GB2026289A - Improvements in or relating to self-adaptive linear prediction filters - Google Patents

Abstract

A form of self-adaptive linear prediction filter for use in speech communications, based on the PARCOR (partial autocorrelation) lattice structure of Itakura and Saito which conventionally employs a division process, in the correlation 2 Fig. 2, to update the PARCOR coefficient estimates for each stage. The performance of these division processes presents great difficulty where the PARCOR coefficient estimates are to be updated at frequent intervals particularly in an analogue implementation. In filters according to the present invention successive PARCOR coefficient estimates (Kp) in each stage of the lattice Fig. 3 are derived using a recursive relationship which requires no division processes in its implementation. <IMAGE>

Description

SPECIFICATION Improvements in or relating to self-adaptive linear prediction filters This invention relates to self-adaptive linear prediction filters, and in particular to linear predictors for use in such filters for extracting partial autocorrelation (PARCOR) coefficients from a data signal.

Linear prediction is a technique used in the time series analysis of data signals, for example speech signals, in which a sample of the signal can be predicted from a linearly weighted combination of past samples of the signal. The present invention is concerned with linear prediction based on the PARCOR lattice structure described by Itakura and Saito in their article entitled "On the Optimum Quantisation of Feature Parameters in the PARCOR Speech Synthesiser", Conference Record of IEEE 1972 Conference on Speech Communication and Processing, Paper L4, pp 434 to 437. The PARCOR lattice predictor (or analyser) derives, from samples of an input data signal, a set of partial autocorrelation (PARCOR) coefficients which describe the spectrum envelope of the data signal.From these PARCOR coefficients an inverse filter can be defined that has a frequency response closely matching the inverse of the smooth spectral character of the analysed input signal. If the PARCOR coefficients are periodically updated at a rate sufficient to track changes in the input signal, then the frequency response of the associated inverse filter defined by these time-varying PARCOR coefficients can be made to follow the inverse of the spectral envelope of the original input signal. Such filters are commonly called self-adaptive linear prediction filters.

The theory of the PARCOR lattice predictor having (m + 1) lattice stages is given as follows. A signalx(t) to be analysed is sampled at regular intervals T, to obtain a discrete-time signal or time series{xn}, n = 0,1,2, . . . Letxn+ define the forward prediction of samples from a linear combination of m samples xn~m toxn~1, m being an integer:

and l0tXj-(m + t) define the backward prediction of sam plexn~(m + 1) from a linear combination of the same samples.

where ap and bp are respectively the least squares forward and backward predictor coefficients.

Then the least squares forward prediction error, that is the error between the predicted valuexn+ and the actual value is given by

and the least squares backward prediction error is given by

e+p ande-p are also known as the forward and backward prediction residuals.

The expressions (3), (4) fore+p ande-p can be expressed more compactly in terms of Z-transforms as U+p (Z) = Ap (Z) X (Z) and U-p (Z) = Bp (Z) X (Z).....(5) where U*p (i) and U-p (i!) represents the Z-transforms of e+p and e-p, X(iS) is the B-transform of the data sequence{xn}, and Ap(F) and Bp(X) are known as the forward and backward prediction error operators respectively.

From (5) it can be shown that Ap + ,(i) = Ap() - kp Bp(i) (6) and Bp + 1(Z) =iD-' (Bp( - Ap(i!)) (7) where kp are known as the partial autocorrelation (PARCOR) coefficients, being the correlation coefficients between the forward and backward prediction errorse+p, and e-p. A PARCOR lattice predictor is thus defined as a linear prediction filter which implements equations (6) and (7). These equations show that the (p + 1)th prediction error operators Ap +1)(), Bp + ,(gt) are uniquely determined from the pth prediction error operators Ap(Z), Bp(iE) and the PARCOR coefficients kp.

There are at least two known mathematical estimators for determining the PARCOR coefficients kp. One is given by Itakura and Saito in the abovementioned article, in which the average product of the forward and backward residual energiese+p,e-p are normalised by their geometric mean

The other estimator is given by J P Burg in his article "A New Analysis Technique for Time Series Data" presented at NATO Advanced Study Institute on Signal Processing, Enschede 1968, and involves normalising the average product of the two residual energies by their arithmetic mean

where overbar in each case denotes time average, andep,e-p are, as before, the forward and backward prediction errors at the pth stage input.Although equation (9) is slightly easierto compute than (8), since it does not involve taking a square root, both formulae require the computation of a division. Thus if it is required to update all the partial correlation coefficients kp of the PARCOR lattice at frequent intervals, say at every sample of the input signal, performing these divisions at such speed would present great difficulty particularly if analogue hardware is used, and would thus be expensive.

