Active noise control method and system

Abstract

A method for reducing the power of an acoustic primary noise signal (d.sub.m(n)) at one or more control positions in a vehicle passenger compartment using an adaptive filter. The method comprising to compare a mean correlation coefficient (γ.sub.m(n)) between an electrical error signal (e.sub.m(n) and a modelled secondary anti-noise signal ŷ.sub.m(n) with at least one predefined threshold (α, β).

Claims

1. A method for reducing the power of an acoustic primary noise signal (d.sub.m(n), m=1, 2, 3, . . . ) at one or more control positions in a vehicle passenger compartment, the acoustic primary noise signal originating from an acoustic noise signal transmitted from a noise source through a respective primary sound path (P.sub.m, m=1, 2, 3, . . . ) to the respective control position, the method comprising: arranging an adaptive filter to receive input signals comprising: an electrical reference signal (x(n)) representing the acoustic noise signal, and at least one electrical error signal (e.sub.m(n), m=1, 2, 3, . . . ) representing a respective acoustic signal detected by a respective sound sensor at the respective control position, arranging the adaptive filter to provide and transmit at least one electrical control signal (y′.sub.k(n), k=1, 2, 3, . . . ) to at least one acoustic transducer arranged in the compartment, arranging the at least one acoustic transducer to, as a response to the at least one electrical control signal (y′.sub.k(n), k=1, 2, 3, . . . ), provide and transmit a respective anti-noise signal through a respective secondary sound path (S.sub.km, k=1, 2, 3, . . . , m=1, 2, 3, . . . ) between the at least one acoustic transducer and the respective control position, arriving at the at least one control position as a respective acoustic secondary anti-noise signal (y.sub.m(n), m=1, 2, 3, . . . ), such as to minimize the respective electrical error signal (e.sub.m(n), m=1, 2, 3, . . . ), providing a respective modelled secondary anti-noise signal (ŷ.sub.m(n), m=1, 2, 3, . . . ) from a respective secondary sound path model (Ŝ.sub.km, k=1, 2, 3, . . . , m=1, 2, 3, . . . ) calculating a respective mean correlation coefficient (γ.sub.m(n), m=1, 2, 3, . . . ) between the respective electrical error signal (e.sub.m(n), m=1, 2, 3, . . . ) and the respective modelled secondary anti-noise signal (ŷ.sub.m(n), m=1, 2, 3, . . . ), and comparing at least one of the mean correlation coefficients (γ.sub.m(n), m=1, 2, 3, . . . ) with at least one predefined threshold (α, β), or comparing an average value (γ(n)) of the at least one correlation coefficient (γ.sub.m(n), m=1, 2, 3, . . . ) with at least one predefined threshold (α, β).

2. The method of claim 1, wherein providing a modelled secondary anti-noise signal (ŷ(n)) comprises passing an electrical reference signal (x(n)) consecutively through a secondary sound path model (Ŝ) and then through the digital filter (W) of the adaptive filter.

3. The method of claim 1, wherein providing a modelled secondary anti-noise signal (ŷ(n)) comprises passing an electrical reference signal (x(n)) consecutively through the digital filter (W) of the adaptive filter and then through a secondary sound path model (Ŝ).

4. The method of claim 1, wherein a mean correlation coefficient (γ(n)) at a current time step is calculated as a function of a correlation coefficient (r(n)) at the current time step and a mean correlation coefficient at a previous time step (γ(n−1)), wherein a correlation coefficient (r(n)) is calculated from the N last samples of an error signal (e(n)) and a modelled secondary anti-noise signal (ŷ(n)), wherein the number of samples N is in the range of 100-10000, preferably 500-5000.

5. The method of claim 1, wherein if an amplitude of at least one mean correlation coefficient (γ.sub.m(n), m=1, 2, 3, . . . ) or an amplitude of the average value (γ(n)) of the at least one mean correlation coefficient (γ.sub.m(n), m=1, 2, 3, . . . ) is smaller than a first threshold value α, this is indicative of an optimally performing method, wherein the first threshold value α is in the range of 0.01-0.3, preferably 0.05-0.2.

6. The method of claim 5, wherein vehicle operative conditions and method parameters are registered in a database when the method is performing optimally.

