u k  (n) are combined with the results of the eigenvector rotation matrix of box 1610 for n ranging from n b  to n e  in box 1615 to form φ(n) signals of box 625 of FIG. 6. Until the end of the speech pattern is detected in decision box 635, the loop including boxes 605, 610, 615, 620, 625 and 630 is iterated so that the complete sequence of speech events for the speech pattern is formed. 
     FIG. 12 shows waveforms illustrating a speech pattern and the speech event feature signals generated therefrom in accordance with the invention. As aforementioned, the speech event feature signals correspond to the articulatory configurations of individual sounds in the speech pattern. Waveform 1201 corresponds to a portion of a speech pattern and waveforms 1205-1 through 1205-n correspond to the sequence of speech event feature signals φ L  (n) obtained from the speech pattern waveform 1201 in the circuit of FIG. 2. Each feature signal is representative of the characteristics of a speech event, i.e., individual sound, of the pattern of waveform 1201. The speech event feature signals may be combined with coefficients a ik  of equation 1 to reform log area parameter signals that are representative of the acoustic features of the speech pattern. 
     Upon completion of the operations shown in FIG. 6, the sequence of speech event feature signals for the speech pattern is stored in store 255. Each speech event feature signal φ I  (n) is encoded and transferred to utilization device 285 as illustrated in the flow chart of FIG. 7. Central processor 275 is adapted to receive the speech event signal encoding program instruction set stored in ROM 235. These instruction codes are listed in Fortran language form in Appendix D. 
     Referring to FIG. 7, the speech event index I is reset to one as per box 701 and the speech event feature signal φ I  (n) is read from store 255. The sampling rate R I  for the current speech event feature signal is selected in box 710 by one of the many methods well known in the art. In Appendix D, the instruction codes perform a Fourier analysis and generate a signal corresponding to the upper band limit of the feature signal from which a sampling rate signal R I  is determined. In this way, the sampling rate of each speech event feature signal is limited to the bandwidth of that speech event signal. FIG. 17 illustrates the arrangement for determining the sampling rate signal R I  of Appendix D. In FIG. 17, each signal φ(n) is analyzed to form a signal x p  (j) corresponding to the real part of the fast Fourier transform of φ(n) and a signal y p  (j) corresponding to the imaginary part of the fast Fourier transform of φ(n) (box 1701). Amplitude spectrum signals a p  (j) are then generated and the frequency f at which the spectral power is 0.02 of the total spectrum power is determined. The sampling interval is then set to 1000/2f milliseconds and the sampling rate R I  is made equal to 2f (box 1715). As is well known in the art, the sampling rate need only be sufficient to adequately represent the feature signal. Thus, a slowly changing feature signal may utilize a lower sampling rate than a rapidly changing feature signal and the sampling rate for each feature signal may be different. 
     Once a sampling rate signal has been determined for speech event feature signal φ I  (n), it is encoded at rate R I  as per box 715. Any of the well-known encoding schemes can be used. For example, each sample may be converted into a PCM, ADPCM or Δ modulated signal and concatenated with a signal indicative of the feature signal location in the speech pattern and a signal representative of the sampling rate R I . The coded speech event feature signal is then transferred to utilization device 285 via input output interface 265. Speech event index I is then incremented (box 720) and decision box 725 is entered to determine if the last speech event signal has been coded. The loop including boxes 705 through 725 is iterated until the last speech event signal has been encoded (I&gt;I F ) at which time the coding of the speech event feature signals is completed. 
     The speech event feature signals must be combined in accordance with equation 1 to form replicas of the log area feature signals therein. Accordingly, the combining coefficients for the speech pattern are generated and encoded as shown in the flow chart of FIG. 8. After the speech event feature signal encoding, central processor 275 is conditioned to read the contents of ROM 225. The instruction codes permanently stored in the ROM control the formation and encoding of the combining coefficients and are listed in Fortran language in Appendix E hereto. 
     The combining coefficients are produced for the entire speech pattern by matrix processing in central processor 275 and arithmetic processor 280. Referring to FIG. 8, the log area parameters of the speech pattern are transferred to processor 275 as per box 801. A speech event feature signal coefficient matrix G is generated (box 805) in accordance with ##EQU22## and a Y-Φ correlation matrix C is formed (box 810) in accordance with ##EQU23## The combining coefficient matrix is then produced as per box 815 according to the relationship 
     
         A=G.sup.-1 C                                               (28) 
    
     The elements of matrix A are the combining coefficients a ik  of equation 1. These combining coefficients are encoded, as is well known in the art, in box 820 and the encoded coefficients are transferred to utilization device 285. 
     In accordance with the invention, the linear predictive parameters sampled at a rate corresponding to the most rapid change therein are converted into a sequence of speech event feature signals that are encoded at the much lower speech event occurrence rate and the speech pattern is further compressed to reduce transmission and storage requirements without adversely affecting intelligibility. Utilization device 285 may be a communication facility connected to one of the many speech synthesizer circuits using an LPC all pole filter known in the art. 
     The circuit of FIG. 2 is adapted to compress a spoken message into a sequence of coded speech event feature signals which are transmitted via utilization device 285 to a synthesizer. In the synthesizer, the speech event feature signals and the combining coefficients of the message are decoded and recombined to form the message log area parameter signals. These log area parameter signals are then utilized to produce a replica of the original message. 
     FIG. 9 depicts a block diagram of a speech synthesizer circuit illustrative of the invention and FIG. 10 shows a flow chart illustrating its operation. Store 915 of FIG. 9 is adapted to store the successive coded speech event feature signals and combining signals received from utilization device 285 of FIG. 2 via line 901 and interface circuit 904. Store 920 receives the sequence of excitation signals required for synthesis via line 903. The excitation signals may comprise a succession of pitch period and voiced/unvoiced signals generated responsive to the voice message by methods well known in the art or may comprise a sequence of multi-pulse excitation signals as described in U.S. patent application Ser. No. 326,371 filed Dec. 1, 1982. Microprocessor 910 is adapted to control the operation of the synthesizer and may be the aforementioned Motorola-type MC68000 integrated circuit. LPC feature signal store 925 is utilized to store the successive log area parameter signals of the spoken message which are formed from the speech event feature signals and combining signals of store 915. Formation of a replica of the spoken message is accomplished in LPC synthesizer 930 responsive to the LPC feature signals from store 925 and the excitation signals from store 920 under control of microprocessor 910. 
