CN113078884B - Adaptive algorithm adding nonlinear fitting - Google Patents
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Abstract
The invention discloses a self-adaptive algorithm added with nonlinear fitting. The algorithm comprises the following steps: step S1, adding a nonlinear filter module into a linear filter module of an adaptive filter, collecting an input signal received by the adaptive filter, and intercepting the input signal to obtain an input signal of the nonlinear filter module; step S2, nonlinear transformation is carried out on the input signal of the nonlinear filtering module, and nonlinear transformation signals are obtained; s3, calculating output signals of the nonlinear filtering module and the linear filtering module; s4, calculating an error signal; step S5, calculating a filter update value; s6, calculating convergence weight coefficients of the linear filtering module and the nonlinear filtering module; and S7, obtaining output signals of the linear filtering module and the nonlinear filtering module according to filtering operation, and overlapping the two output signals to be capable of fitting the expected signal highly. The algorithm is applied to a scene with nonlinear effect, and a better system modeling effect is obtained.
Description
Technical Field
The present invention relates to a method of processing a signal by means of an adaptive filter, in particular an adaptive algorithm adding a nonlinear fit.
Background
An adaptive filter refers to a filter that uses an adaptive algorithm to change parameters and structure of the filter according to a change in the environment. Typically, the structure of the adaptive filter is not changed, and the weight coefficients of the adaptive filter are time-varying coefficients that are updated by an adaptive algorithm. The adaptive algorithm is an algorithm which automatically adjusts the weight coefficient of the filter by adopting a specific algorithm based on the statistical characteristic estimation of the input signal and the output signal so as to achieve the optimal filtering characteristic. The least mean square algorithm (LMS algorithm) is rapidly and widely used because of its ease of implementation, and becomes the standard algorithm for adaptive filtering. The algorithm uses the steepest descent method to iteratively calculate the weight coefficient vector at the next moment from the current moment filter weight coefficient vector by means of the gradient estimation of the mean square error. The method is mainly applied to acoustic system modeling, active noise control, acoustic echo cancellation and the like.
For a linear system, the frequency components in the output signal are the same as the frequency components in the input signal. For nonlinear systems, however, the frequency in the output signal is typically not equal to the frequency in the input signal, and if the input signal has more than one frequency component, the output signal will have intermodulation products, as well as harmonics of the input signal frequency. For example, speaker drivers are prone to nonlinear distortion, particularly in the low frequency range. The main cause of nonlinear distortion is the generation of new frequency components through harmonics and intermodulation products. The conventional LMS algorithm does not consider the influence of nonlinear distortion in a control strategy, and restricts the application of the LMS algorithm in a nonlinear distortion scene.
Disclosure of Invention
The invention aims to provide an adaptive algorithm for optimizing the addition of nonlinear fitting of an LMS algorithm under a nonlinear distortion scene by considering nonlinear effects.
To achieve the above object, the present invention provides an adaptive algorithm adding nonlinear fitting, which is characterized by comprising:
step S1, input signal acquisition: adding a nonlinear filtering module into a linear filtering module of the adaptive filter, collecting an input signal received by the adaptive filter, and intercepting the input signal to obtain an input signal of the nonlinear filtering module;
step S2, nonlinear transformation: performing nonlinear transformation on an input signal of the nonlinear filtering module to obtain a nonlinear transformation signal;
step S3, signal filtering: filtering according to the nonlinear transformation signal and the nonlinear filtering module weight coefficient to obtain an output signal of the nonlinear filtering module, and filtering to obtain an output signal of the linear filtering module;
step S4, error signal calculation: and obtaining an error signal of the output moment according to the output signal of the linear filtering module, the output signal of the nonlinear filtering module and the expected signal of the output moment.
