Filter Design Toolbox

adaptfilt.hswrls

Construct a householder sliding window RLS FIR adaptive filter

Syntax

• ha = adaptfilt.hswrls(l, lambda, sqrtinvcov, swblocklen,...
  dstates, coeffs, states)
  

Description

ha = adaptfilt.hswrls(l, lambda, sqrtinvcov, swblocklen, dstates, coeffs, states) constructs an FIR householder sliding window recursive-least-square adaptive filter ha.

Input Arguments

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

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	Recursive least square (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.
swblocklen	Block length of the sliding window. This integer must be at least as large as the filter length. swblocklen defaults to 16.
dstates	Desired signal states of the adaptive filter. dstates defaults to a zero vector with length equal to (swblocklen - 1).
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 + swblocklen -2) vector. states defaults to a length (l + swblocklen -2) vector of zeros.

adaptfilt.hswrls Object Properties

Since your adaptfilt.hswrls 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.hswrls 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 + projectord - 2).
ForgettingFactor	Scalar	Root-least-square (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	(l,1) vector	Empty when you construct the object, this gets populated after you run the filter.
SqrtInvCov	l-by-l Matrix	Square-root of the inverse of the sliding window input signal covariance matrix. This square matrix should be full-ranked.
SwBlockLength	Integer	Block length of the sliding window. This integer must be at least as large as the filter length. swblocklen defaults to 16.
DesiredSignalStates	Vector	Desired signal states of the adaptive filter. dstates defaults to a zero vector with length equal to (swblocklen - 1).
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. As a check, the number of samples reported processed plus the number of nonprocessed samples should be the total number of input samples. Defaults to zero.

Examples

System Identification of a 32-coefficient 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
  G0 = sqrt(10)*eye(32); % Initial sqrt correlation matrix inverse
  lam = 0.99;            % RLS forgetting factor
  N  = 64;               % block length
  ha = adaptfilt.hswrls(32,lam,G0,N);
  [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.hrls

adaptfilt.hrls

adaptfilt.lms