It is an object of the present invention to provide a self-adaptive linear predictor in which the abovementioned difficulty can be overcome or at least substantially reduced.

According to the present invention, in an adaptive PARCOR lattice predictor, the partial autocorrelation (PARCOR) coefficients for each stage of the lattice are updated at regular intervals with values estimated in accordance with the recursive equation:

where kp (L) and kp (L + 1) are estimates of the PAR COR coefficient of pth stage of the lattice at times L and (L + 1) respectively,e+p ande-p, represent the least squares forward and backward prediction errors of the input to the pth stage of the lattice, and overbar (.) denotes time average.

It can be shown that providing the average input energy

and the time averages e+pe-p,(e+p)2 and (e-p)2 are constants, (ie a stationary input signal) then the above formula will converge to the Burg estimate given by equation (9). Estimates of the PARCOR coefficients kp can thus be computed without the need to carry out a division process, and thus the invention facilitates the use of the PARCOR lattice in its application to self-adaptive filters in which the PARCOR coefficients must be updated at a rate sufficient to track changes in the input signalx(t).In this application, the PARCOR coefficients kp extracted by the predictor can, for example, be used to supply the control parameters for a self-adaptive lattice-type inverse filter to produce a frequency response in the filter closely following the inverse of the spectrum of the input signal. Alternatively, the PARCOR coefficient estimates may be used to define a synthesis filter.

In one implementation of the invention, the three time averages 2e+pe-p, ('*)2 and (ej2 (or the two time averages 2e+pe-p and [(e+p)2 + (e-p)2] ) are continuously updated, and at regular intervals, ie at each coefficient updating time, the current value of these three (or two) averages is taken and used in a number of successive iterations of the recursive equation (10) to update the PARCOR coefficient estimates. The averages may be derived, for example using a rectangular averaging window, from any number of samples of the signalse+p,e-p, and the equation may be iterated any number of times for each coefficient update.However, the updating frequency will depend on the number of times the equation is iterated for each update.

In a more simplified implementation of the invention, particularly suited to analogue implementation, the PARCOR coefficients are estimated in accordance with the modified equation: kp CL+l) = kp ( L ) + (n)ep- (n)+5p (n) ep (n) > (11) where Rp(n) =e+p(n) - kp(L)e-p(n) =e+p + 1(n), Sp(n) e-,(n) - kp(L) e+p(n) = e-p + (n + 1), e+p(n) ande-p(n) represent respectively the forward and backward prediction residuals of the samples, and ( ) denotes short term average taken with kp(L) constant over the time of averaging.

This modified version (11) of equation (10) is based on the following relationship:

(which holds if the short term averages denoted by ( . > are taken while kp is constant over the time of averaging) and is derived by replacing the terms of equation ( 10) containing true time averages denoted by overbar. (.) with the single short term average (Rp(n)e-p(n) + Sp(n)e+p(n)). In implementing the invention using equation (11), the arithmetic operations in each stage of the lattice required to derive the expression:: (Rp(n)e-p(n) + Sp(n)e+p(n)) are carried out first, a process which is facilitated by, and takes advantage of, the basic lattice structure.

This single expression is then averaged (with kp(L) constant) and added to kp(L) to produce the updated estimate kp(L + 1). Such an implementation per forms only one iteration of the recursive equation (11) for each short term average taken, and in the extreme case may be arranged to update the PAR COR estimates at the input signal sampling rate.

The invention may be implemented in both soft ware, ie using a suitably programmed computer, or in digital or analogue hardware, and because each stage of the lattice is identical, the predictor may comprise a single module stage the inputs and delayed sample values of which are supplied by indexed memories which are successively indexed to iterate the lattice structure for successive samples xn of the input signalx(t).

The invention also includes within its scope self adaptive linear prediction filters whose control parameters are provided by an adaptive PARCOR lat tice predictor as aforesaid, and extends to methods of analysing data signals, comprising the steps of applying samples of the input signals to be analysed to a PARCOR lattice predictor as aforesaid.