Step S5, calculating a filter update value: calculating a gradient value updated by a filter each time, and updating filter coefficients of the linear module and the nonlinear module, wherein the derivation principle of the filter updating value is that the error signal function is squared, a loss function is expected to be obtained, and the loss function is used for performing partial derivative operation on the weight coefficient of the linear filter module and the weight coefficient of the nonlinear filter module respectively to obtain a gradient updating value of the weight coefficient of the linear filter module and a gradient updating value of the weight coefficient of the nonlinear filter module;
step S6, updating a filter: according to the gradient update value of the linear filtering module weight coefficient, a gradient descent method is adopted to obtain an update formula of the linear filtering module weight coefficient, and repeated operation is carried out according to the update formula of the linear filtering module weight coefficient to obtain a linear filtering module convergence weight coefficient; according to the gradient update value of the nonlinear filter module weight coefficient, a gradient descent method is adopted to obtain an update formula of the nonlinear filter module weight coefficient, and repeated operation is carried out according to the update formula of the nonlinear filter module weight coefficient to obtain a nonlinear filter module convergence weight coefficient;
and S7, respectively carrying out filtering operation on the convergence weight coefficient of the linear filtering module and the convergence weight coefficient of the nonlinear filtering module to obtain an output signal of the linear filtering module and an output signal of the nonlinear filtering module, and after the two output signals are overlapped, fitting the expected signal to a high degree.
Preferably, in the step S2, the nonlinear transformation signal is:
u(n)＝f(x cut (n))
wherein ,
x cut (n)＝[x(n)，x(n-1)，…，x(n-M+1)] T ，x(n)＝[x(n)，x(n-1)，…，x(n-N+1)] T m is used to represent the nonlinear filter module order, N is used to represent the linear filter module order, and M < N, the superscript T is used to represent the transpose operation, x (N) is used to represent the input signal of the linear filter module, x cut (n) an input signal representing a nonlinear filtering module;
n is used to represent the time of day;
f is used to represent a nonlinear transformation;
u (n) is used to represent the nonlinear transformation signal.
Preferably, in the nonlinear transformation, f may be a square nonlinear transformation, which may generate a second harmonic frequency for a single frequency signal, for modeling a nonlinear system, as follows:
wherein ,
ω is used to represent the frequency of the input signal of the nonlinear filter module;
2 omega is used to represent the second harmonic frequency generated after nonlinear transformation;
() 2 for representing squaring operations;
preferably, in the nonlinear transformation, f may be a RELU nonlinear transformation that may generate each even harmonic component for a single frequency signal, for modeling a nonlinear system, as follows:
wherein ,
ωt is used to represent one frequency of the nonlinear filter module;
2 ωt is used to represent another frequency of the nonlinear filter module;
n is used to represent the time of day;
RELU is used to represent signal negative zeroing operations;
preferably, in the step S3, the output signal of the linear filtering module and the output signal of the nonlinear filtering module obtained by filtering are calculated according to the following formula:
y l (n)＝x(n) T w l (n)
y nl (n)＝u(n) T w nl (n)
wherein ,
x (n) is used to represent the input signal of the linear filtering module;
w l (n) weight coefficients for representing linear filtering modules;
u (n) is used for representing a nonlinear transformation signal of the nonlinear filtering module;
w nl (n) weight coefficients for representing nonlinear filtering modules;
n is used to represent the time of day;
the superscript T is used to denote a transpose operation;
y l (n) means an output signal of the linear filtering module.
y nl (n) means an output signal of the nonlinear filtering module.
Preferably, in the step S4, the error signal of the output time is calculated according to the following formula:
e(n)＝d(n)+y l (n)+y nl (n)
wherein ,
d (n) is used for indicating a desired signal at the output time;
e (n) represents an error signal at the output timing.
Preferably, in the step S5, the loss function is calculated according to the following formula:
J＝E(e 2 (n))
wherein ,
e is used to represent the desired operation;
preferably, in the step S5, the gradient update value of the weight coefficient of the linear filtering module and the gradient update value of the weight coefficient of the nonlinear filtering module are respectively:
wherein ,
x (n) is used to represent the input signal of the linear filtering module;
u (n) is used for representing a nonlinear transformation signal of the nonlinear filtering module;
the superscript T is used to denote a transpose operation.