     The synthesizer operation is directed by microprocessor 910 under control of permanently stored instruction codes resident in a read only memory associated therewith. These instruction codes are listed in FORTRAN language form in Appendix F. The operation of the synthesizer is described in the flow chart of FIG. 10. Referring to FIG. 10, The coded speech event feature signals, the corresponding combining signals, and the excitation signals of the spoken message are received by interface 904 and are transferred to speech event feature signal and combining coefficient signals store 915 and to excitation signal store 920 as per box 1010. The log area parameter signal index I is then reset to one in processor 910 (box 1020) so that the reconstruction of the first log area feature signal y 1  (n) is initiated. 
     The formation of the log area signal requires combining the speech event feature signals with the combining coefficients of index I in accordance with equation 1. Speech event feature signal location counter L is reset to one by processor 910 as per box 1025 and the current speech event feature signal samples are read from store 915 (box 1030). The signal sample sequence is filtered to smooth the speech event feature signal as per (box 1035) and the current log area parameter signal is partially formed in box 1040. Speech event location counter L is incremented to address the next speech event feature signal in store 915 (box 1045) and the occurrence of the last feature signal is tested in decision box 1050. Until the last speech event feature signal has been processed, the loop including boxes 1030 through 1050 is iterated so that the current log area parameter signal is generated and stored in LPC feature signal store 925 under control of processor 910. 
     Upon storage of a log area feature signal in store 925, box 1055 is entered from box 1050 and the log area index signal I is incremented (box 1055) to initiate the formation of the next log area parameter signal. The loop from box 1030 through box 1050 is reentered via decision box 1060. After the last log area parameter signal is stored, processor 910 is conditioned as per the instruction codes described in Appendix F to cause a replica of the spoken message to be formed in LPC synthesizer 930. 
     The synthesizer circuit of FIG. 9 may be readily modified to store the speech event feature signal sequences corresponding to a plurality of spoken messages and to selectively generate replicas of these messages by techniques well known in the art. For such an arrangement, the speech event feature signal generating circuit of FIG. 2 may receive a sequence of predetermined spoken messages and utilization device 285 may comprise a arrangement to permanently store the speech event feature signals and corresponding combining coefficients for the messages and to generate a read only memory containing said spoken message speech event and combining signals. The read only memory containing the coded speech event and combining signals can be inserted as store 915 in the synthesizer circuit of FIG. 9. 
     The invention has been described with reference to a particular embodiment illustrative thereof. It is to be understood, however, that various modifications and changes may be made by one skilled in the art without departing from the spirit and scope of the invention. 
     
