IMPROVED METHOD AND MEANS OF DETERMINING COEFFICIENTS FOR LINEAR PREDICTIVE CODING

Abstract: An improved method and means of determining reflection coefficients that characterize an electrical signal obtains characteristics of an all-zero inverse lattice filter. The reflection coefficients are obtained by filtering the signal, sampling the filtered signal, obtaining the elements of a correlation matrix from the samples, initializing values of matrices of forward residuals, backward residuals, and cross correlation of residuals, combining matrix elements to obtain a first reflection coefficient, removing from the forward, backward an cross-correlation matrices the effect of the first reflection coefficient, calculating from the revised matrices a second reflection coefficient, and repeating the calculations to the desired order.

Description: IMPROVED METHOD AND MEANS OP DETERMINING COEFFICIENTS FOR LINEAR PREDICTIVE CODING Background of the Invention This invention relates to linear predictive coding. In particular, it is an improved method and means of determining coefficients for linear predictive coding. Linear predictive coding is a method of analyzing a speech signal and characterizing that signal in terms of coefficients which can be encoded, broadcast, received, and decoded to recover a close approximation to the original signal. The existence of redundancies in speech makes it possible to use encoded descriptions of the speech that can be carried in a communication channel having a bandwidth that is less than the bandwidth of the speech. This is in distinct contrast to many well-known forms of converting speech into digital signals. Most of these methods require a bandwidth that is greater than the -bandwidth of the speech. Linear predictive coding (LPC) of speech begins conceptually with a model of the human speech-producing system. The model has a source of sound that is analogous to the vocal cords. That source is coupled acoustically to a stacked array of hollow cylindrical tubes that is analogous to the cavities of the throat and mouth in a human speaker. From the model, speech is characterized by four types of quantities; The first of these is a measure of whether speech is voiced or unvoiced. A voiced signal begins with an input from the vocal cords, while an unvoiced signal is produced by the action of the rest of the vocal tract on moving air alone. This produces the differences in sound between "s" which is unvoiced and its voiced equivalent V r for example. A second characteristic of the sound is the pitch, the fundamental frequency produced by the vocal cords in making a voiced sound. A third characteristic is the energy. Finally, the effect of the throat and mouth on either voiced or unvoiced sound is summarized by obtaining some measure of the transfer function of the vocal tract. Such a measure might be the reflection coefficients of the structure, the poles of the transfer function of the structure, the logarithmic area ratios (LAR's) of the structure, or any of several other well-known functions of such resonances. In addition, various mathematical transforms of these functions may have utility for particular purposes. The functions are interrelated so that any one set can be determined from a knowledge of any other set. The present invention is an improved method and means of determining quantities corresponding to reflection coefficients. The reflection coefficients are coefficients with a specific all pole filter structure known as a lattice filter. The reflection coefficients discussed here are the electrical analog of acoustical reflection coefficients. While the reflection coefficient is in general a complex quantity in which the imaginary portion is a measure of loss at a discontinuity, when determining the reflection coefficients that characterize a human vocal tract, the portions of reflection coefficients associated with loss are small enough compared