Preferably, the gradient update value of the weight coefficient of the linear filtering module and the gradient update value of the weight coefficient of the nonlinear filtering module are obtained according to the following formula:
wherein ,
n is used for representing the order of the linear filtering module;
m is used for representing the order of the nonlinear filtering module, and M is smaller than N;
the superscript T is used to denote a transpose operation.
Preferably, in the step S6, the update formula of the linear module filter weight coefficient and the update formula of the nonlinear module filter weight coefficient are respectively as follows:
w l (n+1)＝w l (n)-2μ l e(n)x(n) T
w nl (n+1)＝w nl (n)-2μ nl e(n)u(n) T
wherein ,
w l (n) weight coefficients for representing linear filtering modules;
w nl (n) weight coefficients for representing nonlinear filtering modules;
μ l central control for representing linear modular gradient descent methodPreparing iteration step length of convergence speed;
μ nl the iteration step length is used for representing the control convergence speed in the nonlinear module gradient descent method;
e (n) represents an error signal at the output timing;
x (n)) is used to represent the input signal of the linear filtering module;
u (n) is used to represent the nonlinear transformation signal of the nonlinear filtering module.
The invention has the advantages that:
1. the self-adaptive algorithm for adding nonlinear fitting is characterized in that a nonlinear filtering module is added in a linear filtering module of a self-adaptive filter, nonlinear transformation is carried out on an input signal of the nonlinear filtering module, and a nonlinear fitting term is added on the basis of the filtering algorithm, so that the algorithm obtains a better system modeling effect in a scene with nonlinear effect.
2. The nonlinear transformation strategy proposed by the invention takes the square sum and sets the negative value to zero.
3. The invention provides a derivation process of an algorithm by carrying out strict mathematical proof on the self-adaptive algorithm added with nonlinear fitting.
Drawings
FIG. 1 is a block diagram of a linear fitting adaptive algorithm;
FIG. 2 is a block diagram of an adaptive algorithm incorporating nonlinear fitting in accordance with the present invention;
FIG. 3 is a power spectrum estimation of a white noise signal as an input signal;
FIG. 4 is a plot of the desired signal power spectrum estimate for the white noise signal output time of FIG. 3;
FIG. 5 is a graph comparing MSE convergence curves in an adaptive algorithm and an adaptive algorithm added with nonlinear fitting according to the present invention;
in the figure: speaker 1, microphone 2, MSE convergence curve 3 (adaptive algorithm for N-valued 3072), MSE convergence curve 4 (adaptive algorithm for N-valued 2048), MSE convergence curve 5 (adaptive algorithm for adding nonlinear fit by squaring operation for nonlinear transformation), MSE convergence curve 6 (adaptive algorithm for adding nonlinear fit by negative zero-setting operation for nonlinear transformation).
Detailed Description
The invention is described in further detail below with reference to the attached drawing figures and specific examples:
as shown in fig. 1, the system speaker-enclosure-microphone is modeled using an adaptive algorithm. The input signal x (n) is played through the speaker 1, the sound propagates through, the desired signal at the microphone 2 is d (n), and the system through which x (n) passes mainly includes the speaker 1, air, and the microphone 2. Modeling the process by adopting an adaptive algorithm, wherein an updating formula of the weight coefficient of the adaptive filter is as follows:
w(n+1)＝w(n)-2μe(n)x(n)
wherein ,
w (n) is used to represent the adaptive filter weight coefficients;
w (n+1) is used for representing the weight coefficient of the adaptive filter at the next moment;
μ is used to represent an iteration step for controlling the convergence rate in the adaptive filter gradient descent method;
e (n) represents an error signal at the output timing, e (n) =d (n) +x (n) T w(n)；
x (N) is used to represent the input signal to the adaptive filter, x (N) = [ x (N), x (N-1), …, x (N-n+1)] T The superscript T is used to denote the transpose operation and N is used to denote the adaptive filter order.