         ______________________________________APPENDIX A______________________________________c LPC ANALYSIS (FIG. 3)  common /SPSTOR/ nsampl,s(8000)  common /ARSTOR/ nframe,area(500,16),av(16)  real rc(16),ar(17),avg(16)  data (avg(i),i=1,16)/  &amp;-0.60,1.60,0.50,1.30,0.50,0.60,0.20,0.10,  &amp;+0.10,0.10,0.40,0.40,0.30,0.30,0.20,0.10/  rewind 11  read(11)nsampl,s  call scopy(16,avg,av)  x=0.0  do5n=1,nsampl  x=s(n)5      s(n)=s(n)-0.5*x  nframe=1  n=1  nss=1100    continue  if(nss+160.gt.nsampl)goto1  if(nss.gt.16)call lpcanl(s(nss-16),176,rc)  if(nss.le.16)call lpcanl(s(nss),160+(16-nss),rc)  call rcnlar(rc,16,ar)  do2i=1,162      area(n,i)=ar(i)  nss=nss+16  n=n+1  goto1001      continue  N=n-1  do4i=1,n  do6k=1,166      area(n,k)=area(n,k)-av(k)4      continue  nframe=N  rewind 40  write(40)nframe,area,av  endfile 40  stop  endcCHLSKY Cholesky Decomposition  Subroutine CHLSKY (a,n,t)  dimension a(n,n),t(n)  do100i=1,n  do100j=1,i  sm=a(j,i)  if(j.eq.1)goto102  do101k=1,j-1101    sm=sm-a(i,k)*a(j,k)102    if(j.ne.i)goto103  t(j)=sqrt(sm)  t(j)=1./t(j)  goto100103    a(i,j)=sm*t(j)100    continue500    do400i=1,n400    a(i,i)=1./t(i)  return  endcCOVLPC Covariance LPC Analysis  Subroutine COVLPC (phi,shi,np,rc,ps)  dimension phi(np,np),shi(np),rc(np),d(17)  call chlsky(phi,np,rc)  call lwrtrn(phi,np,rc,shi)  ee=ps  do3i=1,np  ee=ee-rc(i)*rc(i)  d(i)=sqrt(ee)3      continue4      continue  rc(1)=-rc(1)/sqrt(ps)  do5i=2,np5      rc(i)=-rc(i)/d(i-1)  return  endcLPCANL LPC Analysis Program  Subroutine LPCANL (s,ls,c)  real s(1),c(1)  real p(17)  real phi(16,16),shi(16)  real w(160)  data init/0/  if(init.gt.0)goto100  do1i=1,1601      w(i)=0.5-0.5*cos(2.0*3.14159*(i-1)/160)  init=1100    continue  np=16c+++    Compute Covariance Matrix and Correlation Vectorc+++    ps = speech energy c+++ shi = correlationvector c+++ phi = covariance matrix  ps=tdot(s(np+1),s(np+1),w,ls-np)  do2i=1,np  shi(i)=tdot(s(np+1),s(np+1-i),w,ls-np)  do2j=1,i  sm=tdot(s(np+1-i),s(np+1-j),w,ls-np)  phi(i,j)=sm  phi(j,i)=sm2      continue  do4i=1,np4      p(i)=phi(i,i)  call chlsky(phi,np,c)  call lwrtrn(phi,np,c,shi)  ee=ps  do5i=1,np  ee=ee-c(i)*c(i)5      continue  pre=ee*0.10  do6i=1,np  do6j=i,np6      phi(j,i)=phi(i,j)  do7i=1,np  phi(i,i)= p(i)+pre*0.375  if(i.ge.2)phi(i,i-1)=phi(i,i-1)-0.25*pre  if(i.ge.3)phi(i,i-2)=phi(i,i-2)+0.0625*pre  if(i.lt.np)phi(i,i+1)=phi(i,i+1)-0.25*pre  if(i.lt.np-1)phi(i,i+2)=phi(i,i+2)+0.0625*pre7      continue  shi(1)=shi(1)-0.25*pre  shi(2)=shi(2)+0.0625*pre  ps=ps+pre*0.375  call covlpc(phi,shi,np,c,ps)  return  endcLWRTRN Solve Lower Triangular Equations  Subroutine LWRTRN (a,n,x,y)  dimension a(n,n),x(1),y(1)  x(1)=y(1)/a(1,1)  do1i=2,n  sm=y(i)  do2j=2,i2      sm=sm-a(i,j-1)*x(j-1)1      x(i)=sm/a(i,i)  return  endcRCNLAR Convert Reflection Coefficients to Normalized LogAreas  Subroutine RCNLAR (rc,np,area)  real rc(np),area(np)  call reflar(rc,np,area)  do1i=1,np1      area(i)=-alog(area(i)/area(np+1))  return  endcREFLAR Convert Reflection Coefficients to Area  Subroutine REFLAR (rc,nrc,ar)  dimension rc(nrc),ar(nrc)  ar(1)=1.0  do32i=2,nrc+132     ar(i)=ar(i-1)*(1+rc(i-1))/(1-rc(i-1))  return  endcSCOPY Copy A to B  Subroutine SCOPY (n,x,y)  real x(n),y(n)  do1i=1,n1      y(i)=x(i)  return  endcTDOT Tripple Dot Product Function  Function tdot(x,y,z,n)  real x(n),y(n),z(n)  tdot=0  do1i=1,n1      tdot=tdot+x(i)*y(i)*z(i)  return  end______________________________________ 
    
     
         ______________________________________APPENDIX B______________________________________c Timing Analysis (FIG. 4)common /ARSTOR/ nframe,area(500,16),av(16)common /TIMING/ lval,nu(160)common /LSSTOR/lmax,loc(20)real ax(16,16),bx(10,10)real v(16,16),ev(125,16),dev(16)real u(125,4),wu(125,4)real z(125,16),phi(125)data np/16/,inctim/5/,ltsegm/125/,dtpar/0.002/rewind 40read(40)nframe,area,avL=1n=1100  continuec+++  Set Window for Timing Analysisn1=n-(ltsegm-1)/2n2=n+(ltsegm-1)/2n1=max0(n1,1)n2=min0(n2,nframe)ltseg=n2-n1+1if(ltseg.lt.np+10)ltseg=np+10n1=min0(n1,nframe-ltseg+1)c+++  Read New Frames of Area Datado101k=1,np101  call scopy(ltseg,area(n1,k),z(1,k))c+++  Compute Principal Components of zncomp=4do1i=1,npdo1j=1,iax(i,j)=sdot(ltseg,z(1,i),z(1,j))1    ax(j,i)=ax(i,j)call svd(ax,np,16,np,ev,np,dev,v,np,16)do2j=1,ltsegdo2i=1,ncompsm=0do4k=1,np4    sm=sm+z(j,k)*v(k,i)2    u(j,i)=sm/dev(i)c+++  