7. The method of claim 1, wherein if at least one of the mean correlation coefficients (γ.sub.m(n), m=1, 2, 3, . . . ) or the average value (γ(n)) of the at least one mean correlation coefficient (γ.sub.m(n), m=1, 2, 3, . . . ) is larger than or equal to a second threshold value β, this is indicative of a diverging method, wherein the second threshold value β is in the range of 0.4-0.9, preferably 0.5-0.8.

8. The method of claim 7, further comprising changing one or more filter parameters chosen from step size (μ), sign of step size (μ), phase of step size (μ) and leakage factor.

9. The method of claim 8, wherein at least one of the step size (μ) and leakage factor is changed by multiplication with a correction factor negatively dependent on the amplitude of the mean correlation coefficient.

10. The method of claim 8, wherein a recovery rate of at least one of a modified step size (μ) and leakage factor is limited to a predefined value.

11. The method of claim 7, further comprising changing a secondary sound path model (Ŝ.sub.km, k=1, 2, 3, . . . , m=1, 2, 3, . . . ) used in the method to a secondary sound path model selected from a set of pre-measured secondary sound path models.

12. The method of claim 7, wherein when two or more sound sensors are used in the method, the method further comprises changing a spatial distribution of acoustic transducers and/or sound sensors in the compartment by switching on or off one or more acoustic transducers and/or sound sensors.

13. The method of claim 7, further comprising a step of stopping the method.

14. The method of claim 1, wherein if at least one of an amplitude of the mean correlation coefficients (γ.sub.m(n), m=1, 2, 3, . . . ) or an amplitude of the average value (γ(n)) of the at least one mean correlation coefficient (γ.sub.m(n), m=1, 2, 3, . . . ) is larger than or equal to a second threshold value β, this is indicative of a diverging method, wherein the second threshold value β is in the range of 0.4-0.9, preferably 0.5-0.8.

15. The method of claim 1, wherein if an amplitude of the at least one mean correlation coefficient (γ.sub.m(n), m=1, 2, 3, . . . ) or an amplitude of the average value (γ(n)) of the at least one mean correlation coefficient (γ.sub.m(n), m=1, 2, 3, . . . ) is larger than or equal to a first threshold value α and at least one of the mean correlation coefficients (γ.sub.m(n), m=1, 2, 3, . . . ) or the average value (γ(n)) of the at least one mean correlation coefficient (γ.sub.m(n), m=1, 2, 3, . . . ) is smaller than a second threshold value β, this is indicative of a non-optimally performing method, wherein the first threshold value α is in the range of 0.01-0.3, preferably 0.05-0.2, and the second threshold value β is in the range of 0.4-0.9, preferably 0.5-0.8.

16. The method of claim 1, wherein if an amplitude of the at least one mean correlation coefficient (γ.sub.m(n), m=1, 2, 3, . . . ) or an amplitude of the average value (γ(n)) of the at least one mean correlation coefficient (γ.sub.m(n), m=1, 2, 3, . . . ) is larger than or equal to a first threshold value α and at least one of an amplitude of the mean correlation coefficients (γ.sub.m(n), m=1, 2, 3, . . . ) or an amplitude of the average value (γ(n)) of the at least one mean correlation coefficient (y.sub.m(n), m=1, 2, 3,...) is smaller than a second threshold value β, this is indicative of a non-optimally performing method, wherein the first threshold value α is in the range of 0.01-0.3, preferably 0.05-0.2, and the second threshold value β is in the range of 0.4-0.9, preferably 0.5-0.8.

17. The method of claim 1, wherein the adaptive filter is a filter selected from a group consisting of filtered-x-LMS, leaky filtered-x-LMS, filtered-error-LMS and modified-filtered-x-LMS.