to the real part that denotes lossless reflection that it is adequate to use a lossless model in which the reflection coefficients are real. One way of obtaining the reflection coefficients that characterize a sample of a signal such as speech is to determine the characteristics of an inverse lattice filter that will reproduce the signal when excited by an impulse. Examples of several approaches of performing such an analysis are given in an article entitled "Stable and Efficient Lattice Methods for Linear Prediction" by Makhoul in "IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. ASSP-25, No. 5, October, 1977. This article points out that an analysis based on the all-pole lattice filter is stable without windowing but at a computational cost that is several times the cost of the auto-correlation and covariance methods of calculation. What Makhoul refers to as the computational costs of computer analysis are proportional to the equipment costs of realizing a circuit for comparable analysis on a semiconductor chip. Summary of the Invention It is an object of the present invention to provide an improved method and means of determining reflection coefficients of a signal. It is a further object of the present invention to provide an improved method and means of determining parameters of an all-pole lattice filter that characterize an electrical signal. Other objects will become apparent in the course of a detailed description of the invention. An improved method and means of determining reflection coefficients that characterize an electrical signal obtains characteristics of an all-zero inverse lattice filter. The reflection coefficients are obtained by filtering the signal, sampling the filtered signal. obtaining the elements of a correlation matrix from the samples, initializing values of matrices of forward residual autocorrelations, backward residual autocorrelations, and cross correlation of residuals, combining matrix elements to obtain a first reflection coefficient, removing from the forward, backward and cross-correlation matrices the effect of the first reflection coefficient, calculating from the revised matrices a second reflection coefficient, and repeating the calculations to the desired order. Brief Description of the Drawings Fig. 1 is an overall block diagram of a circuit for the practice of the present invention. Fig. 2 is an expanded circuit diagram of the address calculator of Fig. 1. Fig. 3 is an expanded circuit diagram of the update calculator of Fig. 1. Fig. 4 is an expanded circuit diagram of the reflection-coefficient calculator of Fig. 1. Fig. 5 is a flowchart of a method for practicing the invention. Fig. 6 is a block diagram of a section of a typical lattice filter for the practice of the present invention. Detailed Description of the Invention Fig. 1 is an overall block diagram of a circuit for the practice of the invention. In Fig. 1 an electrical analog signal that is to be analyzed is applied at terminal 10. That signal will typically be an electrical analog of a voice signal, although it may be any electrical signal that exhibits redundancies analogous to those of speech. Examples of such other signals include video scans and seismic analysis records. Whatever the source, the signal at terminal 10 is applied to a filter 12, if necessary, to limit its bandwidth. If the bandwidth is already adequate, filter 12 may comprise a direct wire connection, or filter 12 may combine a bandpass filter with any of a number of systems of pre-emphasis that are commonly used in radio broadcasting. The output of filter 12, treated as described, is applied to analog-to-digital converter (ADC) 14. The digital output of ADC 14 will be separated into frames of a convenient length, of the order of tens of milliseconds. That function is here indicated as being performed by framer 16 as a means of insuring that the digital input to correlator 18 establishes correlation