EP4117306A1 - Electro-acoustic method using an lms algorithm - Google Patents

Abstract

Electro-acoustic method using an LMS algorithm. This can be used, among other things, for feedback suppression, echo suppression, feedback suppression, hum suppression and many other areas. The method is characterized in that a sign LMS is combined with a PEAK filter according to a given system of equations.

Description

The invention relates to an electro-acoustic method using an LMS algorithm according to the preamble of claim 1.

LMS algorithms, the collective term for algorithms in which the squares of error are minimized (least mean squares) have long been used in electroacoustics, in particular for adaptive filters in numerous variants and for the most diverse areas of application. The currently most used variants are known by the following abbreviations: LMS-NLMS, sign-LMS, LMS with variable increment (VSS-LMS), LMS with correlation factor or NLMS and for special applications variants such as filtered-x LMS or filtered-e LMS (please refer International Journal of Electrical and Computer Engineering Vol. 7, No. 5, October 2017, LMS Adaptive Filters for Noise Cancellation: A Review, pp. 2520ff ).

As an example of usage is just the U.S. 9,807,503 in which an equalizer is applied to optimize the playback of a digital acoustic source (e.g. Bluetooth audio). The equalizer is controlled by an adaptive filter whose filter coefficients are obtained, for example, by using LMS and then smoothed using linear interpolation and/or the exponential method.

Regarding exponential smoothing, it should be said that it uses the same coefficient for the attack and release case and that with adaptive filters, under certain unfavorable conditions, the filter coefficients can converge towards infinitely high values, whereby they are limited by the word length of the processor used ( clipping). A typical case is acoustic feedback suppression: if feedback occurs (the microphone records the loudspeaker), this can be heard as a very loud sine wave ("howling"). In this case, an adaptive filter is configured to filter the speaker output and subtract at the microphone. In the best case, it filters the feedback sine exactly and subtracts it from the microphone, ergo the sine is eliminated. However, if the system is confronted with a sine-like tone from an external source (e.g music) the adaptive filter tries to eliminate it. Since it does not get weaker despite subtraction (the source is no longer the loudspeaker but external), the filter coefficients swell towards infinity. The result is a distorted sound. In order to avoid this erroneous convergence, it is also known in the prior art to monitor the coefficients using an external algorithm and to limit them at a specific threshold value, which is favorable in terms of the result, but entails greater outlay in terms of complexity and computing power.

This should be clarified with an example:
Consider a typical case of feedback cancellation, such as that found in ANC headphones or hearing aids.

• die Fig. 1 den schematischen Aufbau einer Rückkopplungs-Unterdrückung,
• die Fig. 2 stabile Werte für die Koeffizienten des Filters,
• die Fig. 3 stetig wachsende Filterkoeffizienten im Problemfall,
• die Fig. 4 ein stabiles Verhalten für das gewählte Verfahren,
• die Fig. 5 die Anwendung der Erfindung auf die Regelung eines Verstärkers,
• die Fig. 6 die Abfolge optisch, in Form eines Schaltbildes,
• die Fig. 7 die Schrittantwort des Filters,
• die Fig. 8 in einer Variante,
• die Figs 9a und 9b in zwei weiteren Varianten und
• die Fig. 10 in einer bevorzugten Variante.

It shows or show.

• the 1 the schematic structure of a feedback suppression,
• the 2 stable values for the coefficients of the filter,
• the 3 constantly increasing filter coefficients in case of problems,
• the 4 a stable behavior for the selected method,
• the figure 5 the application of the invention to the control of an amplifier,
• the 6 the sequence visually, in the form of a circuit diagram,
• the 7 the step response of the filter,
• the 8 in a variant,
• the Figures 9a and 9b in two other variants and
• the 10 in a preferred variant.

1 shows the schematic structure of feedback suppression. Microphone 1 records the output of the driver (loudspeaker 2), creating what is known as acoustic feedback (audible as a very loud sine wave). An adaptive filter 3 attempts to estimate the transfer function of the feedback path and subtracts the filtered output from the driver at the microphone input. If the transfer function is estimated correctly, the filter 'clips' the sine and subtracts it from itself at the input, suppressing feedback.