18. An active noise control system for reducing the power of an acoustic primary noise signal (d.sub.m(n), m=1, 2, 3, . . . ) at one or more control positions in a vehicle passenger compartment, the acoustic primary noise signal originating from an acoustic noise signal transmitted from a noise source through a respective primary sound path (P.sub.m, m=1, 2, 3, . . . ) to the respective control position, wherein the system comprises: an adaptive filter, which is arranged to take as input signals an electrical reference signal (x(n)) representing the acoustic noise signal, and at least one electrical error signal (e.sub.m(n), m=1, 2, 3, . . . ) representing a respective acoustic signal detected by a respective sound sensor at the respective control position, and which adaptive filter is arranged to provide and transmit at least one electrical control signal (y′.sub.k(n), k=1, 2, 3, . . . ) to at least one acoustic transducer arranged in the compartment, which at least one acoustic transducer in response to the at least one electrical control signal (e.sub.m(n), m=1, 2, 3, . . . ) is arranged to provide and transmit a respective acoustic anti-noise signal through a respective secondary sound path (S.sub.km, k=1, 2, 3, . . . , m=1, 2, 3, . . . ) between the at least one acoustic transducer and the respective control position, arriving at the at least one control position as a respective acoustic secondary anti-noise signal (y.sub.m(n), m=1, 2, 3, . . . ), such as to minimize the respective electrical error signal (e.sub.m(n), m=1, 2, 3, . . . ), wherein the system further comprises a performance monitoring unit arranged to: provide a respective modelled secondary anti-noise signal (ŷ.sub.m(n), m=1, 2, 3, . . . ) from a respective secondary sound path model (Ŝ.sub.km, k=1, 2, 3, . . . , m=1, 2, 3, . . . ), calculate a respective mean correlation coefficient (γ.sub.m(n), m=1, 2, 3, . . . ) between the respective electrical error signal (e.sub.m(n), m=1, 2, 3, . . . ) and the respective modelled secondary anti-noise signal (ŷ.sub.m(n), m=1, 2, 3, . . . ), and to compare at least one of the mean correlation coefficients (γ.sub.m(n), m=1, 2, 3, . . . ) with at least one predefined threshold (α, β), or compare an average value (γ(n)) of the at least one correlation coefficient (γ.sub.m(n), m=1, 2, 3, . . . ) with at least one predefined threshold (α, β).

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 shows a diagram of an active noise control system equipped with a performance monitoring unit.

(2) FIG. 2 shows a diagram of the active noise control system in FIG. 1 equipped with a performance monitoring unit implemented in an FXLMS adaptive control system.

(3) FIG. 3 shows a diagram of the active noise control system in FIG. 1 equipped with a performance monitoring unit implemented in an FXLMS adaptive control system, with an alternative implementation for the determination of the modelled control signal.

(4) FIG. 4 shows a block diagram illustrating an active noise control system with a performance monitoring unit.

(5) FIGS. 5a and 5b show an example of the evolution in time of the control signal and of the mean correlation coefficient for a stable active noise control system.

(6) FIGS. 6a and 6b show an example of the evolution in time of the control signal and of the mean correlation coefficient for a diverging active noise control system with a diverging control signal.

(7) FIG. 7 shows a diagram of the active noise control system in FIG. 3, wherein the performance monitoring unit controls the step size and leakage factor of the LMS unit.

(8) FIG. 8 shows an example of the evolution in time of the step size for a diverging active noise control system with a diverging control signal, when equipped with the performance monitoring unit as shown in FIG. 7.

DETAILED DESCRIPTION OF THE DRAWINGS

(9) FIGS. 1-4 illustrate an active noise control (ANC) system with a performance monitoring unit and also show the corresponding ANC method. Such an ANC system may be used to eliminate or reduce disturbing noise radiated into a vehicle passenger compartment of a motor vehicle from a noise source. Such noise may be generated by mechanical vibrations of an engine and/or components mechanically coupled thereto (e.g., a fan), wind passing over and around the vehicle, and/or tires contacting, for example, a paved surface.

(10) At M control positions, positions at which a suppression of an acoustic noise signal is desired in the vehicle passenger compartment, the power of an acoustic primary noise signal d.sub.m(n) is to be reduced. The acoustic primary noise signal originating from an acoustic noise signal transmitted from a noise source through a respective primary sound path P.sub.m to the control position.

(11) The system comprises M sound sensors, such as a microphone, arranged at the control position in the vehicle compartment, K acoustic transducers, such as loudspeakers, arranged in the vehicle compartment, and an adaptive filter with a digital filter W. The number M of sound sensors and number K of transducers used in the system may be from 1 to 10. Sound sensors and transducers are used all together to reduce the acoustic power at the sound sensors.

(12) The adaptive filter is arranged to take as input signals an electrical reference signal x(n) representing the acoustic noise signal and the electrical error signal(s) e.sub.m(n) (m=1, 2, 3, . . . , M). The electrical error signal e.sub.m(n) representing a respective acoustic signal detected by a respective sound sensor at the control position. The electrical reference signal may be determined from e.g. engine speed, accelerometer signal etc.