Select Nearest Most Compact Component phido12j=1,ncompdo11i=1,ltsegwtf=(i-n+n1-1)11   wu(i,j)=u(i,j)*wtf12   continuedo13i=1,ncompdo13j=1,ibx(i,j)=sdot(ltseg,wu(1,i),wu(1,j))13   bx(j,i)=bx(i,j)call svd(bx,ncomp,10,ncomp,ev,ncomp,dev,v,ncomp,16)phimax=0imax=1do42i=1,ltsegsm=0do41k=1,ncomp41   sm=sm+u(i,k)*v(k,ncomp)if(abs(sm).gt.phimax)imax=iphimax=amax1(phimax,abs(sm))42   phi(i)=smif(phi(imax).lt.0.0)call chgsgn(phi,ltseg)nu(L)=n1+imax-nL=L+1n=n+5if(n.lt.nframe)goto100lmax=L-1call zercrsdo20l=1,lmax20   loc(l)=(loc(l)-1)*inctim+1rewind 45write(45)lval,nuendfile 45rewind 50write(50)lmax,locendfile 50stopendcCHGSGN change sign of an array w)*(y+Subroutine CHGSGN (x,1x)dimension x(1x)do1i=1,lx1    x(i)=-x(i)returnendcSCOPY Copy A to BSubroutine SCOPY (n,x,y)real x(n),y(n)do1i=1,n1    y(i)=x(i)returnendcSDOT Inner Product of Two VectorsFunction SDOT (n,x,y)real x(n),y(n)sdot=0do1i=1,n1    sdot=sdot+x(i)*y(i)returnendc SVD Singular-Value Decomposition of a Rectangular MatrixSubroutine SVD(a,m,mmax,n,u,nu,s,v,nv,nmax)dimension a(mmax,n),u(mmax,n),v(nmax,n)integer m,n,p,nu,nvdimension s(n)dimension b(100),c(100),t(100)data eta,tol/1.5e-8,1.e-31/p=01    np=n+pn1=n+1c householder reductionc(1)=0.e0k=110   k1=k+1c elimination of a(i,k), i=k+1,...,mz=0.e0do 20 i=k,m20   z=z+a(i,k)**2b(k)=0.e0if(z.le.tol) goto 70z=sqrt(z)b(k)=zw=abs(a(k,k))q=1.e0if(w.ne.0.e0) q=a(k,k)/wa(k,k)=q*(z+w)if(k.eq.np) goto 70do 50 j=k1,npq=0.e0do 30 i=k,m30   q=q+a(i,k)*a(i,j)q=q/(z*(z+w))do 40 i=k,m40   a(i,j)=a(i,j)-q*a(i,k)50   continuec phase transformationq=-a(k,k)/abs(a(k,k))do 60 j=k1,np60   a(k,j)=q*a(k,j)c elimination of a(k,j), j=k+2,...,n70   if(k.eq.n) goto 140z=0.e0do 80 j=k1,n80   z=z+a(k,j)**2c(k1)=0.e0if(z.le.tol) goto 130Z=sqrt(z)c(k1)=zw=abs(a(k,k1))q=1.e0if(w.ne.0.e0) q=a(k,k1)/wa(k,k1)=q*(z+w)do 110 i=k1,mq=0.e0do 90 j=k1,n90   q=q+a(k,j)*a(i,j)q=q/(z*(z+w))do 100 j=k1,n100  a(i,j)=a(i,j)-q*a(k,j)110  continuec phase transformationq=-a(k,k1)/abs(a(k,k1))do 120 i=k1,m120  a(i,k1)=a(i,k1)*q130  k=k1goto 10c tolerance for negligible elements140  eps=0.e0do 150 k=1,ns(k)=b(k)t(k)=c(k)150  eps=amax1(eps,s(k)+t(k))eps=eps*etac initialization of u and vif(nu.eq.0) qoto 180do 170 j=1,nudo 160 i=1,m160  u(i,j)=0.e0170  u(j,j)=1.e0180  if(nv.eq.0) goto 210do 200 j=1,nvdo 190 i=1,n190  v(i,j)=0.e0200  v(j,j)=1.e0c qr diagonalization210  do 380 kk=1,nk=n1-kkc test for split220  do 230 ll=1,kl=k+1-llif(abs(t(l)).le.eps) goto 290if(abs(s(l-1)).le.eps) goto 240230  continuec cancellation240  cs=0.e0sn=1.e0l1=l-1do 280 i=l,kf=sn*t(i)t(i)=cs*t(i)if(abs(f).le.eps) goto 290h=s(i)w=sqrt(f*f+h*h)s(i)=wcs=h/wsn=-f/wif(nu.eq.0) goto 260do 250 j=1,nx=u(j,l1)y=u(j,i)u(j,l1)=x*cs+y*sn250  u(j,i)=y*cs-x*sn260  if(np.eq.n) goto 280do 270 j=n1,npq=a(l1,j)r=a(i,j)a(l1,j)=q*cs+r*sn270  a(i,j)=r*cs-q*sn280  continuec test for convergence290  w=s(k)if(l.eq.k) goto 360c origin shiftx=s(l)y=s(k-1)g=t(k-1)h=t(k)f=((y-w)*(y w)+(g-h)*(g+h))/(2.e0*h*y)g=sqrt(f*f+1.e0)if(f.lt.0.e0) g=-gf=((x-w)*(x+w)+(y/(f+g)-h)*h)/xc qr stepcs=1.e0sn=1.e0l1=l+1do 350 i=l1,kg=t(i)y=s(i)h=sn*gg=cs*gw=sqrt(h*h+f*f)t(i-1)=wcs=f/wsn=h/wf=x*cs+g*sng=g*cs-x*snh=y*sny=y*csif(nv.eq.0) goto 310do 300 j=1,nx=v(j,i-1)w=v(j,i)v(j,i-1)=x*cs+w*sn300  v(j,i)=w*cs-x*sn310  w=sqrt(h*h+f*f)s(i-1)=wcs=f/wsn=h/wf=cs*g+sn*yx=cs*y-sn*gif(nu.eq.0) goto 330do 320 j=1,ny=u(j,i-1)w=u(j,i)u(j,i-1)=y*cs+w*sn320  u(j,i)=w*cs-y*sn330  if(n.eq.np) goto 350do 340 j=n1,npq=a(i-1,j)r=a(i,j)a(i-1,j)=q*cs+r*sn340  a(i,j)=r*cs-q*sn350  continuet(l)=0.e0t(k)=fs(k)=xgoto 220c convergence360  if(w.ge.0.e0) goto 380s(k)=-wif(nv.eq.0) goto 380do 370 j=1,n370  v(j,k)=-v(j,k)380  continuec sort singular valuesdo 450 k=1,ng=-1.e0j=kdo 390 i=k,nif(s(i).le.g) goto 390g=s(i)j=i390  continueif(j.eq.k) goto 450s(j)=s(k)s(k)=gif(nv.eq.0) goto 410do 400 i=1,nq=v(i,j)v(i,j)=v(i,k)400  v(i,k)=q410  if(nu.eq.0) goto 430do 420 