Block 4 for adapting the filter calculates new filter coefficients from the reference signal (reproduction) and the error signal (result of the subtraction). In 1 is entered in the adaptation block LMS / SignLMS / PEAK-LMS. These three variants are compared below under identical conditions:
In a simulation, white noise (duration 1 second, sampling rate 48kHz) is fed to the microphone. The same learning rate is always used for the three algorithms. For PEAK-LMS, the individual coefficients are limited by µ _pos = 1 and µ _neg = -1. For this use case, the attack time is equal to the release time. In this case, the time constants must be selected as a function of the sampling rate in a manner known to a person skilled in the art from the prior art. For the sampling rate of 48kHz given here, for example, it would be 300ms.

A) Sensitivity to the learning rate

The learning rate is a factor here by which the adaptation takes place. LMS is a gradient method, where the gradient is based on the least squares error. The learning rate thus defines an increment by which the coefficients are adjusted. The sensitivity of the learning rate is shown for LMS: For a learning rate of 0.00005, the algorithm produces NAN (Not A Number), for the filter coefficients, for a learning rate of 0.000005, the adaptation is too slow. Sign LMS shows a similar behavior and becomes unstable if the learning rate is too high or adapts too slowly if the learning rate is too low. For this example, 0.00001 is a near-optimal learning rate. PEAK-LMS shows a significantly higher tolerance: for 0.00005 the suppression performance is reduced, but the algorithm remains as it is 2 evident, with stable values for the coefficients.

B) susceptibility to failure

A typical problem for feedback cancellation is the case of an 'outer' tone (sine-like). The adaptive filter finds sine tones and wants to suppress them because they are considered feedback. For a sound whose source is not feedback but e.g. music, the problem arises with the adaptive filter that the supposed feedback does not become weaker due to the subtraction at the microphone and the filter gets into an incorrect setting (this effect is called 'entrainment').

For LMS it can be seen that the filter coefficients tend towards infinity since the gradient - due to the constant error - always remains the same.

the 3 clearly shows how the filter coefficients always increase. The number range -4000 to +2000 may no longer be mappable in a fixed-point processor; the result of the filtering cannot be played under any circumstances (DA converters are limited to a value range +/-1 in acoustics). In the above example, the filter coefficients reach ± ∞ after a short time and the simulation stops because it can no longer be calculated.

PEAK LMS, on the other hand, will limit µ _pos and µ _neg , which avoids instabilities. Under identical conditions as above, PEAK LMS shows according to 4 a stable behavior:
The range of values ±1 can be easily represented in conventional fixed-point processors for audio (eg 24-bit). Here, PEAK-LMS prevents the coefficients from increasing too much. In the extreme case, the algorithm would limit at 1, but here it generally prevents an incorrect setting.

Example gain control:

One application is controlling an amplifier based on estimating the gain of a transfer function, as in figure 5 shown.

In the case of an in-ear ANC (Active Noise Canceling) headphone, the gain of a transfer function must be controlled in real time. Real-time means with the lowest possible latency and time-invariant. The processing cannot therefore take place independently of the temporal signal. For example, the processing of an audio file that has already been recorded would not be real-time, since a calculation is theoretically not subject to any time pressure. For ANC, on the other hand, incoming microphone data must be processed as soon as possible. Depending on the wearing situation (insertion depth; individual shape of the auditory canal), the amplification of the primary route (outer microphone) and/or the amplification of the secondary route (inner microphone) must be adapted in order to optimize the performance of the ANC system.

In this example, too, conventional LMS variants will always converge towards a theoretical optimum. A problem arises when the device is removed from the ear: there is no longer any passive damping and LMS would try to increase the gain of the ANC filter to infinity, since there is no longer any ANC power. Thus, additional sensors would have to be used to detect whether the device is in the ear or not. PEAK-LMS will automatically limit at µ _pos and µ _neg and thus avoid clipping and the resulting artefacts on the driver.

There is therefore a need for an LMS algorithm that does not have the disadvantages mentioned and can be used not only in ANC systems, but wherever adaptive filters are used, for example in echo suppression, feedback suppression, System estimation (detection of an unknown transfer function), channel equalization (also applies to HF technology), adaptive inverse control, hum suppression (50Hz hum of the power supply filter for e.g. ECG sensors), vector voltmeter, separation of signals with different correlations, interference suppression in audiological measurement systems (e.g. measurement of otoacoustic emissions) and many others.

