Contents

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.

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.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'); grid on;
 xlabel('Coefficient #'); ylabel('Coefficient Value');

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