i=1,nq= u(i,j)u(i,j)=u(i,k)420  u(i,k)=q430  if(n.eq.np) goto 450do 440 i=n1,npq=a(j,i)a(j,i)=a(k,i)440  a(k,i)=q450  continuec back transformationif(nu.eq.0) goto 510do 500 kk=1,nk=n1-kkif(b(k).eq.0.e0) goto 500q=-a(k,k)/abs(a(k,k))do 460 j=1,nu460  u(k,j)=q*u(k,j)do 490 j=1,nuq=0.e0do 470 i=k,m470  q=q+a(i,k)*u(i,j)q=q/(abs(a(k,k))*b(k))do 480 i=k,m480  u(i,j)=u(i,j)-q*a(i,k)490  continue500  continue510  if(nv.eq.0) goto 570if(n.lt.2) goto 570do 560 kk=2,nk=n1-kkk1=k+1if(c(k1).eq.0.e0) goto 560q=-a(k,k1)/abs(a(k,k1))do 520 j=1,nv520  v(k1,j)=q*v(k1,j)do 550 j=1,nvq=0.e0do 530 i=k1,n530  q=q+a(k,i)*v(i,j)q=q/(abs(a(k,k1))*c(k1))do 540 i=k1,n540  v(i,j)=v(i,j)-q*a(k,i)550  continue560  continue570  returnendcZERCRS Zero Crossings of Timing SignalSubroutine ZERCRScommon /TIMING/ lval,nu(160)common /LSSTOR/lmax,loc(20)im=1lmax=1loc(lmax)=1100  continuei1=imiz=0 c+++  Determine the Next Peakdo1i=im+1,lval-1ip=iif(nu(i).le.nu(i+1))goto1if(nu(i).lt.nu(i-1))goto1if(nu(i).gt.nu(i-1))goto61if(i-2.gt.0.and.nu(i).gt.nu(i-2))goto61if(i-3.gt.0.and.nu(i).gt.nu(i-3))goto61goto161   continuegoto111    continuegoto50c+++  Determine the Next Minimum11   do2i=ip,lval-1im=iif(nu(i).gt.nu(i+1))goto2if(nu(i).ge.nu(i-1))goto2goto122    continuegoto5012   continueif(im-ip.lt.2)goto100c+++  Find the Nearest Zero Crossingdo3i=ip,imiz=iif(nu(i).gt.0.0.and.nu(i+1).le.0.0)goto133    continueif(nu(im).gt.0.0)iz=imif(nu(ip).lt.0.0)iz=imgoto3013   continue30   continuelmax=lmax+1loc(lmax)=(iz)goto10050   continuelmax=lmax+1loc(lmax)=lvalreturnend______________________________________ 
    
     
                       APPENDIX C______________________________________c       Generate Speech Event Feature Signals (FIG. 6)   common /ARSTOR/ nframe,area(500,16),av(16)   common /TIMING/ lval,nu(160)   common /LSSTOR/ lmax,loc(20)   common /PHISTO/ lbeg(20),lend(20),phi(125,20)   real ax(16,16),bx(10,10)   real v(16,16),ev(125,16),dev(16)   real u(125,4),wu(125,4)   real z(125,16)   data np/16/,inctim/5/,ltsegm/125/,dtpar/0.002/   I=1   rewind 40   read(40)nframe,area,av   rewind 45   read(45)lval,nu   rewind 50   read(50)lmax,loc100     continue   l=I c+++ Set Window for Timing Analysis   n1=max0(1,loc(1))   n2=min0(loc(lmax),lval)   if(l.gt.2)n1=loc(1-2)   if(l.le.lmax-2)n2=loc(l+2)   ltseg=n2-n1+1   if(ltseg.lt.np+10)ltseg=np+10   n1=min0(n1,nframe-ltseg+1)   lbeg(l)=n1   lend(l)=n2c+++    Determine Number of Speech Events in the Window   m=0   do32j=1,lmax   if(loc(l).lt.lbeg(l))goto32   if(loc(l).gt.lend(l))goto32   m=m+132      continue   m=min0(6,m)   m=max0(4,m)c+++    Read New Frames of Area Data   do101k=1,np101     call scopy(ltseg,area(n1,k),z(1,k))c+++    Compute Principal Components of z   ncomp=m   do1k=1,np   do1j=1,k   ax(k,j)=sdot(ltseg,z(1,k),z(1,j))1       ax(j,k)=ax(k,j)   call svd(ax,np,16,np,ev,np,dev,v,np,16)   do2n=1,ltseg   do2j=1,m   sm=0   do4k=1,np4       sm=sm+z(n,k)*v(k,j)2       u(n,k)=sm/dev(k)c+++    Select Nearest Most Compact Component phi   do12j=1,m   do11n=1,ltseg   wtf=(n-loc(l)+n1-1)11      wu(n,j)=u(n,j)*wtf12      continue   do13j=1,m   do13k=1,j   bx(j,k)=sdot(ltseg,wu(1,j),wu(1,k))13      bx(k,j)=bx(j,k)   call svd(bx,m,10,m,ev,m,dev,v,m,16)   phimax=0   nmax=1   do42n=1,ltseg   sm=0   do41j=1,m41      sm=sm+u(n,j)*v(j,m)   if(abs(sm).gt.phimax)nmax=n   phi(nmax)=amax1(phimax,abs(sm))42      phi(n,I)=sm   if(phimax.lt.0.0)call chgsgn(phi(1,I),ltseg)   I=I+1   if(I.lt.lmax)goto100   rewind 55   write(55)lbeg,lend,phi   endfile 55   stop   endcCHGSGN change sign of an array   Subroutine CHGSGN (x,lx)   dimension x(lx)   do1i=1,lx1       x(i)=-x(i)   return   endcSCOPY  Copy A to B   Subroutine SCOPY (n,x,y)   real x(n),y(n)   do1i=1,n1       y(i)=x(i)   return   endcSDOT   Inner Product of Two Vectors   Function SDOT (n,x,y)   real x(n),y(n)   sdot=0   do1i=1,n1       sdot=sdot+x(i)*y(i)   return   endc SVD   