(13) The adaptive filter, which may be of the type filtered-x-LMS, leaky filtered x-LMS, filtered-error-LMS or modified-filtered-x-LMS, is arranged to provide and transmit electrical control signal(s) y′.sub.k(n) to the acoustic transducer(s) arranged in the compartment. In response to the electrical control signal(s) y′.sub.k(n) the transducer(s) is (are) arranged to provide and transmit a respective acoustic anti-noise signal y.sub.m(n) through respective secondary sound path(s) S.sub.km between the acoustic transducer(s) and the control position, arriving at the control position as a respective acoustic secondary anti-noise signal y.sub.m(n), such as to minimize the respective electrical error signal e.sub.m(n). The filter W is updated to reduce the electrical error signal e.sub.m(n) for example in a least mean square sense by using a known adaption algorithm, e.g., LMS, NLMS, RLS, etc.

(14) At a control position, the respective sound sensor is arranged to detect a combined sound signal comprising the acoustic primary noise signal d.sub.m(n) and the respective acoustic secondary anti-noise signal y.sub.m(n). The aim of the acoustic secondary anti-noise signal y.sub.m(n) is to be an opposite-phase image of the acoustic primary noise signal d(n). The degree to which the acoustic secondary anti-noise signal y.sub.m(n) matches the acoustic primary noise signal d.sub.m(n) determines the electrical error signal e.sub.m(n). If the acoustic primary noise signal and the acoustic secondary anti-noise signal were matched exactly, both in space and time, the primary noise signal would be completely eliminated at the control position and the electrical error signal e.sub.m(n) would be zero.

(15) The system comprises a performance monitoring unit arranged to provide a respective modelled secondary anti-noise signal ŷ.sub.m(n), by providing a filter(s) Ŝ.sub.km(w) that model(s) the respective secondary sound path(s), hereinafter referred to as secondary sound path model(s).

(16) The performance monitoring unit is further arranged to calculate a respective mean correlation coefficient γ.sub.m(n) between the respective electrical error signal e.sub.m(n) .sub.and the respective modelled secondary anti-noise signal ŷ.sub.m(n) and optionally to calculate an average value γ(n) of the mean correlation coefficients γ.sub.m(n).

(17) The monitoring unit, hence, measures in real-time the correlation between the respective electrical error signal(s) e.sub.m(n) and the respective modelled secondary anti-noise signal(s) ŷ.sub.m(n), that is the degree of dependence between the respective signals.

(18) A secondary sound path model Ŝ.sub.km used to provide a modelled secondary anti-noise signal ŷ.sub.m(n) represents a transfer function between an acoustic transducer and a sound sensor. It may be determined offline (when there is no disturbing acoustic noise signal) in a calibration step, or online (in presence of the disturbing acoustic noise signal), through so-called online secondary path modelling techniques.

(19) Providing a modelled secondary anti-noise signal ŷ.sub.m(n) may comprise passing the electrical reference signal consecutively through a secondary sound path model Ŝ.sub.km and then through the filter W.

(20) Alternatively, providing a modelled secondary anti-noise signal ŷ.sub.m(n) may comprise passing the electrical reference signal consecutively through the filter W and then through a secondary sound path model Ŝ.sub.km.

(21) A mean correlation coefficient with a value of 0 indicates that the electrical error signal and the modelled secondary anti-noise signal are not correlated. A mean correlation coefficient with a value of 1 indicates that the signals are perfectly correlated.

(22) A mean correlation coefficient γ may be computed from a correlation coefficient defined as e.g. the Pearson correlation coefficient (PCC)

(23) $\begin{array}{cc}r\text{:}\frac{\mathrm{cov}\left(e,\hat{y}\right)}{\mathrm{var}\left(e\right)\mathrm{var}\left(\hat{y}\right)},& \left(1\right)\end{array}$
wherein e is an electrical error signal and ŷ is a modelled secondary anti-noise signal.

(24) A mean correlation coefficient may be calculated from a function of a current correlation coefficient r(n) and a mean correlation coefficient at a previous time step γ(n-1), wherein a correlation coefficient r(n) is calculated from the N last samples of an error signal e(n) and a modelled secondary anti-noise signal ŷ(n), wherein the number of samples N is in the range of 100-10000, preferably 500-5000.

