Filter Design Toolbox

adaptfilt.ftf

Construct a Fast transversal least squares adaptive filter object

Syntax

• ha = adaptfilt.ftf(l,lambda,delta,gamma,gstates,coeffs,states)
  

Description

ha = adaptfilt.ftf(l,lambda,delta,gamma,gstates,coeffs,states) constructs a fast transversal least squares adaptive filter object ha.

Input Arguments

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

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 that should lie in the range (1-0.5/l, 1]. lambda defaults to 1.
delta	Soft-constrained initialization factor. This scalar should be positive and sufficiently large to prevent an excessive number of Kalman gain rescues. delta defaults to one.
gamma	Conversion factor. gamma defaults to one specifying soft-constrained initialization.
gstates	States of the Kalman gain updates. gstates defaults to a zero vector of length l.
coeffs	Length l vector of initial filter coefficients. coeffs defaults to a length l vector of zeros.
states	vector of initial filter States. STATES defaults to a zero vector of length (L-1).

adaptfilt.ftf Object Properties

Since your adaptfilt.ftf 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.ftf objects. To show you the properties that apply, this table lists and describes each property for the fast transversal least squares 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		RLS forgetting factor. This is a scalar that should lie in the range (1-0.5/l, 1]. lambda defaults to 1.
InitFactor
FwdPrediction
BkwdPrediction
KalmanGain
ConversionFactor
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. States that the filter does not change are not affected. Defaults to 'on'.
NumSamplesProcessed	Any integer	Returns the number of samples processed during filtering. Defaults to zero.

Examples

System Identification of a 32-coefficient FIR filter by running the identifaction process for 500 iterations.

• 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
  N  = 31;               % Adaptive filter order
  lam = 0.99;            % RLS forgetting factor
  del = 0.1;             % Soft-constrained initialization factor
  ha = adaptfilt.ftf(32,lam,del);
  [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.swftf, adaptfilt.rls, adaptfilt.lsl

Reference

D.T.M. Slock and Kailath, T., "Numerically Stable Fast Transversal Filters for Recursive Least Squares Adaptive Filtering," IEEE Trans. Signal Processing, vol. 38, no. 1, pp. 92-114.

adaptfilt.filtxlms

adaptfilt.gal