Filter Design Toolbox™

adaptfilt.hrls - FIR adaptive filter that uses householder (RLS)

Syntax

ha = adaptfilt.hrls(l,lambda,sqrtinvcov,coeffs,states)

Description

ha = adaptfilt.hrls(l,lambda,sqrtinvcov,coeffs,states) constructs an FIR householder RLS adaptive filter ha.

Input Arguments

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

Input Argument	Description
`l`	Adaptive filter length (the number of coefficients or taps) and it must be a positive integer. `l` defaults to 10.
`lambda`	RLS forgetting factor. This is a scalar and should lie in the range (0, 1]. `lambda` defaults to 1 meaning the adaptation process retains infinite memory.
`sqrtinvcov`	Square-root of the inverse of the sliding window input signal covariance matrix. This square matrix should be full-ranked.
`coeffs`	Vector of initial filter coefficients. It must be a length `l` vector. `coeffs` defaults to being a length `l` vector of zeros.
`states`	Vector of initial filter states. It must be a length `l`-1 vector. `states` defaults to a length `l`-1 vector of zeros.

Properties

Since your adaptfilt.hrls filter is an object, it has properties that define its behavior in operation. Note that many of the properties are also input arguments for creating adaptfilt.hrls objects. To show you the properties that apply, this table lists and describes each property for the affine projection filter object.

Name	Range	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.
`FilterLength`	Any positive integer	Reports the length of the filter, the number of coefficients or taps
`ForgettingFactor`	Scalar	RLS forgetting factor. This is a scalar and should lie in the range (0, 1]. Same as input argument `lambda`. It defaults to 1 meaning the adaptation process retains infinite memory.
`KalmanGain`	Vector of size (`l`,1)	Empty when you construct the object, this gets populated after you run the filter.
`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. Defaults to `false`.
`SqrtInvCov`	Matrix of doubles	Square root of the inverse of the sliding window input signal covariance matrix. This square matrix should be full-ranked.
`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).

Examples

Use 500 iterations of an adaptive filter object to identify a 32-coefficient FIR filter system. Both the example code and the resulting figure show the successful filter identification through adaptive filter processing.

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
G0 = sqrt(10)*eye(32); % Initial sqrt correlation matrix inverse
lam = 0.99;            % RLS forgetting factor
ha = adaptfilt.hrls(32,lam,G0);
[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;