Filter Design Toolbox

adaptfilt.fdaf

Construct a frequency-domain FIR adaptive filter with bin step size normalization

Syntax

• ha = adaptfilt.fdaf(l,step,leakage,delta,lambda,blocklen,...
  offset,coeffs,states) 
  

Description

ha = adaptfilt.fdaf(l,step,leakage,delta,lambda,blocklen,offset,...
coeffs,states) constructs a frequency-domain FIR adaptive filter ha with bin step size normalization. If you omit all the input arguments you create a default object with l = 10 and step = 1.

Input Arguments

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

Input Argument	Description
l	Adaptive filter length (the number of coefficients or taps). l must be a positive integer; it defaults to 10 when you omit the argument.
step	Step size of the adaptive filter. This is a scalar and should lie in the range (0,1]. step defaults to 1.
leakage	Leakage parameter of the adaptive filter. If this parameter is set to a value between zero and one, you implement a leaky FDAF algorithm. leakage defaults to 1--no leakage provided in the algorithm.
delta	Initial common value of all of the FFT input signal powers. Its initial value should be positive. delta defaults to 1.
lambda	Specifies the averaging factor used to compute the exponentially-windowed FFT input signal powers for the coefficient updates. lambda should lie in the range (0,1]. lambda defaults to 0.9.
blocklen	Block length for the coefficient updates. This must be a positive integer. For faster execution, (blocklen + l) should be a power of two. blocklen defaults to l.
offset	Offset for the normalization terms in the coefficient updates. Use this to avoid divide by zeros or by very small numbers when any of the FFT input signal powers become very small. offset defaults to zero.
coeffs	Initial time-domain coefficients of the adaptive filter. coeff should be a length l vector. The adaptive filter object uses these coefficients to compute the initial frequency-domain filter coefficients via an FFT computed after zero-padding the time-domain vector by the blocklen.
states	The adaptive filter states. states defaults to a zero vector that has length equal to l.

adaptfilt.fdaf Object Properties

Since your adaptfilt.fdaf 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.fdaf objects. To show you the properties that apply, this table lists and describes each property for the adaptfilt.fdaf 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
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. 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. 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.
Leakage		Leakage parameter of the adaptive filter. if this parameter is set to a value between zero and one, you implement a leaky FDAF algorithm. leakage defaults to 1--no leakage provided in the algorithm.
Power		A vector of 2*l elements, each initialized with the value delta from the unput arguments. As you filter data, Power gets updated by the filter process.
AvgFactor	(0, 1]	Specifies the averaging factor used to compute the exponentially-windowed FFT input signal powers for the coefficient updates. Same as the input argument lambda.
BlockLength	Any integer	Block length for the coefficient updates. This must be a positive integer. For faster execution, (blocklen + l) should be a power of two. blocklen defaults to l.
Offset	Any positive real value	Offset for the normalization terms in the coefficient updates. Use this to avoid dividing by zero or by very small numbers when any of the FFT input signal powers become very small. offset defaults to zero.
FFTCoefficients		Stores the discrete Fourier transform of the filter coefficients in coeffs.
FFTStates
StepSize	Any scalar from zero to one, inclusive	Specifies the step size taken between filter coefficient updates

Examples

Quadrature Phase Shift Keying (QPSK) adaptive equalization using 1024 iterations of a 32-coefficient FIR filter.

• D = 16;                         % Number of samples of delay
  b  = exp(j*pi/4)*[-0.7 1];      % Numerator coefficients of channel
  a  = [1 -0.7];                   % Denominator coefficients of channel
  ntr= 1024;                      % Number of iterations
  s  = sign(randn(1,ntr+D)) + j*sign(randn(1,ntr+D));  % Baseband 
                                  % QPSK signal
  n  = 0.1*(randn(1,ntr+D) + j*randn(1,ntr+D));        % Noise signal
  r  = filter(b,a,s)+n;            % Received signal
  x  = r(1+D:ntr+D);               % Input signal (received signal)
  d  = s(1:ntr);                   % Desired signal (delayed QPSK 
                                   % signal)
  del = 1;                         % Initial FFT input powers
  mu  = 0.1;                       % Step size
  lam = 0.9;                       % Averaging factor
  ha = adaptfilt.fdaf(32,mu,1,del,lam);
  [y,e] = filter(ha,x,d); 
  subplot(2,2,1); plot(1:ntr,real([d;y;e]));
  title('In-Phase Components');
  legend('Desired','Output','Error');
  xlabel('Time Index'); ylabel('signal value');
  subplot(2,2,2); plot(1:ntr,imag([d;y;e]));
  title('Quadrature Components');
  legend('Desired','Output','Error');
  xlabel('Time Index'); ylabel('signal value');
  subplot(2,2,3); plot(x(ntr-100:ntr),'.'); axis([-3 3 -3 3]);
  title('Received Signal Scatter Plot'); axis('square'); 
  xlabel('Real[x]'); ylabel('Imag[x]'); grid on;
  subplot(2,2,4); plot(y(ntr-100:ntr),'.'); axis([-3 3 -3 3]);
  title('Equalized Signal Scatter Plot'); axis('square');
  xlabel('Real[y]'); ylabel('Imag[y]'); grid on;
  

See Also

adaptfilt.ufdaf, adaptfilt.pbfdaf, adaptfilt.blms, adaptfilt.blmsfft

Reference

J.J. Shynk, "Frequency-Domain and Multirate Adaptive Filtering," IEEE Signal Processing Magazine, vol. 9, no. 1, pp. 14-37, Jan. 1992

adaptfilt.dlms

adaptfilt.filtxlms