Singular-Value Decomposition of a   Rectangular Matrix   Subroutine SVD(a,m,mmax,n,u,nu,s,v,nv,nmax)   dimension a(mmax,n),u(mmax,n),v(nmax,n)   integer m,n,p,nu,nv   dimension s(n)   dimension b(100),c(100),t(100)   data eta,tol/1.5e-8,1.e-31/   p=01       np=n+p   n1=n+1c       householder reduction   c(1)=0.e0   k=110      k1=k+1c       elimination of a(i,k), i=k+1, . . . ,m   z=0.e0   do 20 i=k,m20      z=z+a(i,k)**2   b(k)=0.e0   if(z.le.tol) goto 70   z=sqrt(z)   b(k)=z   w=abs(a(k,k))   q=1.e0   if(w.ne.0.e0) q=a(k,k)/w   a(k,k)=q*(z+w)   if(k.eq.np) goto 70   do 50 j=k1,np   q=0.e0   do 30 i=k,m30      q=q+a(i,k)*a(i,j)   q=q/(z*(z+w))   do 40 i=k,m40      a(i,j)=a(i,j)-q*a(i,k)50      continuec       phase transformation   q=-a(k,k)/abs(a(k,k))   do 60 j=k1,np60      a(k,j)=q*a(k,j)c       elimination of a(k,j), j=k+2, . . . ,n70      if(k.eq.n) goto 140   z=0.e0   do 80 j=k1,n80      z=z+a(k,j)**2   c(k1)=0.e0   if(z.le.tol) goto 130   z=sqrt(z)   c(k1)=z   w=abs(a(k,k1))   q=1.e0   if(w.ne.0.e0) q= a(k,k1)/w   a(k,k1)=q*(z+w)   do 110 i=k1,m   q=0.e0   do 90 j=k1,n90      q=q+a(k,j)*a(i,j)   q=q/(z*(z+w))   do 100 j=k1,n100     a(i,j)=a(i,j)-q*a(k,j)110     continuec       phase transformation   q=-a(k,k1)/abs(a(k,k1))   do 120 i=k1,m120     a(i,k1)=a(i,k1)*q130     k=k1   goto 10c       tolerance for negligible elements140     eps=0.e0   do 150 k=1,n   s(k)=b(k)   t(k)=c(k)150     eps=amax1(eps,s(k)+t(k))   eps=eps*etac       initialization of u and v   if(nu.eq.0) goto 180   do 170 j=1,nu   do 160 i=1,m160     u(i,j)=0.e0170     u(j,j)=1.e0180     if(nv.eq.0) goto 210   do 200 j=1,nv   do 190 i=1,n190     v(i,j)=0.e0200     v(j,j)=1.e0c gr    diagonalization210     do 380 kk=1,n   k=n1-kkc       test for split220     do 230 ll=1,k   l=k+1-ll   if(abs(t(l)).le.eps) goto 290   if(abs(s(l-1)).le.eps) goto 240230     continuec       cancellation240     cs=0.e0   sn=1.e0   l1=l-1   do 280 i=l,k   f=sn*t(i)   t(i)=cs*t(i)   if(abs(f).le.eps) goto 290   h=s(i)   w=sqrt(f*f+h*h)   s(i)=w   cs=h/w   sn=-f/w   if(nu.eq.0) goto 260   do 250 j=1,n   x=u(j,l1)   y=u(j,i)   u(j,l1)=x*cs+y*sn250     u(j,i)=y*cs-x*sn260     if(np.eq.n) goto 280   do 270 j=n1,np   q=a(l1,j)   r=a(i,j)   a(l1,j)=q*cs+r*sn270     a(i,j)=r*cs-q*sn280     continuec       test for convergence290     w=s(k)   if(l.eq.k) goto 360c       origin shift   x=s(l)   y=s(k-1)   g=t(k-1)   h=t(k)   f=((y-w)*(y+w)+(g-h)*(g+h))/(2.e0*h*y)   g=sqrt(f*f+1.e0)   if(f.lt.0.e0) g=-g   f=((x-w)*(x+w)+(y/(f+g)-h)*h)/xc       qr step   cs=1.e0   sn=1.e0   l1=l+1   do 350 i=l1,k   g=t(i)   y=s(i)   h=sn*g   g=cs*g   w=sqrt(h*h+f*f)   t(i-1)=w   cs=f/w   sn=h/w   f=x*cs+g*sn   g=g*cs-x*sn   h=y*sn   y=y*cs   if(nv.eq.0) goto 310   do 300 j=1,n   x=v(j,i-1)   w= v(j,i)   v(j,i-1)=x*cs+w*sn300     v(j,i)=w*cs-x*sn310     w=sqrt(h*h+f*f)   s(i-1)=w   cs=f/w   sn=h/w   f=cs*g+sn*y   x=cs*y-sn*g   if(nu.eq.0) goto 330   do 320 j=1,n   y=u(j,i-1)   w=u(j,i)   u(j,i-1)=y*cs+w*sn320     u(j,i)=w*cs-y*sn330     if(n.eq.np) goto 350   do 340 j=n1,np   q=a(i-1,j)   r=a(i,j)   a(i-1,j)=q*cs+r*sn340     a(i,j)=r*cs-q*sn350     continue   t(l)=0.e0   t(k)=f   s(k)=x   goto 220c       convergence360     if(w.ge.0.e0) goto 380   s(k)=-w   if(nv.eq.0) goto 380   do 370 j=1,n370     v(j,k)=-v(j,k)380     continuec       sort singular values   do 450 k=1,n   g=-1.e0   j=k   do 390 i=k,n   if(s(i).le.g) goto 390   g=s(i)   j=i390     continue   if(j.eq.k) goto 450   s(j)=s(k)   s(k)=g   if(nv.eq.0) goto 410   do 400 i=1,n   q=v(i,j)   v(i,j)=v(i,k)400     v(i,k)=q410     if(nu.eq.0) goto 430   do 420 i=1,n   q=u(i,j)   u(i,j)=u(i,k)420     u(i,k)=q430     if(n.eq.np) goto 450   do 440 i=n1,np   q=a(j,i)   a(j,i)=a(k,i)440     a(k,i)=q450     continuec       back transformation   if(nu.eq.0) goto 510   do 500 kk=1,n   k=n1-kk   if(b(k).eq.0.e0) goto 500   q=-a(k,k)/abs(a(k,k))   do 