Other features of the invention will become appar ent from the following description made-by way of example only, with reference to the accompanying drawings of which Figure 1 is a block schematic diagram of a generalised PARCOR lattice predictor; Figure 2 is a block schematic diagram representing a single stage of a prior art PARCOR lattice predictor; Figure 3 is a block schematic diagram representing a single stage of a PARCOR lattice predictor in accordance with the invention; Figure 4 is a block schematic diagram showing an analogue implementation of a PARCOR lattice predictor in accordance with the invention; Figure 5 is a timing diagram for the predictor shown in Figure 4; and Figure 6 is a block schematic diagram representing a single stage of a further PARCOR lattice predictor in accordance with the invention.

Referring to the drawings, Figure 1 shows the basic generalised PARCOR lattice structure of a linear predictor for extracting partial autocorrelation (PARCOR) coefficients from a series of samples xn,n=1,2,3, of or an input signalx(t). The predictor or analyser comprises a plurality, m+ 1, of cascaded identical filter stages 1 of the lattice type, each arranged to produce outputs representing the respective least squares forward and backward prediction errors or residualse+,,e-,, p=1,2 ... m+ 1, defined by equations (3) and (4) above. Figure 2 shows a conventional form for each stage 1 of the Fig 1 lattice structure (as described in the above article by Itakura and Saito).

Each filter stage comprises a correlator 2 arranged to estimate the PARCOR coefficient kp using the prediction residualse+p,e-p from the preceding stage by the estimation formulae (9).

The structure further includes a pair of multiplying elements 3,4 arranged to multiply the two inputs e-p(n) ande+,(n) respectively with the output kp of the correlator 2, to give respective products kpe-p(n),kpe+p(n), and a pair of summation elements 5,6 arranged to subtract these products from the two inputse+,(n)p-,(n) respectively to produce the following results:: R,(n) =e+p(n) - kg-,(n) (12) Sp(n) =e-p(n) - ks-,(n) (13) where R,(n) = e*+1(n) and Sp(n) = e-p+,(n+1) The output Sp(n) is then delayed one sampling interval T, by a unit delay element7 to produce an output e-p+i (n).

At the input to the lattice (Fig 1), the input signal data sequence is divided along two paths, one of which is delayed one sampling interval T, by a unit delay element 8 to generate the two inputs to the initial filter stage 1 as follows: e+O(n) =xn e-O(n) =xn~l The PARCOR coefficient kp is then estimated as the correlation coefficient between these values by the correlator 2 of filter stage (p=o), and this coefficient then used to computee1+(n), ande1-(n) which in turn provide the inputs for the next filter stage (p=1).In this filter stage the coefficient k1 is computed as the correlation coefficient between e1 (n) ande1-(n), and from k1, the outputse2+(n) ande2-(n) are computed using the equations (12) and (13).

The same computations are carried out in each successive stage of the filter to produce final outputs e+m+1(n),e-m+1(n) from the (m+1 )th stage (p=m), and a series of PARCOR coefficients kp, p=0,1,2 . . . . ,2 m.

These coefficients can then be used as the control parameters for a filter having a transfer which is the inverse of the prediction error operator Am(Z) defined in (5).

The arrangement so far described with reference to Figs 1 and 2 constitutes prior art and has been described in order to provide a background for the understanding of the present invention. As discussed earlier the estimation of the PARCOR coefficients kp in the correlators 2 of each stage 1 of the lattice involves a division, and if these coefficients are to be upgraded at frequent intervals, the performance of these divisions would present great difficulties.

Figure 3 shows an alternative structure for each stage 1 of the PARCOR lattice shown in Fig 1, in which the PARCOR coefficients kp are estimated by a divisionless process, using the formula of equation (10), but replacing the time averages (overbar) by short term averages ( < . > ) taken such that the coefficients kp remain constant over the time of averaging.

where kp (L+1) and kp(L) are estimates of the pth stage PARCOR coefficient at time Land (L+1) respectively. From equation (10), it will be shown that the estimates of the partial correlation coeffi cients kp converge to the formula of equation (9) in an exponential fashion. If the inputs to the pth stage of the lattice are stationary so that (e+p)2, (e-p)2 and are are constants, then if the pth stage estimates have converged so that kp(L+ 1) = kp (L), then they must have converged to the same value as would be estimated using equation (9), since by equation (10)

when kp(L+1)=kp(L) Conversely, if kp (L+1) is not equal to kp(L), a condition can be derived under which kp (L) will converge to the equation (9) value. Let D (L) = kp (L+1) - kp(L).