According to the invention , these problems are solved by using an LMS algorithm which has the features specified in the characterizing part of claim 1 in other words, where different coefficients are used for attack and release. In one embodiment, upper and lower limits are set for the coefficients in the method/algorithm itself, so that the risk of upward convergence is intrinsically excluded, which also eliminates the need for complex, external monitoring.

$$\mathit{c}\left(n+1\right)=\mathit{c}\left(n\right)+\mathit{\mu }\ast e\left(n\right)\ast \mathit{x}\left(n\right)$$

The LMS algorithm in its known form is (Formula I): $$e\left(n\right)=x\left(n\right)-y\left(n\right)$$

$$\mathit{c}\left(n+1\right)=\mathit{c}\left(n\right)+\mathit{\mu }\ast e\left(n\right)\ast \mathit{x}\left(n\right)$$

The vectors are printed in bold, the scalars in normal. x(n) is the element of the vector x(n) at time n.

Specifically, c ( n +1) stand for the result of the nth adaptation of c , c ( n ) for the value of c obtained in the n-1th step; µ (also mu) for the adaptation rate; e ( n ) for the error signal at step n, x ( n ) for the nth input value, and y ( n ) for the output of the filter at the nth step.

In 6 the sequence is shown optically in the form of a circuit diagram (with n for n ), with the input signal x, the adaptive filter c ( n ), the difference formation of the obtained value y with the given value x, which leads to e and the LMS block , which determines the necessary adaptations of the filter c ( n ).

$$\mathit{c}\left(n+1\right)=\mathit{c}\left(n\right)+\mathit{\mu }\ast \mathit{sgn}\left(e\left(n\right)\ast \mathit{x}\left(n\right)\right)$$

In the 6 The basic form shown from the prior art is sensitive to level fluctuations in the input signal x in that it has a negative effect on the convergence of the algorithm. Various adaptations of the LMS method have been proposed, which are part of the prior art under the designations NLMS and sign-LMS and reduce this sensitivity. NLMS is unfavorable on fixed-point processors because it requires division for normalization. Divisions mean increased computational effort and are subject to quantization effects on fixed-point systems. Sign-LMS does not require division, but does so at the expense of convergence speed and occurrence of one larger residual error of the adaptation. For sign-LMS, the formulas II derived from formulas I are as follows: $$e\left(n\right)=x\left(n\right)-y\left(n\right)$$

$$\mathit{c}\left(n+1\right)=\mathit{c}\left(n\right)+\mathit{\mu }\ast \mathit{so\; called}\left(e\left(n\right)\ast \mathit{x}\left(n\right)\right)$$

$$y\left(n\right)=y\left(n-1\right)+C\left(\alpha ,\beta \right)\ast \left(x\left(n\right)-y\left(n-1\right)\right)$$

As can be seen directly, a small step ( µ ) is added or subtracted to a coefficient. In the event of an incorrect setting (as explained above with reference to feedback suppression, filter coefficients can converge to infinity under unfavorable conditions) it can theoretically go to infinity this change, which is prevented by the so-called PEAK algorithm, also known as the exponential window method (Formula III): $$\begin{array}{c}C\left(a,\beta \right)=\{\begin{array}{c}x\left(n\right)>y\left(n-1\right):a\\ x\left(n\right)\le y\left(n-1\right):\beta \end{array}\end{array}$$

$$y\left(n\right)=y\left(n-1\right)+C\left(a,\beta \right)\ast \left(x\left(n\right)-y\left(n-1\right)\right)$$

.The time constants α and β stand for the attack and release case and thus determine the rise and fall time of the algorithm. α and β are purely numerical, their temporal significance depends on the selected sampling rate. Both move in the interval [0;1].

.

This is a one-pole, recursive filter that has an attack and a release time constant. If the input signal is greater than the filter output, the attack time constant is applied, otherwise the release time constant.

