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FIR adaptive filter that uses LMS

adaptfilt.lms will be removed in a future release. Use dsp.LMSFilter instead.


ha = adaptfilt.lms(l,step,leakage,coeffs,states)


ha = adaptfilt.lms(l,step,leakage,coeffs,states) constructs an FIR LMS adaptive filter object ha.

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

Input Arguments

Entries in the following table describe the input arguments for adaptfilt.lms.

Input Argument



Adaptive filter length (the number of coefficients or taps) and it must be a positive integer. l defaults to 10.


LMS step size. It must be a nonnegative scalar. You can use maxstep to determine a reasonable range of step size values for the signals being processed. step defaults to 0.1.


Your LMS leakage factor. It must be a scalar between 0 and 1. When leakage is less than one, adaptfilt.lms implements a leaky LMS algorithm. When you omit the leakage property in the calling syntax, it defaults to 1 providing no leakage in the adapting algorithm.


Vector of initial filter coefficients. it must be a length l vector. coeffs defaults to length l vector with elements equal to zero.


Vector of initial filter states for the adaptive filter. It must be a length l-1 vector. states defaults to a length l-1 vector of zeros.


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



Property Description



Reports the adaptive filter algorithm the object uses during adaptation


Vector of elements

Vector containing the initial filter coefficients. It must be a length l vector where l is the number of filter coefficients. coeffs defaults to a length l vector of zeros when you do not provide the vector as an input argument.


Any positive integer

Reports the length of the filter, the number of coefficients or taps


0 to 1

LMS leakage factor. It must be a scalar between zero and one. When it is less than one, a leaky NLMS algorithm results. leakage defaults to 1 (no leakage).


false or true

Determine whether the filter states and coefficients 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 property value that the filter changes during processing. Property values that the filter does not change are not affected. Defaults to false.


Vector of elements, data type double

Vector of the adaptive filter states. states defaults to a vector of zeros which has length equal to (l - 1).


0 to 1

LMS step size. It must be a scalar between zero and one. Setting this step size value to one provides the fastest convergence. step defaults to 0.1.


Use 500 iterations of an adapting filter system to identify and unknown 32nd-order FIR filter.

x  = randn(1,500);     % Input to the filter
b  = fir1(31,0.5);     % FIR system to be identified
n  = 0.1*randn(1,500); % Observation noise signal
d  = filter(b,1,x)+n;  % Desired signal
mu = 0.008;            % LMS step size.
ha = adaptfilt.lms(32,mu);
[y,e] = filter(ha,x,d);
subplot(2,1,1); plot(1:500,[d;y;e]);
title('System Identification of an FIR Filter');
xlabel('Time Index'); ylabel('Signal Value');
subplot(2,1,2); stem([b.',ha.coefficients.']);
xlabel('Coefficient #'); ylabel('Coefficient Value');  grid on;

Using LMS filters in an adaptive filter architecture is a time honored means for identifying an unknown filter. By running the example code provided you can demonstrate one process to identify an unknown FIR filter.


Shynk J.J., "Frequency-Domain and Multirate Adaptive Filtering," IEEE® Signal Processing Magazine, vol. 9, no. 1, pp. 14-37, Jan. 1992.

Introduced in R2011a

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