among samples in the same frame. The function of framer 16 could also be combined into correlator 18 or ADC 14. It should be noted that the ADC 14 is not necessary if the signal is already in digital form. The correlation parameters are obtained in the circuit of Fig. 1 because that circuit will be used to determine reflection coefficients. The output of correlator 18 is applied, if necessary, to a nor alizer 20 to normalize output values to a common level. The output of normalizer 20 is taken to random-access memory (RAM) 22 where it is stored in an address that is directed by a signal from multiplexer 23. Normalizer 20 also generates a signal indicating the completion of the operation of correlator 18 for one frame. That signal is taken as an input to sequencer 24. Signals from sequencer 24 are coupled out to control an address calculator 26, an update calculator 28, a reflection coefficient calculator 30, multiplexer 23, and multiplexer 32. Normalizer 20 determines the appropriate addresses in RAM 22 for storing the coefficients of a correlation matrix so that their serial readout will be in a desired order. The output of normalizer 20 is applied to multiplexer 23 to apply first an initial condition to RAM 22 that is determined from normalizer 20, and then accessed by address instructions from address calculator 26. The output of RAM 22 is applied through multiplexe 32 to RAM 34. Multiplexer 32 selects as an input to RA 34 either the output of RAM 22 or the output of update calculator 28. Multiplexer 32 is controlled by a signa from sequencer 24. The location of storage elements in RAM 34 is controlled by a signal from address calculato 26. The output of RAM 34 is read into update calculato 26 and reflection coefficient calculator 30. update calculator 28 also receives as an input the calculated reflection coefficients from reflection coefficient calculator 30, which coefficients are taken as the outp of the circuit of Fig. 1. Fig. 2 is a circuit diagram of the address calculator 26 of Fig. 1. Address calculator 26 produce the addresses that direct the retrieval of matrix elements in RAMs 22 and the storage and retrieval of matrix elements in RAM 34. In Fig. 2 sequencer 24 supplies addresses to read-only memory (ROM) 40. ROM 4 is read out into multiplexers 42 and 44. The output of multiplexer 42 is taken to RAM 46 which is loaded under the control of signals from sequencer 24. The output o RAM 46 is taken directly as the input to RAM 34 of Fig. 1, and it is also applied to latches 48 and 50, as well as the add/subtract unit 42. The output of latch 48 is taken to multiplexer 23 of Fig. 1, and then to RAM 22. The output of latch 50 is multiplexed in multiplexer 44 with the output of ROM 40 under the control of a signal from sequencer 24. The output of multiplexer 44 is applied to add-subtract unit 52 where it is supplied as an input to be either added or subtracted from the outp of RAM 46, depending upon a control signal from sequenc 24. The add/subtract unit 52 also has an output connected to sequencer 24 which indicates a zero result from the add/subtract operation. Fig. 3 is a circuit diagram of the update calculator 28 of Fig. 1. In Fig. 3 data inputs are applied at terminals 60 and 62. The input at terminal 60 is the output of RAM 34 of Fig. 1. Terminal 60 is connected to a shifter 64, the output of which is taken to a RAM 66 and to a multiplexer 68. The output of RAM 66 is taken to multiplexer 70 which, in turn, is connected to multiplier 72. The output of multiplier 72 is taken as an input to multiplexer 68, as an input to register 74, and as an input to multiplexer 76. The output of register 74 is coupled through multiplexer 78 to supply a second input to multiplier 72. Terminal 62 is connected to reflection-coefficient calculator 30 of Fig. 1 to receive calculated reflection coefficients which are then coupled to register 80 of Fig. 3. The outputs of registers 74 and 80 are applied