The so-called step response of the filter, the value to which the filter tends for an input signal that jumps from 0 to 1 and then remains constant, is in 7 shown. The influence of the attack time constant can be seen from this.

$$\mathit{c}\left(n+1\right)=\mathit{c}\left(n\right)+C\left(\alpha ,\beta \right)\ast \left(\mathit{w}\left(n\right)-\mathit{c}\left(n\right)\right)$$

The invention now also includes a combination of the sign LMS with the PEAK filter; each individual coefficient is no longer calculated by addition a step size, but via the step response of the PEAK filter. This results in the formulas IV according to the invention: $$\mathit{w}\left(n\right)=\mathit{so\; called}\left(e\left(n\right)\ast \mathit{x}\left(n\right)\right)$$

$$\mathit{c}\left(n+1\right)=\mathit{c}\left(n\right)+C\left(a,\beta \right)\ast \left(\mathit{w}\left(n\right)-\mathit{c}\left(n\right)\right)$$

The inputs to the algorithm e ( n ) and x(n) could be filtered before being fed to the algorithm. This has the advantage of focusing the adaptation on a frequency range. The desired frequency range depends on the application and can be defined individually by a person skilled in the art. Due to the exponential function of the PEAK filter, the LMS method can no longer converge to infinity, even if, for example, constant + increment µ is calculated for a coefficient due to an incorrect setting (see feedback cancellation example above). The embodiment given in formula IV sets the attack and release time constants equal, namely with C ( α,β ) , which means that the algorithm (example rectangular pulse) converges in both directions at the same speed; this is in 8 shown.

$$\begin{array}{c}C\left(\alpha ,\beta \right)=\{\begin{array}{c}\mathit{w}\left(n\right)>\mathit{c}\left(n\right):\alpha \\ \mathit{w}\left(n\right)\le \mathit{c}\left(n\right):\beta \end{array}\end{array}$$

$$\mathit{c}\left(n+1\right)=\mathit{c}\left(n\right)+C\left(\alpha ,\beta \right)\ast \left(\mathit{w}\left(n\right)-\mathit{c}\left(n\right)\right)$$

In one embodiment of the invention, different values are used for the attack and release time constants, with the result that different convergence times are obtained for positive and negative coefficients, formulas V: $$\mathit{w}\left(n\right)=\mathit{so\; called}\left(e\left(n\right)\ast \mathit{x}\left(n\right)\right)$$

$$\begin{array}{c}C\left(a,\beta \right)=\{\begin{array}{c}\mathit{w}\left(n\right)>\mathit{c}\left(n\right):a\\ \mathit{w}\left(n\right)\le \mathit{c}\left(n\right):\beta \end{array}\end{array}$$

$$\mathit{c}\left(n+1\right)=\mathit{c}\left(n\right)+C\left(a,\beta \right)\ast \left(\mathit{w}\left(n\right)-\mathit{c}\left(n\right)\right)$$

These and other modifications open up possibilities and areas of application that are not accessible with the various LMS variants of the prior art.

$$\begin{array}{c}C\left(\alpha ,\beta \right)=\{\begin{array}{c}\mathit{w}\left(n\right)>\mathit{c}\left(n\right):\alpha \\ \mathit{w}\left(n\right)\le \mathit{c}\left(n\right):\beta \end{array}\end{array}$$

$$\mathit{c}\left(n+1\right)=\mathit{c}\left(n\right)+C\left(\alpha ,\beta \right)\ast \left(\mathit{w}\left(n\right)-\mathit{c}\left(n\right)\right)$$

As an example: The signum operator returns 1, or 0, or -1; by introducing a factor µ , the limit of the coefficient can be controlled, as shown by formulas VI: $$\mathit{w}\left(n\right)=\mathit{\mu }\ast \mathit{so\; called}\left(e\left(n\right)\ast \mathit{x}\left(n\right)\right)$$

$$\begin{array}{c}C\left(a,\beta \right)=\{\begin{array}{c}\mathit{w}\left(n\right)>\mathit{c}\left(n\right):a\\ \mathit{w}\left(n\right)\le \mathit{c}\left(n\right):\beta \end{array}\end{array}$$

$$\mathit{c}\left(n+1\right)=\mathit{c}\left(n\right)+C\left(a,\beta \right)\ast \left(\mathit{w}\left(n\right)-\mathit{c}\left(n\right)\right)$$

The factor µ is fundamentally freely definable and application-related. For audio, however, the interval [0,1] makes sense.