Then from equation (10)

subtracting,

The solution to this homogeneous difference equa sive coefficient estimates is always proportional to the difference between the current coefficient estimate and that predicted by equation (9) using shortterm averages ( < . > ) instead of true averages (overbar), the constant of proportionality being the new short-term input energy estimate [ < (e+p)2 > + < (e~p)2 > ] . If this is equal to unity, then each PARCOR estimate is precisely the short-term average equation (9) estimate. It falls short of the short-term equation (9) estimate if the total short-term average input energy is less than unity and overshoots if greater than unity.In this context, unity is just that value which, when multiplied with the input signal, leaves the input signal unchanged. Should the short-term equation (9) estimate remain constant over consecutive updating times, the adaptive estimate computed in accordance with the invention will converge to it in the exponential manner of equation (13). Also, because the absolute value of the short-term equation (9) estimate is guaranteed to be less than unity regardless of the length of the averaging window, a total input energy slightly less than unity will ensure that the adaptive PARCOR coefficient estimates will also be less than unity, thereby maintaining stability afthe associated filter using these coefficients.It can be shown also that for a stationary input, the convergence of the first stage of the lattice in accordance with the invention ensures the convergence of all subsequent stages.

The PARCOR coefficient estimates kp extracted from the signaix(t) may provide the control parameters for either a synthesis filter or an inverse filter to produce in known manner, a frequency response which follows closely the spectrum, or the inverse of the spectrum of the input signal, respectively.

The PARCOR lattice structure lends itself well to implementations in both software and digital or analogue hardware. Because each stage of the lattice is identical, the predictor may be implemented using a single stage module whose inputs and delayed sample values come from indexed memories. Indexing through the memories once will then iterate the lattice for a single sample of the input signal. Such a one module arrangement would be particularly convenient for a signal processing computer since the filter stage can be computed in the manner of a pair of complex multiplications. On the other hand, in its hardware implementation where each stage of the lattice is implemented separately, the lattice structure permits maximum use of parallel hardware due to its pipeline structure.

The energy constraint for convergence in the adaptive predictorofthe invention, ie that[(e+p)2 + (e-p)2] must be less than 2, implies by virtue of the property that convergence of the first stage ensures convergence of all subsequent stages, that the inputs to the predictor must be scaled so that the average energy ofthe predictor input signal is less than unity. Its physical representation thus depends on how the multiplications in the predictor are performed. Scaling is no problem in a fixed-point digital implementation in which all signals are by definition less than unity and fractional fixed-point arithmetic is used.The above energy constraint implies that a fractional fixed-point implementation is the natural tion is

Thus, provided that[(e+p)2 + (e-p)2] < 2 and provided that the time averages (denoted by overbars) are constants, the difference between successive estimates for the pth PARCOR coefficient kpwill decrease as a power sequence. By equation (10) the estimate will as rapidly converge to the equation (9) estimate. If (e*,)2 + (e-p)2 = 1, then kp (L+ 1) will be precisely the equation (9) estimate.

The predictor lattice of the present invention, one stage of which is shown in Fig 3, takes advantage of the general structure of the lattice to compute part of equation (10) as will become apparent. Multiplying equation (12) bye-(n) and equation (13) bye+p(n), adding, and then taking short-term averages of the prediction residuals such that kp(n) is a constant over the timepf averaging, gives

where < .> denotes short-term average Comparing equation (15) with equation (10), replacement of the time averages (denoted by overbar) in equation (10) with their short-term estimates results in the adaptive form of PARCOR lattice in which each stage is of the form shown in Fig 3 with Kp(L+1) = (rep (n)ep(n)+Sp (n)+5p con,)+ (n) > + kp (L) which is equation (11).