to multiplexer 78 to be selected under the control of a signal from sequencer 24 of Fig. 1. The output of register 80 of Fig. 3 is also taken as an input to multiplexer 70. Multiplexer 76 produces an output that is taken to registers 82 and 84, the outputs of which supply inputs to multiplexer 86. The output of multiplier 86 is taken as an input to multiplexer 70 and as an input to summer 88. The output of summer 88 is taken as input to multiplexer 76 as a data input to RAM 34 of Fig. 1 and as an input to OR gate 90 of Fig. 3. The output of OR gate 90 is taken to register 92 which supplies an output that is taken both as a second input to OR gate 90 and as an input to priority encoder 94. The output of priority encoder 94 controls register 96 that operates shifter 64. The combination of shifter 64, register 96, OR gate 90, register 92 and priority encoder 94 comprises a normalizer that normalizes the output of RAM 34 of Fig. 1. If it is not desired or is considered O PI unnecessary to normalize coefficients, then terminal 60 can supply an input directly to RAM 66 and the elements just described could be removed from the circuit of Fig. 3. Fig. 4 is a circuit diagram of the reflection coefficient calculator 30 of Fig. 1. In Fig. 4 terminal 100 receives a signal from RAM 34 that is applied to a subtractor 102 and a multiply-by-two circuit 104. The output of subtractor 102 is connected to register 106, which produces one output that is connected as a input to subtractor 102, and another output that is taken to divider 108. The output of divider 108 may be taken directly as a reflection coefficient. In the alternative, it may be desirable to quantize that value as in quantizer 110. In either case, the signal at terminal 112 is a reflection coefficient of the equivalent filter of the original input signal. The reflection coefficients may be used directly as the coefficients in LPC or they may be transformed into a different function, as described earlier. If it is desired to convert reflection coefficients into LAR's, this can be combined readily with the quantization that is performed by quantizer 110. The choice of the particular functions is one of design. Consider now the elements of Fig. 1 in terms of their functions. Filter 12 has already been described as optional. If the circuit of Fig. 1 is to be applied to speech for use in a typical radio speech bandwidth, then the input signal may need to be subjected to bandpass filtering. It may also be desirable to combine some form of pre-emphasis with filter 12. Filter 12 may also be used to prevent aliasing when the filtered signal is applied to ADC 14. The sample rate produced by ADC 14 is a design parameter. According to the well-known sampling theorem, it will be necessary to sample the input at a rate that is at least twice the frequency of the highest component contained in the input. Thus, sampling rates for speech are typically between 6.4 kHz and 10 kHz. Each sample is then encoded into a number of bits that typically ranges between 8 and 15, with 12 as a typical number. It follows that a typical frame will have of the order of one hundred samples. Correlator 18 takes these samples and determines from them the elements of a covariance matrix. This matrix is symmetric. Element (i,k) of the covariance matrix is obtained by summing, from n = p to the total number of samples, the product of the (n - i)th and the (n - k)th samples for zero less than or equal to k, less than or equal to i, less than or equal to p. In this statement, p is the prediction order, a number that is typically between 8 and 12 for speech. The index k is kept less than or equal to i to avoid recalculating equal terms on both sides of the axis of the symmetric matrix. Normalizer 20 of Fig. 1 performs a function that is here indicated separately but that might also be included in correlator 18. Normalizer 20 shifts the elements of the correlation matrix so that