From the computational formula of the adaptive algorithm, it can be seen that the algorithm only considers a linear fit to the signal. As shown in fig. 2, the system of speaker-enclosure-microphone is re-modeled, and nonlinear fitting terms are added in the LMS algorithm to obtain a new adaptive algorithm, which comprises the following steps:
step S1, input signal acquisition: adding a nonlinear filter module into a linear filter module of the adaptive filter, collecting an input signal received by the adaptive filter, and intercepting the input signal to obtain an input signal of the nonlinear filter module;
step S2, nonlinear transformation: performing nonlinear transformation on an input signal of a nonlinear filtering module to obtain a nonlinear transformation signal;
step S3, signal filtering: filtering according to the nonlinear transformation signal and the weight coefficient of the nonlinear filtering module to obtain an output signal of the nonlinear filtering module; simultaneously filtering to obtain an output signal of the linear filtering module;
step S4, error signal calculation: and obtaining an error signal of the output moment according to the output signal of the linear filtering module, the output signal of the nonlinear filtering module and the expected signal of the output moment.
Step S5, calculating a filter update value: calculating a gradient value updated by the filter each time, and updating the filter coefficients of the linear module and the nonlinear module, wherein the derivation principle of the filter updating value is that an error signal function is squared, a loss function is expected to be obtained, and the loss function is subjected to partial derivative operation on the linear filter module weight coefficient and the nonlinear filter module weight coefficient respectively to obtain a gradient updating value of the linear filter module weight coefficient and a gradient updating value of the nonlinear filter module weight coefficient;
step S6, updating a filter: according to the gradient update value of the weight coefficient of the linear filter module, a gradient descent method is adopted to obtain an update formula of the weight coefficient of the linear filter module, and repeated operation is carried out according to the update formula of the weight coefficient of the linear filter module to obtain a convergence weight coefficient of the linear filter module; according to the gradient updating value of the nonlinear filtering module weight coefficient, a gradient descent method is adopted to obtain an updating formula of the nonlinear filtering module weight coefficient, and according to the updating formula of the nonlinear filtering module weight coefficient, repeated operation is carried out to obtain a nonlinear filtering module convergence weight coefficient;
and S7, respectively carrying out filtering operation on the convergence weight coefficient of the linear filtering module and the convergence weight coefficient of the nonlinear filtering module to obtain an output signal of the linear filtering module and an output signal of the nonlinear filtering module, and after the two output signals are overlapped, highly fitting the expected signal.
In a preferred embodiment of the present invention, in step S2, the nonlinear transformation signal is:
u(n)＝f(x cut (n))
wherein ,
x cut (n)＝[x(n)，x(n-1)，…，x(n-M+1)] T ，x(n)＝[x(n)，x(n-1)，…，x(n-N+1)] T m is used to represent the nonlinear filter module order, N is used to represent the linear filter module order, and M < N, the superscript T is used to represent the transpose operation, x (N) is used to represent the input signal of the linear filter module, x cut (n) an input signal representing a nonlinear filtering module;
n is used to represent the time of day;
f is used to represent a nonlinear transformation;
u (n) is used to represent the nonlinear transformation signal.
In the preferred embodiment of the present invention, the nonlinear transformation, f, may take the form of a square nonlinear transformation that generates a second harmonic frequency for a single frequency signal for modeling the nonlinear system as follows:
wherein ,
ω is used to represent the frequency of the input signal of the nonlinear filter module;
2 omega is used to represent the second harmonic frequency generated after nonlinear transformation;
() 2 for representing squaring operations;
in a preferred embodiment of the present invention, in the nonlinear transformation, f may take the form of a RELU nonlinear transformation that may generate even harmonic components for a single frequency signal for modeling the nonlinear system as follows:
wherein ,
ωt is used to represent one frequency of the nonlinear filter module;
2 ωt is used to represent another frequency of the nonlinear filter module;
n is used to represent the time of day;
RELU is used to represent signal negative zeroing operations;
in a preferred embodiment of the present invention, in step S3, the output signal of the linear filtering module and the output signal of the nonlinear filtering module obtained by filtering are calculated according to the following formula:
y l (n)＝x(n) T w l (n)
y nl (n)＝u(n) T w nl (n)
wherein ,
x (n) is used to represent the input signal of the linear filtering module;
w l (n) weight coefficients for representing linear filtering modules;
u (n) is used for representing a nonlinear transformation signal of the nonlinear filtering module;
w nl (n) weight coefficients for representing nonlinear filtering modules;
n is used to represent the time of day;
the superscript T is used to denote a transpose operation;
y l (n) an output signal representing the linear filtering module;
y nl (n) means an output signal of the nonlinear filtering module.