$$\begin{array}{c}\mathit{\mu }=\{\begin{array}{c}\mathit{w}\left(n\right)>0:{\mathit{\mu }}_{+}\\ \mathit{w}\left(n\right)=0:0\\ \mathit{w}\left(n\right)<0:{\mathit{\mu }}_{-}\end{array}\end{array}$$

$$\begin{array}{c}C\left(\alpha ,\beta \right)=\{\begin{array}{c}\mathit{w}\left(n\right)>\mathit{c}\left(n\right):\alpha \\ \mathit{w}\left(n\right)\le \mathit{c}\left(n\right):\beta \end{array}\end{array}$$

$$\mathit{c}\left(n+1\right)=\mathit{c}\left(n\right)+C\left(\alpha ,\beta \right)\ast \left(\mathit{\mu }-\mathit{c}\left(n\right)\right)$$

With this it is also possible to set different limits for the coefficients in the negative and positive area and also own limits for each individual coefficient, formula VII: $$\mathit{w}\left(n\right)=\mathit{so\; called}\left(e\left(n\right)\ast \mathit{x}\left(n\right)\right)$$

$$\begin{array}{c}\mathit{\mu }=\{\begin{array}{c}\mathit{w}\left(n\right)>0:{\mathit{\mu }}_{+}\\ \mathit{w}\left(n\right)=0:0\\ \mathit{w}\left(n\right)<0:{\mathit{\mu }}_{-}\end{array}\end{array}$$

$$\begin{array}{c}C\left(a,\beta \right)=\{\begin{array}{c}\mathit{w}\left(n\right)>\mathit{c}\left(n\right):a\\ \mathit{w}\left(n\right)\le \mathit{c}\left(n\right):\beta \end{array}\end{array}$$

$$\mathit{c}\left(n+1\right)=\mathit{c}\left(n\right)+C\left(a,\beta \right)\ast \left(\mathit{\mu }-\mathit{c}\left(n\right)\right)$$

By using different attack and release time constants, the adaptation of the filter can be handled extremely flexibly, while the advantages of the sign-LMS over other variants, as well as the NLMS, are retained, no divisions are required during the calculation process, which is implementation on a fixed-point DSP is advantageous.

An example implementation of the above is adaptive gain control. An amplification should regulate adaptively in the range of ± 6 dB FS. By setting an upper limit for µ of 2 and a lower limit of 0.5, the PEAK-LMS algorithm automatically regulates ± 6 dB without the need for additional calculations, such as converting linear values to decibels and vice versa. The elegance of the solution is thus evident.

The interval -/+6dB here is application-related for an adaptive gain control in an ANC receiver. Other areas of application include feedback suppression, ANC, echo cancellation, adaptive beamforming, adaptive gain control and similar applications. The range of the gain control depends on the respective product and the calculated ANC filters. In any case, the sensible interval range is +/- 10dB. The volume of the pressure chamber created by the auditory canal and the in-ear headphones varies depending on the wearing situation, e.g. This in turn must be taken into account and compensated for by an adaptive ANC system.

As briefly mentioned above, the sign-LMS has a residual error of convergence, the size of which depends on the step size µ, also called mu: Larger mu leads to fast convergence, but with a larger residual error; smaller mu leads to slower convergence with smaller residual error. The variant used according to the invention shows a behavior similar to that shown in FIG Figure 9a shows, this represents the adaptation speed and the residual error with a time constant of the PEAK filter of 0.001, the Figure 9b at a time constant of 0.0025.

$$e\left(n\right)=x\left(n\right)-y\left(n\right)$$

$$\mathit{c}\left(n+1\right)=\mathit{c}\left(n\right)+\mathit{\mu }\left(n\right)\ast e\left(n\right)\ast \mathit{x}\left(n\right)$$

It is now known in LMS algorithms in general to improve them by choosing the step size adaptively depending on the size of the error, this is commonly known as variable step-size LMS as indicated by Formulas VIII: $$\mathit{\mu }\left(n+1\right)=a\ast \mathit{\mu }\left(n\right)+b\ast e^2\left(n\right)$$

$$e\left(n\right)=x\left(n\right)-y\left(n\right)$$

$$\mathit{c}\left(n+1\right)=\mathit{c}\left(n\right)+\mathit{\mu }\left(n\right)\ast e\left(n\right)\ast \mathit{x}\left(n\right)$$

$$\mathit{c}\left(n+1\right)=\mathit{c}\left(n\right)+\mathit{C}\left(n\right)\ast \left(\mathit{w}\left(n\right)-\mathit{c}\left(n\right)\right)$$

$$\mathit{C}\left(n+1\right)=a\ast \mathit{C}\left(n\right)+b\ast e^2\left(n\right)$$