The Fig 3 lattice stage differs from that of Fig 2 in that the correlator2 is replaced by a different form of correlator 10 which performs the above described operations of multiplying, adding and short-term averaging to produce a new estimate kp(L). The correlator 10 comprises a pair of multiplying elements 12,13 arranged to multiply the inputse+,(n)-,(n) with outputs S,(n), Rp(n) of summation elements 6,5 respectively, a summation element 14 arranged to add togetherthe outputs of the multiplying elements 12,13, and an averaging element 15fortaking the short-term time average of the output of summation element 74 to give < Rp(n)e-p (n)+ Sp(n)e+p(n) > . This is then added to the existing PARCOR coefficient estimate kp(L), to give the new PARCOR estimate kp(L+1) according to equation (11).

At each coefficient updating time the lattice computes a new PARCOR coefficient estimate. If a rectangular averaging window is used in the averaging element 15, then the length of the window, ie the size of the sample from which the average is esti mated, will correspond to the time interval between coefficient updates. In the extreme case the window length may correspond to the sampling interval T of the input signalx(t) in which case the PARCOR coefficients will be updated once for every input signal sample.

It can be shown that the difference between succe one to use since the scaling problem does not arise.

However, in other implementations the scaling problem must be taken into account. There are two ways of doing this. Either the input to the predictor can be scaled using a knowledge of the value which the predictor multipliers define as unity, or the scalefactor can be included at each stage of the lattice. The latter approach is most easily done by using an attenuation constant C, in the averaging part of the adaptive loop.

The adaptive equation then becomes

This has the same effect as scaling the input energies.

The first approach lends itself most naturally to floating-point digital implementations in which signals are not necessarily less than unity while the second approach lends itself to analogue implementations in which the physical value of unity is not necessarily defined a priori.

An advantage of self-adaptive linear predictor in accordance with the invention is that they may be constructed relatively inexpensively in analogue hardware, using for example sample and hold amplifiers for both implementing the lattice delay elements and buffering the individual lattice stages.

Two stages (of the Fig 3 type) of a typical arrangement are shown in Fig 4 in which the arithmetic elements ie the summation, multiplication and integration elements required for each stage are represented by boxes 20. These elements may conveniently take the form of readily available linear integrated circuit elements. Each lattice stage also includes two sample and hold buffer amplifiers, S/H 1, S/H2; Sly4, S/H5 for the two stages shown (subsequent stages following the sequence as follows S/H7, S/H8; Six10, S/H11 etc) and one sample and hold delay amplifier, S/H3, S/H6 for the two stages shown, (subsequent stages following the sequence 9,12,15 etc) providing the delay element for that stage.

Digital counters and gates (not shown) would normally provide the control signals to the sample and hold amplifiers to crystal controlled accuracy, and a typical timing diagram for such a predictor arranged to update the PARCOR coefficients kp at each sample of the input signal is shown in Fig 5.

Alternate stages operate 180 degrees out of phase.

The tracking time of each cycle of the buffer amplifiers S/H1, S/H2, S/H4, S/H5 etc corresponds to the settle time required by the arithmetic elements of the preceding stage to estimate the new PARCOR coefficients. During the hold time of these buffer amplifiers the inputs of the succeeding stage are held fixed at the most recent updated values of the residual energiese+p,e-p from the preceding stage and, during this time, the succeeding stage performs its arithmetic computations to produce a new PAR COR coefficient estimate and prediction residuals.

Delay amplifiers S/H3, S/H6 etc convert values for Sp(n) (ire+, (n + 1)) intoe-p+1(n) simply by holding Sp(n) at its old sample value during the following operating cycle of the succeeding stage. The tracking time of these delay amplifiers corresponds to the minimum acquisition time required.

Adaptive PARCOR lattice predictors in accordance with the invention incorporating lattice stages of the Fig 3 type, while possessing the advantages of simplicity, (requiring only a single averaging element for each stage) and speed, (performing only one recursive iteration per update of the PARCOR estimates) do require, for complete stability of the associated (inverse or synthesis) filter, the short term averages derived by the averaging element 15 to be constants.

In practice, for a non-stationary input signal they are not; they are changed once for every iteration of equation (11). Thus, as the coefficient kp are computed, it is possible for one or more of the stages to overshoot the equation (9) estimate in such a way that occasionally some of the coefficients kp will have an absolute value greater than unity. This implies that the associated filter will be briefly unstable.