In a preferred embodiment of the present invention, in step S4, the error signal of the output time is calculated according to the following formula:
e(n)＝d(n)+y l (n)+y nl (n)
wherein ,
d (n) is used for indicating a desired signal at the output time;
e (n) represents an error signal at the output timing.
In the preferred embodiment of the present invention, in step S5, the loss function is calculated according to the following formula:
J＝E(e 2 (n))
wherein ,
e is used to represent the desired operation;
in the preferred embodiment of the present invention, in step S5, the gradient update values of the weight coefficients of the linear filtering module and the gradient update values of the weight coefficients of the nonlinear filtering module are respectively:
wherein ,
x (n) is used to represent the input signal of the linear filtering module;
u (n) is used for representing a nonlinear transformation signal of the nonlinear filtering module;
the superscript T is used to denote a transpose operation.
In a preferred embodiment of the present invention, the gradient update value of the weight coefficient of the linear filtering module and the gradient update value of the weight coefficient of the nonlinear filtering module are obtained according to the following formula:
wherein ,
n is used for representing the order of the linear filtering module;
m is used for representing the order of the nonlinear filtering module, and M is smaller than N;
the superscript T is used to denote a transpose operation.
In the preferred embodiment of the present invention, in step S6, the update formula of the linear module filter weight coefficient and the update formula of the nonlinear module filter weight coefficient are as follows:
w l (n+1)＝w l (n)-2μ l e(n)x(n) T
w nl (n+1)＝w nl (n)-2μ nl e(n)u(n) T
wherein ,
w l (n) weight coefficients for representing linear filtering modules;
w nl (n) weight coefficients for representing nonlinear filtering modules;
μ l the iteration step length is used for representing the control convergence speed in the linear module gradient descent method;
μ nl the iteration step length is used for representing the control convergence speed in the nonlinear module gradient descent method;
e (n) represents an error signal at the output timing;
x (n) is used to represent the input signal of the linear filtering module;
u (n) is used to represent the nonlinear transformation signal of the nonlinear filtering module.
The following describes the above technical solution in detail with a specific embodiment:
as shown in fig. 3 to 4, in the speaker-enclosure-microphone system, a white noise signal is used as an input signal x (n) through the speaker 1, and the power spectrum thereof is shown in fig. 3. The desired signal of the played white noise propagating to the microphone is d (n), and the power spectrum is shown in fig. 4. In order to increase the nonlinear components in the system, speakers and microphones with poor performance are employed. Comparing fig. 3 and 4, it can be seen that the desired signal d (n) is severely lost in high frequency with respect to the input signal x (n).
Substituting x (n) and d (n) into the adaptive algorithm and the adaptive algorithm added with nonlinear fitting according to the invention respectively to obtain y (n) and y (y) l (n)、y nl (n) determining the Mean Square Error (MSE), i.e
A comparison of MSE convergence curves is obtained as shown in fig. 5.
wherein ,
Therefore, the noise reduction amount of the MSE convergence curve obtained by the self-adaptive algorithm added with the nonlinear fitting is obviously improved, and the modeling capability of the self-adaptive filter on a nonlinear system can be effectively improved.
The foregoing description is only illustrative of the preferred embodiments of the present invention and is not to be construed as limiting the scope of the invention, and it will be appreciated by those skilled in the art that equivalent substitutions and obvious variations may be made using the description and illustrations of the present invention, and are intended to be included within the scope of the present invention.