An upper limit and a lower limit can be introduced for µ ; the step size is chosen large when the error is large and small when it is small, thus making a compromise between convergence speed and residual error. In an advantageous embodiment of the invention, this method can also be applied to the adaptation speed, which provides the formulas IX for the case of the same attack and release time constants: $$\mathit{w}\left(n\right)=\mathit{\mu }\ast \mathit{so\; called}\left(e\left(n\right)\ast \mathit{x}\left(n\right)\right)$$

$$\mathit{c}\left(n+1\right)=\mathit{c}\left(n\right)+\mathit{C}\left(n\right)\ast \left(\mathit{w}\left(n\right)-\mathit{c}\left(n\right)\right)$$

$$\mathit{C}\left(n+1\right)=a\ast \mathit{C}\left(n\right)+b\ast e^2\left(n\right)$$

$$\mathit{c}\left(n+1\right)=\mathit{c}\left(n\right)+\mathit{C}\left(n\right)\ast \left(\mathit{w}\left(n\right)-\mathit{c}\left(n\right)\right)$$

$$\mathit{C}\left(n+1\right)=a\ast \mathit{C}\left(n\right)+b\ast e^2\left(n\right)$$

Improved convergence is off 10 clearly evident. If this method is also used in the illustrated embodiment of the invention with different time constants, the formula X is obtained: $$\mathit{w}\left(n\right)=\mathit{\mu }\ast \mathit{so\; called}\left(e\left(n\right)\ast \mathit{x}\left(n\right)\right)$$

$$\mathit{c}\left(n+1\right)=\mathit{c}\left(n\right)+\mathit{C}\left(n\right)\ast \left(\mathit{w}\left(n\right)-\mathit{c}\left(n\right)\right)$$

$$\mathit{C}\left(n+1\right)=a\ast \mathit{C}\left(n\right)+b\ast e^2\left(n\right)$$

A note: in this case there are no predetermined attack/release times, since the formula in the bottom line recalculates the time constants in each iteration!

The invention is not limited to the example and its variants, but can be used wherever LMS algorithms are used and there is a risk of instability due to the external conditions or a rapid reaction is desired.

The two terms "step response" and "step response" are used synonymously in this application.

In the formulas given, the algorithm was always defined in the time domain. A person skilled in the art can easily define this using appropriate methods, for example the Laplace transformation, with the same result over the frequency range.

Claims (9)

Electro-acoustic method using an LMS algorithm, in feedback suppression, echo suppression, feedback suppression, system estimation, in the detection of an unknown transfer function, in channel equalization, in HF technology, in adaptive inverse control , in hum suppression, such as filtering the 50Hz hum of the power supply, in particular in ECG sensors, in vector voltmeters, in the separation of signals with different correlations, in suppressing interference in audiological measuring systems, in particular when measuring otoacoustic emissions that a sign-LMS is combined with a PEAK filter, and that the calculation of each individual coefficient via the step response of the PEAK filter using the following formulas (IV): $$\mathit{w}\left(n\right)=\mathit{so\; called}\left(e\left(n\right)\ast \mathit{x}\left(n\right)\right)$$

$$\mathit{c}\left(n+1\right)=\mathit{c}\left(n\right)+\mathit{C}\left(a,\beta \right)\ast \left(\mathit{w}\left(n\right)-\mathit{c}\left(n\right)\right)$$

takes place, where c ( n +1) for the result of the nth adaptation of c, c(n) for the value of c obtained in the n-1th step; C (α ,β ) Attack- the release time constant; e ( n ) stands for the error signal in step n and x(n) for the nth input value. Electro-acoustic method according to claim 1, characterized in that the inputs of the algorithm e ( n ) and x(n) are filtered before being fed to the algorithm. Electro-acoustic method according to one of claims 1 or 2, characterized in that different values according to the following formulas (V) are used for attack and release time constants: $$\mathit{w}\left(n\right)=\mathit{so\; called}\left(e\left(n\right)\ast \mathit{x}\left(n\right)\right)$$

$$\begin{array}{c}C\left(a,\beta \right)=\{\begin{array}{c}\mathit{w}\left(n\right)>\mathit{c}\left(n\right):a\\ \mathit{w}\left(n\right)\le \mathit{c}\left(n\right):\beta \end{array}\end{array}$$

$$\mathit{c}\left(n+1\right)=\mathit{c}\left(n\right)+C\left(a,\beta \right)\ast \left(\mathit{w}\left(n\right)-\mathit{c}\left(n\right)\right)$$