the maximum value of any element in the array is between one-half and one in magnitude. Normalizer 20 then truncates the values of the elements thus shifted to a number of bits equal to the word length of the system. The covariance matrix thus has a number of elements equal to (p + 1) 2 . Since the covariance matrix is symmetric, it can be described completely by storing the elements of the diagonal and the elements below the diagonal, a total of (p + 1)(p + 2)/2 elements. These elements are stored in RAM 22 in a location that is controlled by address calculator 26. A convenient method of loading RAM 22 is to load the diagonal elements, beginning with the element of highest order and proceeding to the diagonal element of lowest order, and then repeat in sequence down paths in the matrix that are parallel to the main diagonal. It should be noted that the F and B matrices are also symmetric and may be stored in a similar .fashion. The operation of the circuits of Figs. 1, 2, 3 and 4 is explained further in the flowchart of Fig. 5 which shows the sequence of operations that are performed by those circuits. In Fig. 5, after a start 120, an operations block 122 directs the determination of correlation coefficients. Such a determination is well known. For discrete or sampled components, it is normally accomplished by a calculation such as that of the following equation: N-1 J2f(i,k) * Σ s(n-i)s(n-k) , 0<K<i<p n=p where s(n) , O N-1 are samples of the audio signal during a frame and p is the order of the filter. The next step in the flowchart of Fig. 5 is to initialize the matrices of F, B and C as indicated in operations block 126. The quantities F, B and C are intermediate quantities used in the determination of LPC coefficients. Their initial values are determined as follows: F 0 (i,k) = j7(i f k) B 0 (i,k) = ør(i+1,k+1) C 0 (i,k) = ITU, k+1) for 0 i, k _< p-1 Operations box 1 28 next directs that the value of j equal 1 . Operations box 1 30 then calls for the determination of the quantity kj , the jth reflection coefficient. This is determined as follows: kj = -2Cj_i(0,0) Fj.-I (ϋ,ϋ) 4- β ., IU,U) A variety of techniques are available for determining the reflection coefficient and the above technique is intended as an illustration of one embodiment of the present invention. After the value of kj is determined, it is quantized according to the instruction from operations block 132 at a quantization level that is determined by the number of bits reserved to broadcast the particular LPC coefficient in question. Decision block 134 next tests to see whether j = p. If it does, all of the LPC coefficients have been calculated, and exit is to operations block 136 to end the calculation. If j does not equal p, the calculated value of k is used in operations block 138 to update values of F, B and C according to the following relations: F j ( .i,k ) =F j _ 1 ( i,k)+k j tC j _ 1 Ci,k)+C j _ 1 (k,i)]+k j 2 B j _ 1 (i k) Bj ( i,k)=B j _ 1 (i+l,k+l)+k. [C. 1 Ci+l,k+l)+C. χ (k+l,i+l) ]+ K J 'P._ 1 Ci+l,k+l) C j ( i,k ) =C j _ 1 ( i,k+l ) +k j [B j _ 1 ( i,k+l)+P j _ 1 (i,k+l)]+k ; . 2 C : ._ ;L (k+l,i 0<i,k (p-j-l) The value of j is increased by 1 in operations block 140, and control returns to operations block 130 to continue the calculations. The preceding description shows a circuit for determining LPC coefficients and a flowchart of the steps performed by that circuit. The flowchart of Fig. 5 is also useful in directing the steps of a program for determining LPC coefficients by the same method using a computer. This has been done, and a computer program for determining LPC coefficients using this method is included as an appendix to this application. The computer program has the particular advantage that, using the method of the present invention, calculations may be performed efficiently in integer arithmetic. This speeds calculations and makes it possible to determine LPC coefficients in real time