Claims (7)
1. An adaptive method of adding a nonlinear fit, comprising:
step S1, input signal acquisition: adding a nonlinear filtering module into a linear filtering module of the adaptive filter, collecting an input signal received by the adaptive filter, and intercepting the input signal to obtain an input signal of the nonlinear filtering module, wherein the input signal is an audio signal;
step S2, nonlinear transformation: performing RELU nonlinear transformation on an input signal of the nonlinear filtering module, wherein the RELU nonlinear transformation can generate each even harmonic component for a single-frequency signal and is used for modeling a nonlinear system to obtain a nonlinear transformation signal; the RELU nonlinear transformation is as follows:
wherein ,
ω is used to represent the frequency of the input signal;
t is used to represent time;
RELU is used to represent signal negative zeroing operations;
step S3, signal filtering: filtering according to the nonlinear transformation signal and the nonlinear filtering module weight coefficient to obtain an output signal of the nonlinear filtering module, and filtering to obtain an output signal of the linear filtering module;
step S4, error signal calculation: obtaining an error signal of the output moment according to the output signal of the linear filtering module, the output signal of the nonlinear filtering module and the expected signal of the output moment;
step S5, calculating a filter update value: calculating a gradient value updated by a filter each time, and updating filter coefficients of the linear module and the nonlinear module, wherein the derivation principle of the filter updating value is that the error signal function is squared, a loss function is expected to be obtained, and the loss function is used for performing partial derivative operation on the weight coefficient of the linear filter module and the weight coefficient of the nonlinear filter module respectively to obtain a gradient updating value of the weight coefficient of the linear filter module and a gradient updating value of the weight coefficient of the nonlinear filter module;
step S6, updating a filter: according to the gradient update value of the linear filtering module weight coefficient, a gradient descent method is adopted to obtain an update formula of the linear filtering module weight coefficient, and repeated operation is carried out according to the update formula of the linear filtering module weight coefficient to obtain a linear filtering module convergence weight coefficient; according to the gradient update value of the nonlinear filter module weight coefficient, a gradient descent method is adopted to obtain an update formula of the nonlinear filter module weight coefficient, and repeated operation is carried out according to the update formula of the nonlinear filter module weight coefficient to obtain a nonlinear filter module convergence weight coefficient;
s7, respectively carrying out filtering operation on the convergence weight coefficient of the linear filtering module and the convergence weight coefficient of the nonlinear filtering module to obtain an output signal of the linear filtering module and an output signal of the nonlinear filtering module, wherein the two output signals can be highly fitted with the expected signal after being overlapped;
in the step S2, the nonlinear transformation signal is:
u(n)＝f(x cut (n))
wherein ,
x cut (n)＝[x(n),x(n-1),…x(n-M+1)] T
x(n)＝[x(n),x(n-1),…x(n-M+1)] T
m is used to represent the nonlinear filter module order, N is used to represent the linear filter module order, and M < N, the superscript T is used to represent the transpose operation, x (N) is used to represent the input signal of the linear filter module, x cut (n) an input signal representing a nonlinear filtering module;
n is used to represent the time of day;
f is used to represent a nonlinear transformation;
u (n) is used to represent the nonlinear transformation signal;
in the nonlinear transformation, f may be a square nonlinear transformation that may generate a second harmonic frequency for a single frequency signal, and may be used to model a nonlinear system, as follows:
ω is used to represent the frequency of the input signal of the nonlinear filter module;
2 omega is used to represent the second harmonic frequency generated after nonlinear transformation;
() 2 for representing squaring operations.
2. The adaptive method for adding nonlinear fitting according to claim 1, wherein in step S3, the output signal of the linear filtering module and the output signal of the nonlinear filtering module obtained by filtering are calculated according to the following formulas:
y l (n)＝x(n) T w l (n)
y nl (n)＝u(n) T w nl (n)
x (n) is used to represent the input signal of the linear filtering module;
wl (n) is used to represent the weight coefficient of the linear filtering module;
u (n) is used for representing a nonlinear transformation signal of the nonlinear filtering module;
w nl (n) weight coefficients for representing nonlinear filtering modules;
the superscript T is used to denote a transpose operation;
y l (n) an output signal representing the linear filtering module;
y nl (n) means an output signal of the nonlinear filtering module.
3. The adaptive method of adding nonlinear fitting of claim 2, wherein: in the step S4, the error signal at the output time is calculated according to the following formula:
e(n)＝d(n)+y l (n)+y nl (n)
d (n) is used for indicating a desired signal at the output time;
e (n) represents an error signal at the output timing.
