Adaptive, digital filter including a non-recursive part and a recursive part

Adaptive digital filter comprising a non-recursive part and a recursive part

Technical area

The invention relates to an adaptive digital filter comprising a non-recursive part and a recursive part. For example, the filter can be used as echo extinguisher or equalizer in telecommunication equipment.

The state of the art

The impulse response from a filter used for echo cancellation in a telecommunications equipment shall as closely as possible imitate the impulse response of the relevant transmission line. The transmission line also includes this connected two to four-tree transitions, analogue digital converters, etc., which affect the impulse response. The impulse response is generally relatively long in time. It is therefore difficult to obtain a suitable impulse response with a filter having only a finite impulse response. Such filters are called non-recursive filters or FIR (finite impulse response) filters. In order to obtain a suitable impulse response, a filter for echo cancellation should consist of a non-recursive part and a recursive part. Recursive filters are also called infinite impulse response (IIR) filters.

There are known, reliable methods for updating adaptive FIR filters, ie. setting such filter coefficients. They can be updated by minimizing the square of an error signal, which is the difference between a so-called. desired signal and the output of the filter. The desired signal may then be a signal appearing on a receiver side in a communication equipment where the filter is included. The square of the error signal can be minimized according to, for example, the so-called. LMS (least mean square) method. The LMS method is described in, for example, the book: Widrow and Stearns Adaptive signal processing, p. 99-101.

Minimizing the square of an error signal as described above is a so-called. least square problem because the square of the error signal is a square function of the coefficient values ​​of the filter. This means that this square can be represented by a square error surface, in an N-dimensional space, where N is the number of coefficients, whereby the optimal filter setting corresponds to the minimum point on this surface.

However, the corresponding square of an HR filter is not represented by a square error area as above, but the error area may instead have local minimum points. Known update algorithms can get stuck in such a local minimum point, which results in the optimal setting being achieved.

In addition, recursive filters can become unstable, as the poles of the Z-transform of the transfer function, at least temporarily, can be moved outside the unit circle. For a first-degree IIR filter, this means that the filter coefficient can be greater than one, making the filter unstable.

To avoid the problem of local minima, it is known to use a so-called. equation error structure. This is used, inter alia, two FIR flits, one of which is connected to a transmitter side and the other to a receiver side in one and the same telecommunication equipment. An error signal is generated by subtracting one filter's output signal from the other filter's output signal. The square of this error signal has a square error surface, but a structure of this kind has the disadvantage that the error signal that is minimized does not represent the actual error. This applies to where interference occurs and voice signals appear on the transmitter side and receiver side simultaneously. It has also proven difficult to set up two filters that are connected in this way because the filters interact. The equation error method is described in, for example, the above-mentioned book: Widrow and Stearns Adaptive signal processing, p. 250-253.

Disclosure of the Invention

The object of the present invention is to provide an adaptive digital filter comprising a non-recursive part and a recursive part, and which can be updated in a simple and secure manner. This is achieved by having the recursive part of the filter have a number of separate, fixed recursive filters with different impulse responses, and that a linear combination with adaptive weight factors is formed by the output signals of the recursive filters. The filter is updated by using the same signal to update the non-recursive part and the adaptive weight factors in the recursive part.

In this way, a stable filter is also attached, due to the fact that the poles of the recursive filters are not moved.

The features of the invention are set forth in the claims.

Figure Description

The invention will be described in more detail with reference to the drawings, in which figure 1 shows a known device for echo cancellation, figure 2 shows an example of a desired impulse response from a filter according to the invention, figure 3 shows a first embodiment of a filter according to the invention, figure 4 shows a more detailed embodiment of the filter according to Figure 3, Figure 5 is a graph showing examples of various impulse responses of certain separate filters included in the filter of the invention and Figure 6 shows a second embodiment of a filter according to the invention.

Preferred embodiments

Figure 1 shows a known device for echo extinguishing. A digital input signal x (n) appearing on a transmitter side in a telecommunications equipment is applied to a two to four-tree junction 2, i.e. and sk. hybrid or fork, which is connected to a receiver side of the telecommunications equipment and over a washing line to a telephone set. 4. Echo signals propagate in the hybrid and in the washing line. The output signal to the receiver side from the hybrid 2 is denoted d (n) and consists only of echo signals if no signal is received from the telephone set 4. This signal corresponds to the above-mentioned desired signal.

The input signal x (n) is applied to Sven an adaptive FIR filter 1, which generates an expected echo signal y (n). In an addition means 3 a so-called. error signal e (n), which is the difference between signals d (n) and y (n), and which is used to update the filter. As above, an FIR filter can be updated according to known methods, e.g. LMSmetoden. However, the filter's impulse response is generally too short for an effective echo cancellation to be achieved.

Figure 2 shows an example of a desired impulse response h (n) with relatively long extension in time, where n indicates the order number of the respective sample value. The impulse response can be divided into two main parts. First comes a strong swing-in course within which most of the signal energy of the impulse lies. Then follows a long and mainly exponentially declining part, a so-called. tail. Negative values ​​can also occur in the impulse response.

Figure 3 shows a first embodiment of a filter according to the invention. The filter receives as an input signal a digital signal x (n), which corresponds, for example, to the signal x (n) in the device according to Figure 1. The input signal is applied to an FIR filter 11 directly and a number of IIR filters 13-16 after delay with a time τ in a delay means. 12. The IIR filters are preferably of the first degree and have fixed filter coefficients with different values. The output of the FIR filter 11 is supplied with an addition means 22, and the output signals of the IIR filters 13-16 are supplied with their multiplication means 1821. Each of them has an adaptive multiplication factor. These multiplication factors are assumed to have the values ​​WOWS, and they are set in the manner given below. Finally, the output signals from the FIR filter 11 and from the multiplier means 18-21 are added in the addition means 22.