using the present invention. Fig. 6 is a block diagram of a lattice filter that provides a further explanation of the process by which the circuit of Fig. 1 obtains reflection coefficients. In Fig. 6 a terminal 150 receives as an input the sampled signal. This signal is applied to an upper leg 152 which will calculate a forward residual, and it is applied to a lower leg 154 which will apply the signal to the first of a sequence of delay elements 156 to calculate a backward residual. Fig. 6 comprises a cascade of elements, each of which applies the forward signal to a multiplier 158 and a summer 165. The backward signals are applied to a multiplier 162 and a summer 164. Both multipliers 158 and 162 receive as additional inputs the current reflection coefficient. Thus, the current forward residual is multiplied by the current reflection coefficient and added to the current backward residual in summer 164 to generate as an output the next backward residual. The current backward residual is multiplied in multiplier 162 with the current reflection coefficient and added to the current forward residual in summer 160 to generate the next forward residual. The process just described continues through a number of sections of the lattice filter that is determined by the designer as a number adequate to characterize the particular signal in question. This is typically a number of stages equal to 8, 10 or 12. The last such stage is shown here as OMPI «. IPO , receiving a current forward residual signal on terminal 166 and a current backward residual signal on terminal 168. The current forward residual signal is applied to a multiplier 170 and a summer 172, while the current backward residual is delayed in delay element 174, and the delayed signal is applied to multiplier 176 and summer 178. Both multipliers 170 and 176 receive as additional inputs the current reflection coefficient. If the lattice filter has been designed with an adequate number of sections to approximate the input signal sufficiently well, then the output of the final forward residual signal at terminal 180 will be close to zero and so will the final backward residual signal at terminal 182. The result of applying a signal to this circuit of Fig. 6 is the production in forward line 152 of a sequence of elements of a forward residual vector and to produce in line 156 the elements of a backward residual vector. Individual elements are combined to produce an autocorrelation matrix of the forward residual elements, and autocorrelation matrix of the backward residual elements, and a cross-correlation matrix between forward and backward residual elements. These matrices are used as described earlier to calculate the reflection coefficients. Lattice methods of determining coefficients for linear predictive coding have been used in the past. However, circuits and programs used to determine the lattice coefficients have used intermediate variables that varied in magnitude over a wide range. This required a wide range of quantize values to characterize the intermediate variables, and thus took more compu¬ tational time. The circuit arrangement and method of the present invention uses only variable and intermediate variables which are bounded in magnitude by unity. This permits operations and calculations to be performed in a fixed-point fractional implementation. In addition if the input signal is windowed so that it is stationary in a statistical sense, then it can be shown that the number of computations necessary. to determine lattice coeficients is reduced still further. The method and means of the present invention has been used with a frame length of approximately 15 milloseconds to determine 12 lattice coefficients in real time. By completing the calculations for the data of one frame before the end of the next succeeding frame. What is claimed is: OMPI APPENDIX FORTRAN PROGRAM FOR COEFFICIENTS C C FLAT C MODIFIED COVAR LATTICE LPC