Filter Design Toolbox™

adaptfilt.dlms - FIR adaptive filter that uses delayed LMS

Syntax

ha = adaptfilt.dlms(l,step,leakage,delay,errstates,coeffs, ...states)

Description

ha = adaptfilt.dlms(l,step,leakage,delay,errstates,coeffs, ...states) constructs an FIR delayed LMS adaptive filter ha.

Input Arguments

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

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.
`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.
`delay`	Update delay given in time samples. This scalar should be a positive integer — negative delays do not work. `delay` defaults to 1.
`errstates`	Vector of the error states of your adaptive filter. It must have a length equal to the update delay (`delay`) in samples. `errstates` defaults to an appropriate length vector of zeros.
`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 you create. This table lists the properties for the block LMS object, their default values, and a brief description of the property.

Property	Default Value	Description
`Algorithm`	None	Defines 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 length `l` vector of zeros when you do not provide the argument for input. LMS FIR filter coefficients. Should be initialized with the initial coefficients for the FIR filter prior to adapting. You need `l` entries in `coeffs`.
`Delay`	1	Specifies the update delay for the adaptive algorithm.
`ErrorStates`	Vector of zeros with the number of elements equal to `delay`	A vector comprising the error states for the adaptive filter.
`FilterLength`	Any positive integer	Reports the length of the filter, the number of coefficients or taps.
`Leakage`	1	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.
`PersistentMemory`	`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 if you have not changed the filter since you constructed it. `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`.
`StepSize`	0.1	Sets the 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.
`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` + `projectord` - 2).

Example

System identification of a 32-coefficient FIR filter. Refer to the figure that follows to see the results of the adapting filter process.

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.
delay = 1;              % Update delay
ha = adaptfilt.dlms(32,mu,1,delay);
[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 a delayed LMS adaptive filter in the process to identify an unknown filter appears to work as planned, as shown in this figure.

References

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

adaptfilt.blmsfft

adaptfilt.fdaf