According to the inventive idea, the first portion of the impulse response is generated in the FIR filter 11 and the second portion as a linear combination of the output signals from the IIR filters 13-16. The weights in the linear combination are thereby determined by the adaptive multiplication factors, or the weight factors, WO-W3. By appropriately delaying the input signal x (n) to the IIR filters, both portions of the impulse response can be generated independently of one another. The filters according to the invention thus consist of two separate filter parts, a non-recursive filter part, a non-recursive filter part and a recursive filter part and a recursive filter part, whose output signals are added.

The output signal of the filter is designated y (n) and is subtracted from any desired signal d (n) in an addition means 3. A difference signal e (n) thus obtained appears on line 17 and is used to update the non-recursive filter portion, i.e. The FIR filter 11, and of the recursive filter portion. The latter is done by updating the adaptive weight factors WOWS of the multiplication means 18-21. For example, the signals y (n), d (n) and e (n), and the addition means 3 correspond to the corresponding signals and means in Figure 1, but the range of application of the filter is obviously not limited to echo extinguishing. For the sake of completeness, it is noted that the bed at the FIR filter 11 and the multiplication means 18-21 requires updating means, which are generally known in connection with digital filters.

Figure 4 shows a more detailed embodiment of the filter according to Figure 3. The FIR filter 11 in the known manner consists of delay means 38-40, multiplication means 34-37, and addition means 31-33. The IIR filters 13-16 are of the first degree, each with a fixed filter coefficient. Also, these filters are constructed in known manner and control each of one of an addition means, e.g. 131, a delay means, e.g. 132, and a multiplication means, e.g. 133rd Multiplication means are each assigned a set coefficient PO-P3, which have different values ​​between themselves, and thus constitute the filter coefficients of the IIR filters.

Each of the delay means 38-40 entering the FIR filter 11 delays the input signal x (n) by a sample value, and together these means correspond to the delay means 12 shown in Figure 3. In the example shown, τ = 3 T. Thus, separate delay means are not required in practice but can instead be included in the FIR filter. The addition member 22 of Figure 3 is shown in Figure 4 as a number of separate addition means 221-224.

As explained above, the difference signal e (n) is used for updating the FIR filter 11 and for updating the adaptive weight factors W0-W3 of the multiplication means 18-21 in the recursive filter part. The problem of minimizing the difference signal e (n) is tantamount to minimizing the sum of the squares of the expression

W0 x P0ⁿ + W1 x Plⁿ + W2 x P2 + W3 x P3ⁿ - f (n) preferably from noil to infinity, where PO-P3 is the fixed recursive filter coefficients and f (n) is the desired impulse response. This sum has a square error area with only a minimum, since the weighting factors are only linear in the expression. This means that the recursive filter part can be updated according to the same method as the non recursive filter part, for example according to the LMS method.

Some advantages obtained by the filter according to the invention are that the difference signal is represented by a square error surface, while the difference signal represents the actual error (as opposed to in an equation error structure). In addition, the recursive filter part is always stable since the poles of the individual IIR filters are not moved. This, in turn, is because the filter coefficients PO-P3 are fixed.

Figure 5 shows a number of curves, which are examples of different impulse responses of the individual IIR filters in the recursive part of the filter. The transfer functions of the IIR filters 1316 are in turn designated h0 (n) -h3 (n). It is assumed that the input signal to the filters is delayed by a number of sample values ​​corresponding to the length of the pulse response of the FIR filter. The filter coefficients P0-P3 are, for example, 0.5, 0.75, 0.875 and 0.9375. The transfer functions are then: h0 (n) = 0.5, hl (n) = 0.75, etc. Other coefficient values ​​can of course also be selected.

The part of the entire desired impulse response that appears to the left of the impulse response shown in Figure 5, ie. earlier than these are generated in the FIR filter 11. This is adapted so that its output signal ceases when the pulse response of Figure 5 begins. However, it is pointed out that the number of delay means in the FIR filter contained in the filter of Figure 4 is not matched to the curves of Figure 5.

By linearly combining a number of given impulse responses in the manner described above, it is possible to obtain impulse responses of widely varying shapes. Both positive and negative weight factors W0-W3 can of course occur. However, the long, declining portion of the desired impulse response may not always be exactly imitated. However, this does not play much importance, since only a relatively small part of the energy of the entire desired impulse response lies in this part. The first, powerful part of the impulse response and generated by the FIR filter 11, on the other hand, can be simulated fairly accurately.

Figure 6 shows a second embodiment of a filter according to the invention. In addition to the means included in the filter of Figure 3, this filter also includes a network designated 50. This includes multiplication means and addition means which are arranged to form linear combinations of the output signals of the IIR filters 13-16. The means are thereby coupled so that the multiplication means 18 receives the output signal from the filter 13 in unchanged condition. The multiplier 19 receives the sum of the output of the filter 14 and the output of the filter 13 multiplied by a factor, etc. according to the figure. The linear combinations can be selected so that the input signals to the multiplication means 18-21 become orthogonal. Subsequently, these orthogonal impulse responses are weighted with adaptive weight factors, as in the filters of Figures 3 and 4. In this case, a change of a certain weight factor does not necessarily entail a change in the other weight factors. Thereby a faster convergence is achieved. However, the number of calculations increases slightly.

The filter according to the invention can be used in various seam applications where a relatively long pulse response is desired and not only for adaptive echo cancellation. Of course, the number of IIR filters can be both higher or lower than just four, as shown in the examples. The design of the FIR filter and the IIR filter may also be different from that shown in the examples. Also, it is not necessary to delay the input signal of the IIR filters. However, the delay results in the first portion of the desired impulse response being generated by the FIR filter only, and the second portion being generated by only the recursive filter portion.