Fig 6 shows a single stage of an adaptive PARCOR lattice predictor which enables the abovementioned disadvantage to be substantially reduced to produce more accurate estimates of the PARCOR coefficients at the expense of speed and simplicity. The Fig 3 type lattice stage is based on equation (11), the modified version of equation (10) in which the terms containing true time averages in equation (10) are replaced by a single short term average. Because equation (11) holds only if this single short term average is taken while the current PARCOR coefficient is constant over the time of averaging, the Fig 3 type lattice stage can only iterate the equation once for each short term average taken.The modified Fig 6 lattice stage structure is based on equation (10), and allows the equation to be iterated any number of times for each updating of the PARCOR coefficient estimates by taking separate time averages of the valuese+pe-p and (eat)2 + (e-p)2withoutthe constraint that the coefficients kp remain constant over the time of averaging.

Again, the basic structure of the Fig 6 lattice stage is similar to that of Fig 2, but the correlator of Fig 2 is replaced by a correlator 20 which derives a new estimate kp (L+ N) of the PARCOR coefficients from the input signalse+,(n),e-,(n) and the existing coefficient estimates kp (L). The correlator separately and continuously derives time averages 2e+pe-p and ('*)2 + (e-p)2 from a fixed number of samples of the sign also, and e-,, and for each coefficient update, samples and stores the value of each of these averages and performs several (N) iterations of equation (10) to produce the new estimate kp (L+N).

The time average 2e+pe-p is derived by multiplying together and doubling samples of the input signals e+p,e-p using a multiplying element 21, and applying this product, 2etc,. e-p to an averaging element 22 which continuously applies to it a rectangular averaging window covering a predetermined number of input signal samples.

The time average (e+p)2 + (e-p)2 is derived by a pair of squaring elements 23,24 arranged to square the input signalse+p,e-p respectively, a summation ele ment 25 arranged to add the two squared input sign als together, and an averaging element 27 which similarly continuously applies a rectangular averag ing window to the output of the summation element 25 to produce a continuously updated estimate of the value (e",)2 + (e-,)2 averaged overthe same number of input signal samples. The rectangular averaging window used in each case may be of any suitable length, and is not dependent upon the coefficient updating interval.

Each time the PARCOR coefficient estimate for the stage is to be updated, the outputs of the averaging elements 22,27 are sampled and their values stored in storage elements 29,30 respectively. The estimating equation (10) is then iterated a predetermined number of times (N) using these stored, and therefore fixed, values of the two time averages to eventually produce a new PARCOR coefficient estimate kp (L+N).

These iterations are carried out using a summation element 32 which subtracts the output of a multiplying element 33 from the output of a further summation element 34. During the first iteration of a particular updating sequence, the summation ele ment 34 adds the value of the average 2e+pe-p -, stored in the storage element 29 to the output of the summation element 32 produced by the preceding iteration. ie the latest or current PARCOR coefficient estimate, to produce a value for the expression kp(L) + 2e+pe-p. Atthe same time, the multiplying element multiplies the same output of the summation element 32 with the value of the average (e+p)2 + (e~p)2 stored in the storage element 30 to produce a value for the expression kp(L)je+p)2 + (e-p)2. Subtraction of the output of the multiplying element 33 from that of the summation element 34 gives a new value kp (L+ 1) for the PARCOR coefficient for use only in the next iteration within the correlator 20.This iterative process is then repeated a further (N- 1) times for the same stored averages after which a new PAR COR coefficient estimate kp (L+N) is fed into and stored in the correlator output store 36 until the iteration has been carried out a further N times with a new set of time averages.

Because the time averages are held constant during these N iterations the process will converge of the average input energy to each stage, [(e+p)2 + (eEjR < 2, which condition is achieved if the average energy of the input signalx(t) is less than unity as discussed above. Thus, providing equation (10) is iterated a sufficient number oftimes ( N~ 100 for absolute stability) the updated value of the PARCOR coefficient estimate will be guaranteed to have an absolute value of less than one at each stage of the lattice. In practice any number of iterations (N) may be carried out at each updating time, but the higher the number of iterations, the greater the liklihood of stability in the associated filter.