(25) r may be evaluated at the current time step n using the values
{e(n), e(n−1), . . . , e(n−N+1); ŷ(n), ŷ(n−1), . . . , ŷ(n−N+1)}  (2)
as

(26) $\begin{array}{cc}r\left(n\right)=\frac{\underset{i=0}{\overset{N-1}{.Math.}}\left(e\left(n-i\right)-\mathrm{mean}\left(e\right)\right)\left(\hat{y}\left(n-i\right)-\mathrm{mean}\left(\hat{y}\right)\right)}{\begin{array}{c}\sqrt{\underset{i=0}{\overset{N-1}{.Math.}}{\left(e\left(n-i\right)-\mathrm{mean}\left(e\right)\right)}^2}\\ \sqrt{\underset{i=0}{\overset{N-1}{.Math.}}{\left(\hat{y}\left(n-i\right)-\mathrm{mean}\left(\hat{y}\right)\right)}^2}\end{array}}& \left(3\right)\end{array}$
where mean(e)=1/N Σ.sub.i=0.sup.N−1 e(n−i)   (4)

(27) and with a corresponding definition for ŷ. A larger N results in a more accurate determination of the correlation coefficient r(n), whereas a smaller N makes it more reactive to time evolutions of the signals. The mean correlation coefficient γ is then computed from the value of r and its past history using the recursive relation

(28) $\begin{array}{cc}\gamma \left(n\right)=\frac{1}{1+\eta }\left(\eta \varphi \left(r\left(n\right)\right)+\gamma \left(n-1\right)\right),& \left(5\right)\end{array}$
where η«1 is an update coefficient determining the contribution of the current correlation coefficient r to the mean value γ(n). A typical value for η would be in the range of 0.0001-0.01. ϕ is a function of the form ϕ(x)=|x|.sup.a or alternatively ϕ(x)=x.sup.a, where a is a positive integer. a affects the sensitivity of the mean correlation coefficient to small variations of r. A typical value for a would be 1 or 2.

(29) The performance monitoring unit compares the mean correlation coefficient(s) γ.sub.m(n) or alternatively their average value γ(n) with a first threshold value α and/or a second threshold value β. α and β are typically in the range 0.01-0.3 and 0.4-0.9 respectively, the choice of values being determined by the operator during an initial training period in representative operating conditions.

(30) If the amplitude of all the mean correlation coefficients |γ.sub.m(n)|<α or alternatively the amplitude of their averaged value |γ(n)|<α, this indicates an optimally performing system, in which the adaptive filter used is working optimally or at least close to optimally. The acoustic secondary anti-noise signal y(n) then contributes fully to reduce the acoustic primary noise d(n) at the control position. The electrical error signal e(n) is then weakly or not at all correlated with the secondary anti-noise signal y(n).

(31) If a mean correlation coefficient γ.sub.m(n)≥β or alternatively if the average value of the mean correlation coefficients γ(n)≥β, this may be indicative of a diverging system. If an amplitude of the mean correlation coefficient γ.sub.m(n)≥β or alternatively if an amplitude of the average value of the mean correlation coefficients γ(n)≥β, this may be indicative of a diverging system. The filter used is not adapted and there is a divergent behavior of the adaptive filter. The acoustic secondary anti-noise signal y(n) is then larger in amplitude than required to cancel the acoustic primary noise d(n) at the control position and the electrical error signal e(n) is highly correlated with the acoustic secondary anti-noise signal y(n).

(32) If the amplitude of all or some of the mean correlation coefficients is α≤|γ.sub.m(n)|<62 or alternatively if the average value of the mean correlation coefficients α≤|γ(n)|<β, this may be indicative of a non-optimal system.

(33) The acoustic secondary anti-noise signal then contributes partially to reducing the acoustic primary noise at the control position. The electrical error signal is partially correlated with the secondary anti-noise signal. Such situation may occur e.g. if there is a convergence to a local minimum that would not provide minimized electrical error signal.

(34) Based on the comparison of a mean correlation coefficient γ(n) with the threshold value(s), different measures may be taken, such as to update filter parameters, change the selection of transducer(s) and/or sound sensor(s) used in the method/system, change the secondary path model, end the method/switching off the system etc.

(35) If a mean correlation coefficient |γ.sub.m(n)|>=β or alternatively if an average value of the mean correlation coefficients γ(n)>=β, the step size μ and the leakage factor of the adaptive algorithm may be corrected respectively by factors μ.sub.corr(n) and leak.sub.corr(n) negatively dependent on the mean correlation coefficient. FIG. 7 shows such an algorithm in which the performance monitoring unit controls the values of step size and leakage factor of the LMS unit.