4. The adaptive method for adding nonlinear fitting according to claim 3, wherein in step S5, the loss function is calculated according to the following formula:
J＝E(e 2 (n))
e is used to represent the desired operation.
5. The adaptive method for adding nonlinear fitting according to claim 4, wherein in step S5, the gradient update values of the linear filtering module weight coefficients and the gradient update values of the nonlinear filtering module weight coefficients are respectively:
wherein ,
x (n) is used to represent the input signal of the linear filtering module;
u (n) is used for representing a nonlinear transformation signal of the nonlinear filtering module;
the superscript T is used to denote a transpose operation.
6. The adaptive method of adding nonlinear fitting according to claim 5, wherein the gradient update value of the linear filter module weight coefficient and the gradient update value of the nonlinear filter module weight coefficient are obtained according to the following formula:
wherein ,
n is used for representing the order of the linear filtering module;
m is used to represent the nonlinear filter module order, and M < N.
7. The adaptive method for adding nonlinear fitting according to claim 6, wherein in step S6, the update formula of the linear module filter weight coefficient and the update formula of the nonlinear module filter weight coefficient are as follows:
w l (n+1)＝w l (n)-2μ l e(n)x(n) T
w nl (n+1)＝w nl (n)-2μ nl e(n)u(n) T
w l (n) weight coefficients for representing linear filtering modules;
w nl (n) weight coefficients for representing nonlinear filtering modules;
μ l the iteration step length is used for representing the control convergence speed in the linear module gradient descent method;
μ nl the iteration step length is used for representing the control convergence speed in the nonlinear module gradient descent method;
e (n) represents an error signal at the output timing;
x (n) is used to represent the input signal of the linear filtering module;
u (n) is used to represent the nonlinear transformation signal of the nonlinear filtering module.
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| CN114531176A (en) * | 2022-01-14 | 2022-05-24 | 山东梅格彤天电气有限公司 | Carrier communication quality optimization method, device and storage medium |
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| US4843583A (en) * | 1985-10-15 | 1989-06-27 | Rockwell International Corporation | Nonlinear adaptive filter |
| DE19732606A1 (en) * | 1997-07-29 | 1999-02-04 | Thomson Brandt Gmbh | Procedure for the adaptation of FIR filters |
| US6351740B1 (en) * | 1997-12-01 | 2002-02-26 | The Board Of Trustees Of The Leland Stanford Junior University | Method and system for training dynamic nonlinear adaptive filters which have embedded memory |
| US7012772B1 (en) * | 1998-09-02 | 2006-03-14 | Cirrus Logic, Inc. | Sampled amplitude read channel employing an adaptive non-linear correction circuit for correcting non-linear distortions in a read signal |
| GB0116493D0 (en) * | 2001-07-06 | 2001-08-29 | Koninkl Philips Electronics Nv | Receiver having an adaptive filter and method of optimising the filter |
| CN101889389B (en) * | 2007-10-04 | 2014-04-02 | 网络逻辑微系统公司 | System and method for adaptive nonlinear filtering |
| JP5544359B2 (en) * | 2009-07-06 | 2014-07-09 | パナソニック株式会社 | Nonlinear distortion compensation receiver and nonlinear distortion compensation method |
| US8767869B2 (en) * | 2011-08-18 | 2014-07-01 | Qualcomm Incorporated | Joint linear and non-linear cancellation of transmit self-jamming interference |
| US8649745B2 (en) * | 2011-12-21 | 2014-02-11 | Telefonaktiebolaget L M Ericsson (Publ) | Adaptive predistortion for a non-linear subsystem based on a model as a concatenation of a non-linear model followed by a linear model |
| CN110233607A (en) * | 2019-05-28 | 2019-09-13 | 西安交通大学 | Hammerstein type non-linear spline adaptive filter method based on minimal error entropy |
| CN110492868B (en) * | 2019-06-24 | 2023-08-01 | 东南大学 | Multi-parameter variable-step LMS self-adaptive filtering method |
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