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FIR adaptive filter that uses adjoint LMS algorithm

adaptfilt.adjlms will be removed in a future release.


ha = adaptfilt.adjlms(l,step,leakage,pathcoeffs,pathest,...

    Note:   adaptfilt.adjlms will be removed in a future release.


ha = adaptfilt.adjlms(l,step,leakage,pathcoeffs,pathest,...
constructs object ha, an FIR adjoint LMS adaptive filter. l is the adaptive filter length (the number of coefficients or taps) and must be a positive integer. l defaults to 10 when you omit the argument. step is the adjoint LMS step size. It must be a nonnegative scalar. When you omit the step argument, step defaults to 0.1.

leakage is the adjoint LMS leakage factor. It must be a scalar between 0 and 1. When leakage is less than one, you implement a leaky version of the adjlms algorithm to determine the filter coefficients. leakage defaults to 1 specifying no leakage in the algorithm.

pathcoeffs is the secondary path filter model. This vector should contain the coefficient values of the secondary path from the output actuator to the error sensor.

pathest is the estimate of the secondary path filter model. pathest defaults to the values in pathcoeffs.

errstates is a vector of error states of the adaptive filter. It must have a length equal to the filter order of the secondary path model estimate. errstates defaults to a vector of zeros of appropriate length. pstates contains the secondary path FIR filter states. It must be a vector of length equal to the filter order of the secondary path model. pstates defaults to a vector of zeros of appropriate length. The initial filter coefficients for the secondary path filter compose vector coeffs. It must be a length l vector. coeffs defaults to a length l vector of zeros. states is a vector containing the initial filter states. It must be a vector of length l+ne-1, where ne is the length of errstates. When you omit states, it defaults to an appropriate length vector of zeros.

For information on how to run data through your adaptive filter object, see the Adaptive Filter Syntaxes section of the reference page for filter.


In the syntax for creating the adaptfilt object, the input options are properties of the object created. This table lists the properties for the adjoint LMS object, their default values, and a brief description of the property.


Default Value




Specifies the adaptive filter algorithm the object uses during adaptation


Length l vector with zeros for all elements

Adjoint LMS FIR filter coefficients. Should be initialized with the initial coefficients for the FIR filter prior to adapting. You need l entries in coefficients. Updated filter coefficients are returned in coefficients when you use s as an output argument.



A vector of the error states for your adaptive filter, with length equal to the order of your secondary path filter.



The number of coefficients in your adaptive filter.



Specifies the leakage parameter. Allows you to implement a leaky algorithm. Including a leakage factor can improve the results of the algorithm by forcing the algorithm to continue to adapt even after it reaches a minimum value. Ranges between 0 and 1.


No default

A vector that contains the coefficient values of your secondary path from the output actuator to the error sensor.


pathcoeffs values

An estimate of the secondary path filter model.


Length of the secondary path filter. All elements are zeros.

The states of the secondary path filter, the unknown system


l+ne+1, where ne is length(errstates)

Contains the initial conditions for your adaptive filter and returns the states of the FIR filter after adaptation. If omitted, it defaults to a zero vector of length equal to l+ne+1. When you use adaptfilt.adjlms in a loop structure, use this element to specify the initial filter states for the adapting FIR filter.



Sets the adjoint LMS algorithm step size used for each iteration of the adapting algorithm. Determines both how quickly and how closely the adaptive filter converges to the filter solution.


false or true

Determine whether the filter states get restored to their starting values for each filtering operation. The starting values are the values in place when you create the filter. PersistentMemory returns to zero any state that the filter changes during processing. States that the filter does not change are not affected. Defaults to false.


Demonstrate active noise control of a random noise signal that runs for 1000 samples.

x  = randn(1,1000);      % Noise source
g  = fir1(47,0.4);       % FIR primary path system model
n  = 0.1*randn(1,1000);  % Observation noise signal
d  = filter(g,1,x)+n;    % Signal to be canceled (desired)
b  = fir1(31,0.5);       % FIR secondary path system model
mu = 0.008;              % Adjoint LMS step size
ha = adaptfilt.adjlms(32,mu,1,b);
[y,e] = filter(ha,x,d);
title('Active Noise Control of a Random Noise Signal');
xlabel('Time Index'); ylabel('Signal Value');  grid on;

Reviewing the figure shows that the adaptive filter attenuates the original noise signal as you expect.


Wan, Eric., "Adjoint LMS: An Alternative to Filtered-X LMS and Multiple Error LMS," Proceedings of the International Conference on Acoustics, Speech, and Signal Processing (ICASSP), pp. 1841-1845, 1997

Introduced in R2011a

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