(36) μ.sub.corr(n) may be expressed as μ.sub.corr(n)=1−δ.sub.μ γ(n). leak.sub.corr(n) may be expressed as leak.sub.corr(n)=1−δ.sub.leak γ(n). Typical values for δ.sub.μ and δ.sub.leak are 0.99 and 0.001, respectively.

(37) An additional step of limiting the recovery rate of μ.sub.corr(n), and leak.sub.corr(n), defined as the positive rate of change μ.sub.corr(n+1)−μ.sub.corr(n), and leak.sub.corr(n+1)−leak.sub.corr(n), respectively, to a respective maximal predetermined value may be implemented. The additional step may be used to prevent the step size, and/or the leakage factor, from recovering its initial value too fast, such that the system can have sufficient time to be stabilized. A typical value for the recovery rate may be a fifth of the sampling frequency.

(38) FIG. 8 shows an example of the evolution of the step size μ during an application of the method. In this example, between 0.5 s and 6.5 s, the performance monitoring unit is repetitively detecting a divergence and the step size is reduced accordingly to prevent the divergence. Between 6.5 and 10 s, the step size is slowly recovering its initial value, with a limited recovery rate.

(39) A distribution of acoustic transducers and sound sensors may be spatially optimal for a given noise disturbance, but may not be adapted when the noise disturbance changes or when the conditions in the compartment change. In such case, modifying this distribution may improve the performance of the system. Alternatively, a transducer/sensor may not be working properly, for example if it is defective or if it is covered by an object placed in the compartment. In such cases, deactivating it may result in a better control of the sound field.

(40) In FIG. 2 is illustrated the performance monitoring unit implemented in the well-known filtered-X LMS (FXLMS) ANC system using K acoustic transducers and M sound sensors. An LMS adaptation unit is arranged to receive the electrical error signal(s) e.sub.m(n) and a filtered reference signal(s) x′.sub.km(n), which is (are) provided from the reference signal x(n) after passing through the secondary path model(s) Ŝ.sub.km. The LMS adaptation unit controls the filter W, which receives the reference signal x(n) and sends an electrical control signal(s) y′.sub.k(n) to the acoustic transducer, thus generating a secondary anti-noise signal y.sub.m(n) at the control position(s) via the secondary path(s) Ŝ.sub.km. The monitoring unit receives the error signal(s) e.sub.m(n) and the modelled secondary anti-noise signal(s) ŷ.sub.m, which is (are) obtained from the filtered input(s) x′.sub.km(n) after passing through a copy of the filter W.

(41) FIG. 3 shows an alternative implementation of the performance monitoring unit in a FXLMS system. Here, the modelled secondary anti-noise signal(s) ŷ.sub.m is (are) obtained from the electrical control signal(s) y′.sub.m(n), after passing through the secondary path model(s) Ŝ.sub.km.

(42) In FIGS. 5a and 5b is illustrated an example of a stable active noise control system. An anti-noise signal y(n) is shown in FIG. 5a, and the associated mean correlation coefficient γ(n) in FIG. 5b. In this example, N=1000, η=0,0002, a=2 and the primary noise signal d(n) is time-varying. The values for γ remain small and the control may be qualified as optimal between 25 000 and 60 000 time steps, where γ<0.1.

(43) In FIGS. 6a and 6b is illustrated an example of a diverging active noise control system with a diverging secondary anti-noise signal y(n), FIG. 6a, and associated mean correlation coefficient γ(n), FIG. 6b. In this example N=1000, η=0.0002, a=2 and the mean correlation coefficient γ(n) has a relatively low value as long as the system remains stable. After about 35 000 time steps, the control signal starts diverging. By looking at the plot for y(n) alone, divergence is not clearly apparent before about 50 000 time steps. The plot for γ(n) on the other hand shows an apparent divergent behavior more than 10 000 steps earlier. On this example, by defining β as 0.6, divergence of the system can be detected near the onset of divergence, before it can be heard, which leaves enough time for the system to react and adjust its parameters.

(44) In FIG. 4 the active noise control system discussed above is shown as a block diagram. The performance monitoring unit is used in a supervisory loop to adjust the parameters of the active noise control system when divergent or non-optimal behavior is detected.