460 j=1,nu460     u(k,j)=q*u(k,j)   do 490 j=1,nu   q=0.e0   do 470 i=k,m470     q=q+a(i,k)*u(i,j)   q=q/(abs(a(k,k))*b(k))   do 480 i=k,m480     u(i,j)=u(i,j)-q*a(i,k)490     continue500     continue510     if(nv.eq.0) goto 570   if(n.lt.2) goto 570   do 560 kk=2,n   k=n1-kk   k1=k+1   if(c(k1).eq.0.e0) goto 560   q=-a(k,k1)/abs(a(k,k1))   do 520 j=1,nv520     v(k1,j)=q*v(k1,j)   do 550 j=1,nv   q=0.e0   do 530 i=k1,n530     q=q+a(k,i)*v(i,j)   q=q/(abs(a(k,k1))*c(k1))   do 540 i=k1,n540     v(i,j)=v(i,j)-q*a(k,i)550     continue560     continue570     return   end______________________________________ 
    
     
                       APPENDIX D______________________________________   common /PHISTO/ lbeg(20),lend(20),phi(125,20)   common /LSSTOR/ lmax,loc(20)   real temp(25),xp(50),yp(50),ap(25)   real R(20)   integer dtmsec   rewind 55   read(55)lbeg,lend,phi   rewind 15   I=1100     continue   loczl=loczer(lend(I)-lbeg(I)+1,1,phi(1,I),1,0.10)   loczr=loczer(lend(I)-lbeg(I)+1,2,phi(1,I),1,0.10)   loczl=max0(1,loczl)   if(loczr.eq.0)loczr=lend(I)-lbeg(I)   k=0   do101=loczl,loczr,5   k=k+110      temp(k)=phi(l,I)   call rftpol(temp,k,xp,yp,50)   do12j=1,512      ap(j)=sqrt(xp(j)*kp(j)+yp(j)*yp(j))   pwr=sdot(50,ap,ap)   pp=pwr   kl=0   do5k=2,25   pp=pp-ap(k-1)*ap(k-1)   if(pp/pwr.gt.0.02)kl=k5       continue   kl=max0(kl,4)   dtmsec=max0((125/(kl-1))*2,12)   R(I)=1000.0/dtmsec   k=0   do8l=loczl,loczr,dtmsec/2   k=k+18       temp(k)=phi(l,I)   l1=loczl+lbeg(I)-1   write(15)l1,k,kl,(temp(l),l=1,k)   I=I+1   if(I.lt.lmax)goto100   endfile 15   stop   endcFTRANS Fourier Transform Routine   Subroutine FTRANS (x,nx,freq,smpint,rp,xp)   dimension x(nx)   dd=2.0*3.141592653*freq*smpint   cosr1=cos(dd)   cosr2=cos(2.0*dd)   sinr1=-sin(dd)   sinr2=-sin(2.0*dd)   b1=-2*cosr1   rp=0.0   xp=0.0   do1n=1,nx   cosr=- b1*cosr1-cosr2   sinr=-b1*sinr1-sinr2   cosr2= cosr1   cosr1=cosr   sinr2=sinr1   sinr1=sinr   rp=rp+x(n)*cosr   xp=xp+x(n)*sinr1       continue   return   endcLOCZER Locate Left or Right Zero Crossing of a Function   Function LOCZER (lx,iop,x,inc,frc)   real x(lx)   xmax=x(1)   maxl=1   do7i=2,lx   if(x(i).le.xmax)goto7   maxl=i   xmax=x(i)7       continue   thr=frc*x(maxl)   goto(1,2),iop1       do10i=1,maxl-1,inc   j=maxl+1-i   if(x(j).gt.thr.and.x(j-1).le.thr)goto1510      continue   loczer=0   return15      loczer=j-1   return2       do20i=maxl,lx-1,inc   if(x(i).gt.thr.and.x(i+1).le.thr)goto2520      continue   loczer=0   return25      loczer=i+1   return   endcRFTPOL Regular Fourier Transform Routine   Subroutine RFTP0L (x,lx,rp,xp,nftv)   dimension x(lx),rp(nftv),xp(nftv)   df=1.0/nftv   mftv=nftv/2   do1i=2,mftv   call ftrans(x,(lx),(i-1)*df,1.0,xp(i),xp(nftv+2-i))1       xp(nftv+1-i)=-xp(nftv+1-i)   call ftrans(x,(lx),mftv*df,1.0,rp1,xp1)   call ftrans(x,(lx),0.0,1.0,rp0,xp0)   xp1=-xp1   xp0=-xp0   do2i=2,mftv   rp(nftv+2-i)=xp(i)   rp(i)=xp(i)2       xp(i)=-xp(nftv+2-i)   rp(1)=rp0   rp(mftv+1)=rp1   xp(1)=xp0   xp(mftv+1)=xp1   return   endcSDOT   Inner Product of Two Vectors   Function SDOT (n,x,y)   real x(n),y(n)   sdot=0   do1i=1,n1       sdot=sdot+x(i)*y(i)   return   end______________________________________ 
    
     
                       APPENDIX E______________________________________   common /ARSTOR/ nframe,area(500,16),av(16)   common /PHISTC/ lbeg(20),lend(20),phi(125,20)   common /LSSTOR/lmax,loc(20)   real G(20,20),C(20,16),GINV(20,20),a(16,20)   data np/16/,inctim/5/,ltsegm/125/,dtpar/0.002/   rewind 40   read(40)inframe,area,av   rewind 55   read(55)lbeg,lend,phi   rewind 50   read(50)lmax,locc+++    Compute Speech Event Feature Signal CorrelationMatrix   call zero(G,400)   do15i=1,lmax   do15j=i,lmax   if(lbeg(j).gt.lend(i))goto15   if(lbeg(i).gt.lend(j))goto15   if(lend(i).ge.lbeg(j))ltseg=lend(i)-lbeg(j)+1   if(lend(j).ge.lbeg(i))ltseg=lend(j)-lbeg(i)+1   i1=max0(lbeg(j)-lbeg(i)+1,1)   