Filter Design Toolbox

adaptfilt.hrls

Construct a householder recursive least squares (RLS) FIR adaptive filter object

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.

adaptfilt.hrls Object 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
FilterLength	Any positive integer	Reports the length of the filter, the number of coefficients or taps
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.
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).
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.
SqrtInvCov	Matrix of doubles	Square root of the inverse of the sliding window input signal covariance matrix. This square matrix should be full-ranked.
ResetBeforeFiltering	off or on	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. ResetBeforeFiltering returns to zero any state that the filter changes during processing. Defaults to 'on'.
NumSamplesProcessed	Any integer	Returns the number of samples processed during filtering. Defaults to zero.

Examples

Use 500 iterations of an adaptive filter object to identify a 32-coefficient FIR filter system.

• 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;
  

See Also

adaptfilt.rls, adaptfilt.qrdrls, adaptfilt.hswrls

adaptfilt.gal

adaptfilt.hswrls