ANALYSIS C 0001 LOGICAL*1 IDATE(9) ,ITIME(8) 0002 DIMENSION AR(20,3) ,ISAMP(512) ,F(256) ,AK( 19) ,BA(19) 1,C(20,20) ,S(20),BR(19,19) ,FR(19,19) ,CR( 19, 19) ,DR(19,19) 0003 DATA APAST/0./BA/19*0./ISAMP/512*0/AK/19*0./S/20*1 1/IFLAG/0/NPT/1/IPO/1/IPI/1/IPP/1/JY/Υ 1 / 0004 CALL INITT(960) 0005 CALL TERM (3,1 23) 0006 CALL DATE(IDATE) 0007 CALL TIME(ITIME) 0008 TYPE 5,ITIME,IDATE 0009 5 FORMAT ( * COVAR LATTICE LPC ANALYSIS • , 15X,8A1,5X,9A1 ,/) 0010 TYPE 1 0011 10 FORMAT (' ENTER INPUT FILE NAME 1 ,/) 0012 CALL ASSIGN (1,,-1) 0013 TYPE 20 0014 20 FORMAT (' ENTER OUTPUT FILE NAME',/) 0015 CALL ASSIGN (2,,-1) 0016 DEFINE FILE 1 (0,256,U,IPI) 0017 DEFINE FILE 2(0,128,U,IPO) 0018 TYPE 30 0019 30 FORMAT (' ENTER PREEMPHASIS COEFFICIENT 1 ) 0020 ACCEPT 40,APRE 0021 40 FORMAT (F10.0) 0022 TYPE 50 0023 50 FORMAT (' ENTER NUMBER OF SAMPLES PER FRAME 1 ) 0024 ACCEPT 40,AA 0025 LFRAME=AA 0026 TYPE 60 0027 60 FORMAT ( 1 ENTER ORDER OF PREDICTOR') 0028 ACCEPT 40,AA 0029 NP=AA 0030 69 TYPE 70 0031 70 FORMAT (' ENTER ANALYSIS LENGTH') 0032 ACCEPT 40,AA 0033 LEN=AA 0034 TYPE 80 0035 80 FORMAT (* ENTER MAX # OF FRAMES') 0036 ACCEPT 40,AA 0037 NMAX=AA 0038 TYPE 90 0039 90 FORMAT ( ' ENTER GAIN 1 ) 0040 ACCEPT 40,GAIN 0041 TYPE 92 0042 92 FORMAT ( » ENTER N FOR BINOMIAL SMOOTHINGN' ) 0043 ACCEPT 40,AA 0044 NB=AA 0045 IF (NB.EQ.0) GO TO 97 00 Al DO 93 19=1,NP 0048 93 S(I9+1)=S(I9)*(NB-I9+1)/(NB+I9) 0049 TYPE 94,S 0050 94 FORMAT (5F15.10) 0051 97 TYPE 95 0052 95 FORMAT ( ■ DO YOU WANT QUANT IN RECURSION? Y Y/N' ) 0053 ACCEPT 63,IIY 0054 63 FORMAT (A1) 0055 IF (IIY.NE.JY) GO TO 99 0057 TYPE 96 0058 96 FORMAT ( « ENTER QUANT FILE',/) 0059 CALL ASSIGN (3,,-1) 0060 IFLAG=1 0061 READ (3,40)XXX 0062 KK=XXX+1.01 0063 NP=MIN0(NP,KK-1) . 0064 READ (3,40)((AR(K1, 2) ,K2=1,3) ,K1=1 ,KK) 0065 99 READ (1 , IPI)(ISAMP(IV),IV=257,512) 0066 NPT=(LFRAME-LEN)/2+257 0067 1 0 IF (IPO.GT.NMAX) GO TO 1000 0069 IF (NPT.LE.257) GO TO 115 0071 DO 110 ILO=1,256 0072 110 ISAMP(ILO)=ISAMP(ILO+256) 0073 READ (1 'IPI,END=1 00) (ISAMP(IV) ,IV=257,512) 007 NPT=NPT-256 0075 115 APAST=ISAMP(NPT-1 ) 0076 120 NLEN=LEN 0077 125 DO 130 IL2=1,NLEN 0078 BAST=ISAMP(NPT+IL2-1 ) 0079 F(IL2)=(BAST-APRE*APAST)/32768. 0080 130 APAST=BAST C COMPUTE COVARIANCE MATRIX (EQ. 41) 0081 DO 135 I1=1,NP+1 0082 DO 135 12=1,11 0083 C(I1,I2)= 0084 DO 135 I3=NP+1,NLEN 0085 135 C(I1,I2)=C(I1,I2)+F(I3-I2+1)*F(I3-I1+1) 0086 DO 138 11=1.NP+1 0087 DO 138 12=1,11 OMPI 0088 C(I1,I2)=C(I1,I2)*S(I1-I2+1) 0089 138 C(I2,I1)=C(I1,I2) 0090 R0=(C(1,1)+C(NP+1 ,NP+1 ))*GAIN/(2.*(NLEN-NP) ) C INIT CR,BR AND FR 0091 DO 140 11=1,NP 0092 DO 140 I2=1,NP 0093 FR I1,I2)=C(I1,I2) 0094 BR(I1,I2)=C(I1+1,I2+1) 0095 140 CR(I1,I2)=C(I1,I2+1) 0096 11=1 C LOOP STARTS HERE 0097 150 IND=NP-II+1 C COMPUTE AK(II) 0098 DENOM=FR(1,1)+BR(1,1)+FR(IND,IND)+BR(IND,IND) 0099 IF (DENOM.EQ.0.) GO TO 165 0101 AK(II)=-2.*(CR(1,1)+CR(IND,IND))/DENOM 0102 IF (ABS(AK(II)) .GE.1.) TYPE 155 0104 155 FORMAT (' ERROR IN COMPUTATION') 0105 165 IF (IFLAG.EQ.1) AK(II)=QU(AK(II) ,II,AR) C SEE IF DONE 0107 IF (II.EQ.NP) GO TO 200 0109 Z=AK(II) 0110 ZS=Z*Z C . MODIFY FR,BR AND CR ARRAYS 0111 DO 170 I1=1,NP-II 0112 DO 170 I2=1,NP-II 0113 FR(I1,I2)=FR(I1,I2)+ 1Z*(CR(I1,I2)+CR(I2,I1))+ZS*BR(I1,I2) 0114 BR(I1,I2)=BR(I1+1,I2+1)+ 1Z*(CR(I1+1,I2+1)+CR(I2+1,I1+1))+ZS*FR(I1+1 ,12+1) 0115 170 DR(I1,I2)=CR(I1,I2+1)+ 1Z*(BR(I1,I2+1)+FR(I1,I2+1 ) )+ZS*CR(I2+1 ,11) 0116 DO 180 I1=1,NP-II 0117 DO 180 I2=1,NP-II 0118 180 CR(I1,I2)=DR(I1,I2) 0119 -11=11+1 0120 GO TO 150 0121 200 PO=FR(1 ,1)+2*AK(NP)*CR(1 ,1)+AK(NP)*AK(NP)*BR(1 ,1) 0122 PO=PO*GAIN/(NLEN-NP) 0123 IF(IFLAG.EQ.1) PO=QU(PO,0,AR) 0125 WRITE (2'IPO)NP,LFRAME,PO,APRE,BA,AK,R0 0126 ISW=IPEEK("177570) 0127 IF(ISW.AND."100000) TYPE 160,IPI-1,IPO-1 0129 160 FORMAT ( ' ',218) 0130 -NPT=NPT+LFRAME 0131 .GO TO 100 0132 1000 WRITE (2'IPO)(-1) 0133 CALL CLOSEO) 0134 CALL CLOSE(2) 0135 CALL CLOSE(3) 0136 CALL EXIT 0137 END OMPI