Electro-acoustic method according to claims 1 to 3, characterized in that a factor µ with values of 0 ≤ µ ≤ 1 controls the limit of the coefficient, according to the formulas (VI): $$\mathit{w}\left(n\right)=\mathit{\mu }\ast \mathit{so\; called}\left(e\left(n\right)\ast \mathit{x}\left(n\right)\right)$$

$$\begin{array}{c}C\left(a,\beta \right)=\{\begin{array}{c}\mathit{w}\left(n\right)>\mathit{c}\left(n\right):a\\ \mathit{w}\left(n\right)\le \mathit{c}\left(n\right):\beta \end{array}\end{array}$$

$$\mathit{c}\left(n+1\right)=\mathit{c}\left(n\right)+C\left(a,\beta \right)\ast \left(\mathit{w}\left(n\right)-\mathit{c}\left(n\right)\right)\mathrm{.}$$

Electro-acoustic method according to one of claims 1 to 4, characterized in that different limits are set for the coefficients in the negative and positive range and also separate limits for each individual coefficient according to the formulas (VII): $$\mathit{w}\left(n\right)=\mathit{so\; called}\left(e\left(n\right)\ast \mathit{x}\left(n\right)\right)$$

$$\begin{array}{c}\mathit{\mu }=\{\begin{array}{c}\mathit{w}\left(n\right)>0:{\mathit{\mu }}_{+}\\ \mathit{w}\left(n\right)=0:0\\ \mathit{w}\left(n\right)<0:{\mathit{\mu }}_{-}\end{array}\end{array}$$

$$\begin{array}{c}C\left(a,\beta \right)=\{\begin{array}{c}\mathit{w}\left(n\right)>\mathit{c}\left(n\right):a\\ \mathit{w}\left(n\right)\le \mathit{c}\left(n\right):\beta \end{array}\end{array}$$

$$\mathit{c}\left(n+1\right)=\mathit{c}\left(n\right)+C\left(a,\beta \right)\ast \left(\mathit{\mu }-\mathit{c}\left(n\right)\right)$$

Electro-acoustic method according to one of the preceding claims, characterized in that the step size is chosen adaptively depending on the error size, according to the formulas (VIII): $$\mathit{\mu }\left(n+1\right)=a\ast \mathit{\mu }\left(n\right)+b\ast e^2\left(n\right)$$

$$e\left(n\right)=x\left(n\right)-y\left(n\right)$$

$$\mathit{c}\left(n+1\right)=\mathit{c}\left(n\right)+\mathit{\mu }\left(n\right)\ast e\left(n\right)\ast \mathit{x}\left(n\right),$$

an upper limit and a lower limit preferably being defined for μ . Electro-acoustic method according to one of the preceding claims, characterized in that the adaptation speed is adjusted as a function of the error size, in accordance with the formulas IX: $$\mathit{w}\left(n\right)=\mathit{\mu }\ast \mathit{so\; called}\left(e\left(n\right)\ast \mathit{x}\left(n\right)\right)$$

$$\mathit{c}\left(n+1\right)=\mathit{c}\left(n\right)+\mathit{C}\left(n\right)\ast \left(\mathit{w}\left(n\right)-\mathit{c}\left(n\right)\right)$$

$$\mathit{C}\left(n+1\right)=a\ast \mathit{C}\left(n\right)+b\ast e^2\left(n\right)$$

Electro-acoustic method according to claim 6, characterized in that different values are used for attack and release time constants, corresponding to the formulas X: $$\mathit{w}\left(n\right)=\mathit{\mu }\ast \mathit{so\; called}\left(e\left(n\right)\ast \mathit{x}\left(n\right)\right)$$

$$\mathit{c}\left(n+1\right)=\mathit{c}\left(n\right)+\mathit{C}\left(n\right)\ast \left(\mathit{w}\left(n\right)-\mathit{c}\left(n\right)\right)$$

$$\mathit{C}\left(n+1\right)=a\ast \mathit{C}\left(n\right)+b\ast e^2\left(n\right)\mathrm{.}$$

Electro-acoustic method according to one of the preceding claims, characterized in that the algorithm is applied to the frequency range.

Images