Filter Design Toolbox

adaptfilt.swrls

Construct a sliding window recursive least squares FIR adaptive filter

Syntax

• ha = adaptfilt.swrls(l,lambda,invcov,swblocklen,dstates,...
  coeffs,states)
  

Description

ha = adaptfilt.swrls(l,lambda,invcov,swblocklen,dstates,...
coeffs,states) constructs an FIR sliding window RLS adaptive filter ha.

Input Arguments

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

Input Argument	Description
l	Adaptive filter length (the number of coefficients or taps). It must be a positive integer. l defaults to 10.
lambda	RLS forgetting factor. This is a scalar and should lie within the range (0, 1]. lambda defaults to 1.
invcov	Inverse of the input signal covariance matrix. You should initialize invcov to a positive definite matrix.
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 length l vector of all zeros.
states	Vector of initial filter states. states defaults to a zero vector of length equal to (l + swblocklen - 2).

adaptfilt.swrls Object Properties

Since your adaptfilt.swrls 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.swrls objects. To show you the properties that apply, this table lists and describes each property for the 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	Any vector of l 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 + swblocklen - 2).
ForgettingFactor	Scalar	Forgetting factor of the adaptive filter. This is a scalar and should lie in the range (0, 1]. It defaults to 1. Setting forgetting factor = 1 denotes infinite memory while adapting to find the new filter. Note that this is the lambda input argument.
KalmanGain	Vector with dimensions (l,1)	Empty when you construct the object, this gets populated after you run the filter.
InvCov	Matrix	Square matrix with each dimension equal to the filter length l.
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.

Examples

System Identification of a 32-coefficient FIR filter. Use 500 iterations to adapt to the unknown 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
  P0 = 10*eye(32);       % Initial correlation matrix inverse
  lam = 0.99;            % RLS forgetting factor
  N  = 64;               % Block length
  ha = adaptfilt.swrls(32,lam,P0,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.hswrls

adaptfilt.swftf

adaptfilt.tdafdft