Filter Design Toolbox™

adaptfilt.lms - FIR adaptive filter that uses LMS

Syntax

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

Description

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

Input Arguments

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

Input Argument	Description
`l`	Adaptive filter length (the number of coefficients or taps) and it must be a positive integer. `l` defaults to 10.
`step`	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.
`leakage`	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.
`coeffs`	Vector of initial filter coefficients. it must be a length `l` vector. `coeffs` defaults to length `l` vector with elements equal to zero.
`states`	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.

Properties

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	Range	Property Description
`Algorithm`	None	Reports the adaptive filter algorithm the object uses during adaptation
`Coefficients`	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.
`FilterLength`	Any positive integer	Reports the length of the filter, the number of coefficients or taps
`Leakage`	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).
`PersistentMemory`	`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`.
`States`	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).
`StepSize`	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.

Example

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');
legend('Desired','Output','Error');
xlabel('Time Index'); ylabel('Signal Value');
subplot(2,1,2); stem([b.',ha.coefficients.']);
legend('Actual','Estimated');
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.

References

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

adaptfilt.hswrls

adaptfilt.lsl