A PARCOR lattice predictor employing lattice stages of the Fig 6 type requires more computation and is therefore slower than one using Fig 3 type lattice stages because the iterate equation is executed a multiple number of times for each updat ing of the PARCOR coefficient estimates. It will also be more complicated as at least two time averages per stage ratherthan one must be separately computed.In some cases it may be desirable to compute three time averages, iee"g-,, (e+p)2 and (e-p)2, and then add the lattertwo together to give (e+p)2 + (e-p)2 However, the Fig 6 type lattice stage will produce better estimates of the partial correlations, ie the new estimates will be closer to the short term equation (9) estimate than those produced by the Fig 3 type lattice stage because the iterative calculation is performed more times for each estimate.

While each of the above embodiments has been described in its application as a self adaptive linear predictor for extracting estimates oft'he partial autocorrelation (PARCOR) coefficients of an input signal, it will be noted that each embodiment is itself a selfadaptive inverse filter the output of which may be taken from either of the outputs of the final stage.

Claims (10)

1 A PARCOR lattice predictor as hereinbefore defined wherein the partial autocorrelation (PAR COR) coefficients for each stage of the lattice are updated at regular intervals with values estimated in accordance with the recursive equation: pCL+1) (ee) +Cp3' -KpL)t2p FCL) +2 - where kp(L) and kp(L+1) are estimates of the PAR COR coefficient of the pth stage of the lattice at times Land (L+1) respectively,eAp ande~p representthe least squares forward and backward prediction errors of the input to the pth stage of the lattice, and overbar ( . ) denotes time average.

2 Apparatus as claimed in Claim 1, wherein each stage of the lattice has means for receiving first and second input signals and computing means arranged to derive therefrom first and second output signals, the first and second input signals for successive stages being provided respectively by the first and second output signals of the preceding stage, the computing means comprising for each stage means for determining the correlation coefficient between the first and second input signals, means for multiplying the first and second input signals each with said correlation coefficient, first subtraction means for subtracting the product of the second input signal and the correlation coefficient from the first input signal to produce the first output signal representing the forward prediction error for that stage of the lattice, second subtraction means for subtracting the product of the first input signal and the correlation coefficient from the second input signal, and means for time-delaying the resulting dff- ference signal to produce the second output signal representing the backward prediction error for that stage of the lattice.

3 Apparatus as claimed in Claim 2, wherein the first and second input signals to the first lattice stage are provided by the signal to be processed and a time-delayed version thereof.

4 Apparatus as claimed in Claim 2 or Claim 3, wherein the signal to be processed is in the form of a time series, and each of said time-delays is equal to the sampling interval of the time series.

5 Apparatus as claimed in Claim 2,3 or4, wherein the means for determining said correlation coefficients for each stage comprises means for squaring each of the input signals, means for summing the squares of the two input signals, first averaging means for determining the time average of the sum of the squares of the two input signals, means for doubling the product of the two input signals, second averaging means for determining the time average of the output value from the doubling means, means for periodically sampling the outputs of the two averaging means, subtraction means, means for multiplying the output of said subtraction means with the sampled output value of the first averaging means to produce the subtrahend input to the subtraction means, means for adding the output of the subtraction means to the sampled output value of the second averaging means to produce the minuend input to the subtraction means, sothatthe output of the subtraction means is periodically updated at the sampling rate of the averaging means, and means for periodically sampling the output of the subtraction means to provide successive estimates of the PARCOR coefficient for that stage.

6 Apparatus as claimed in Claim 5, wherein the rate of sampling the outputs of the two averaging means is a number of times greater than the rate of sampling the output of the subtraction means.

7 Apparatus as claimed in Claim 2,3 or 4, wherein said means for determining the correlation coefficients for each stage comprises means for multiplying the output of the first subtraction means with the second input signal, means for multiplying the output of the second subtraction means with the first input signal, addition means for adding together the products of these two multiplying means, means for determining the time average of the output of the addition means, means for periodically sampling the output of the averaging means, and means for deriving a new estimate of the PARCOR coefficient from each output sample of the averaging means by adding it to the existing coefficient estimate derived from the preceding sample.

8 Apparatus as claimed in Claim 7, wherein the time window of the averaging means falls wholly within the output sampling interval thereof.

9 A PARCOR lattice predictor substantially as shown in and as hereinbefore described with reference to Figures 1 and 3, Figures 4 and 5 or Figure 6 of the accompanying drawings.

10 A self-adaptive linear prediction filter the con trol parameters of which are supplied by the partial autocorrelation coefficient estimates derived by a self-adaptive linear predictor as claimed in any preceding Claim.