j1=max0(lbeg(i)-lbeg(j)+1,1)   G(i,j)=sdot(ltseg,phi(i1,i),phi(j1,j))15      G(j,i)=G(i,j)c++++   Compute Y-PHI Correlation Matrix   do20i=1,np   do11m=1,lmax11      C(i,m)=sdot(lend(m)-lbeg(m)+1,area(lbeg(m),i),phi(1,m))20      continuec++++   Generate Combining Coefficients   call matinv(G,GINV,lmax)   do35i=1,np   do35k=1,lmax   sm=0   do30m=1,lmax30      sm=sm+GINV(k,m)*C(i,m)35      a(i,k)=sm   rewind 60   write(60)a   endfile 60   stop   endcMATINV Inverse of a Positive-Definite Matrix   Subroutine MATINV (a,b,n)   real a(n,n),b(n,n)   m=n   mp1=m+1   do100j=1,m   sm=a(j,j)   if(j.eq.1)goto102   do101k=1,j-1101     sm=sm-b(j,k)*b(j,k)102     continue   b(j,j)=sqrt(sm)   xl=1./b(j,j)   if(j.eq.m)goto110   do100i=j+1,m   sm=a(i,j)   if(j.eq.1)goto104   do103k=1,j-1103     sm=sm-b(i,k)*b(j,k)104     continue100     b(i,j)=sm*xl110     continue   do350j=1,m350     b(j,j)=1./b(j,j)   do200j=1,m-1   do200i=j+1,m   sm=0.   do202k=j,i-1202     sm=sm+b(i,k)*b(k,j)200     b(i,j)=-sm*b(i,i)   do300j=1,m   jm=mp1-jm   do300i=1,jm   sm=0.   do302k=jm,m302     sm=sm+b(k,i)*b(k,jm)   b(i,jm)=sm300     continue   do400i=1,m   do400j=1,i400     b(i,j)=b(j,i)   return   endcSDOT   Inner Product of Two Vectors   Function SDOT (n,x,y)   real x(n),y(n)   sdot=0   do1i=1,n1       sdot=sdot+x(i) y(i)   return   endcZERO   Zero An Array   Subroutine ZERO (x,n)   real x(n)   do1i=1,n1       x(i)=0.0   return   end______________________________________ 
    
     
         ______________________________________APPENDIX F______________________________________common /PHIST0/ lbeg(20),lend(20),phi(125)common /ARSTOR/ nframe,area(500,16),av(16)common /RCSTOR/ rcstor(16,100)real avg(16),amp(16,20),philm(25)real temp(500)real h(250),b(250)real exc(80),fmem(16),sp(80)integer dtmsecdata (avg(i),i=1,16)/&amp;-0.60,1.60,0.50,1.30,0.50,0.60,0.20,0.10,&amp;+0.10,0.10,0.40,0.40,0.30,0.30,0.20,0.10/datanp/16/,inctim/5/,ltsegm/125/,dtpar/0.002/,gamma/0.5/c+++    915  call scopy(np,avg,av)  rewind 60  read(60)amp  i=1200    continue  do1n=1,5001      area(n,i)=av(i)  rewind 15  L=1100    continue  call zero(philm,25)  read(15,end=250)l1,k,kl,(philm(j),j=1,k)  lbeg(L)=l1  lend(L)=l1+124  nframe=lend(L)  dtmsec=(125/(kl-1))*2  lh=4*(dtmsec/2)  ld=dtmsec/2  call haming(h,lh)  call zero(b,lh)  call intrpl(philm,k,temp,lh/2+125,h,lh,ld,b)  call scopy(125,temp(lh/2+1),phi)  do33j=lbeg(L),lend(L)33     area(j,i)=area(j,i)+amp(i,L)*phi(j-lbeg(L)+1)  L=L+1  goto100250    continue  i=i+1  if(i.le.np)goto200  do5i=1,np  do5n=1,nframe5      area(n,i)=exp(area(n,1)-area(n,i))  m=0  do10n=1,nframe,inctim  m=m+1  area(n,np+1)=exp(area(n,1))  area(n,1)=1  do6i=2,np+16      rcstor(i-1,m)=-(area(n,i-1)-area(n,i))/(area(n,i-  1)+area(n,i))10     continue  nspfr=mc+++    930 c+++ Synthesize Speech  rewind 21  call zero(fmem,16)  sp0=0  do300m=1,nspfr  read(20,end=500)exc  do30n=1,80  wps=rcstor(np,m)*fmem(1)+exc(n)  do3k=2,np  wps=wps+rcstor(np+1-k,m)*fmem(k)3      fmem(k-1)=fmem(k)-rcstor(np+1-k,m)*wps  fmem(np)=-wps  sp(n)=wps+gamma*sp030     sp0=sp(n)  write(21)sp300    continue500    endfile 21  stop  endcHAMING Haming Window  Subroutine HAMING (x,lx)  dimension x(1)  data lxp/0/  if(lx.eq.lxp)goto100  c1=cos(2.0*3.14159254/float(lx))  c1p=c1100    lxp=lx  c1=c1p  a=2.0*c1  c0=a*c1-1.0  do1n=1,lx  c2=a*c1-c0  x(n)=x(n)*(0.54-0.46*c2)  c0=c11      c1=c2  return  endcINTRPL Interpolate  Subroutine INTRPL (x,lx,y,ly,h,lh,ld,b)  dimension x(lx),y(ly),h(lh),b(lh)  k=0  xld=ld  do1n=1,ly,ld  k=k+1  xk=xld*x(k)  do2i=1,lh-12      b(i)=b(i+1)+xk*h(i)  b(lh)=xk*h(lh)  call scopy(ld,b,y(n))  call scopy(lh,b(ld),b)1      continue  return  endcSCOPY Copy A to B  Subroutine SCOPY (n,x,y)  real x(n),y(n)  do1i=1,n1      y(i)=x(i)  return  endcZERO Zero An Array  Subroutine ZERO (x,n)  real x(n)  do1i=1,n1      x(i)=0.0  return  end______________________________________