Claims: Claims 1. A method of processing an analog electrical signal to obtain lattice coefficient of an inverse lattice filter that characterizes the analog electrical signal, the method comprising the steps of: a) converting the analog electrical signal to a digital signal; b) selecting samples of the digital signal for a time period equal to a predetermined frame length; c) determining correlation coefficients of a selected samples; d) initializing values of F, B, and C matrices; e) determining a first lattice coefficient from initial values of F, B, and C matrices; f) adjusting values of F, B, and C matrices from the first lattice coefficient; and g) determining a second lattice coefficient from the adj sted F, B, and C matrices and repeating the steps of adjusting and determining until a predetermined number of lattice coefficients has been obtained. 2. The method of claim 1 comprising in addition the step of filtering the analog signal before it is converted to a digital signal . 3. The method of claim 1 wherein the step of determining correlation coefficients comprises the step of obtaining the sum of products of sampled signals according to the relationship N-1 0(i,k) = ∑ s(n-i)s(n-k) , 0 K i_p n=p where s( n) , 0<n < N-1 are samples of the audio signal during a frame and p is the order of the filter. 4. The method of claim 1 wherein the F atrice is defined according to the relation and F j ( i,k ) =F j _ 1 ( i / k) +k j [C j _ 1 (i / k) +C j _ 1 Ck, i) ]+k j 2 B . 1 (i,k) 0<i ,k<_(p-j-l) 5. The method of claim 1 wherein the B matrice is determined according to Bj ( i,k ) =B ; ._ 1 ( i+l / k+l).+k. [C. 1 (i+l,k+l)+C._ 1 (k+l,i÷l)3+ k j 2 F j _ 1 (i+l,k+l) 6. The method of claim 1 wherein the C matrice is determined according to, C. ( i / k ) =C j-1 ( i k+l ) +k j [B j _ 1 ( i,k+l)+F^ 1 (i,k+l)I÷k 2 c. (k+l,i) 0<_i r k<_(p-j-l) 7. The method of claim 1 wherein converting the analog electrical signal is not necessary if the signal is already in digital form. OMPI VIPO 8. An apparatus for processing an analog electrical signal to obtain reflection coefficients of an inverse lattice filter that characterizes the analog electrically signal, the apparatus comprising: a) a filter receiving the analog electrical signal and producing a filtered analog electrical signal; b) analog-to-digital converter connected to the filter to produce digital signal , c) a framer to select time interval s of a predetermined amount; d) corel ator connected to the framer and to the analog-to-digital converter to produce corelation coefficients of the digital signals during each framed interval ; e) a normalizer connected to the corelator to normalize the corelation coefficients of the correlator, f) a first RAM connected to the normalizer to receive and store normalized corelation coefficients, g) a sequencer that generates a plurality of control signals, h) an address calculator connected to the sequencer and to the first RAM to control addresses at which normalized corelation coefficients are stored and the first RAM; i) a multiplexer connected to the first RAM and receiving as an input data from the first RAM j) a second RAM connected to the multiplexer and to the address calculator, the second RAM receiving input from the multiplexer and storing that input in a location controlled by the address calculator; k) a reflection coefficient calculator connected to the second RAM and to the sequencer, the reflection coefficient calculator receiving data from the second RAM and caculating reflection coefficients under control from the sequencer; and 1) an update circuit connected to the reflec¬ tion coefficient calculator the second RAM and the sequencer to calculate current coefficients under the control of the sequencer and producing an output that is taken as an input to the multiplier.

Inventors: GERSON IRA ALAN, GERSON, IRA, ALAN
Applicants: MOTOROLA INC, MOTOROLA, INC.
Application year: 1983
Main classification: H03K13
IPC codes: G10L11, G10L19, H03H17, H03H21, H04B3