Filter Design Toolbox

adaptfilt.pbfdaf

Construct a partitioned block frequency-domain PBFDAF) FIR adaptive filter that includes binned step size normalization

Syntax

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

Description

ha = adaptfilt.pbfdaf(l,step,leakage,delta,lambda,blocklen,offset, coeffs,states) constructs a partitioned block frequency-domain FIR adaptive filter ha that uses bin step size normalization during adaptation.

Input Arguments

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

Input Argument	Description
l	Adaptive filter length (the number of coefficients or taps) and it must be a positive integer. L defaults to 10.
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. When you set this argument to a value between zero and one, a leaky version of the PBFDAF algorithm is implemented. leakage defaults to 1-- no leakage.
delta	Initial common value of all of the FFT input signal powers. Its initial value should be positive. delta defaults to 1.
lambda	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 such that (l/blocklen) is also an integer. For faster execution, blocklen should be a power of two. blocklen defaults to two.
offset	Offset for the normalization terms in the coefficient updates. This can be useful to avoid divide by zeros conditions, or dividing by very small numbers, if any of the FFT input signal powers become very small. offset defaults to zero.
coeffs	Initial time-domain coefficients of the adaptive filter. It should be a vector of length l. The PBFDAF algorithm uses these coefficients to compute the initial frequency-domain filter coefficient matrix via FFTs.
states	Specifies the filter initial conditions. states defaults to a zero vector of length l.

adaptfilt.pbfdaf Object Properties

Since your adaptfilt.pbfdaf 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.pbfdaf 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
StepSize		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. When you set this argument to a value between zero and one, a leaky version of the PBFDAF algorithm is implemented. leakage defaults to 1-- no leakage.
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		Averaging factor used to compute the exponentially windowed FFT input signal powers for the coefficient updates. AvgFactor should lie in the range (0,1]. AvgFactor defaults to 0.9. Called lambda as an input argument.
BlockLength		Block length for the coefficient updates. This must be a positive integer such that (l/blocklen) is also an integer. For faster execution, blocklen should be a power of two. blocklen defaults to two.
Offset		Offset for the normalization terms in the coefficient updates. This can be useful to avoid divide by zeros conditions, or dividing by very small numbers, if 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
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.

Examples

An example of Quadrature Phase Shift Keying (QPSK) adaptive equalization using 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 = 1000;                    % 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
  N   = 8;                        % Block size
  ha = adaptfilt.pbfdaf(32,mu,1,del,lam,N);
  [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.fdaf, adaptfilt.pbufdaf, adaptfilt.sbaf, adaptfilt.blmsfft

References

J.S. So and K.K. Pang, "Multidelay Block Frequency Domain Adaptive Filter," IEEE Trans. Acoustics, Speech, and Signal Processing, vol. 38, no. 2, pp. 373-376, February 1990

J.M. Paez Borrallo and M.G. Otero, "On The Implementation of a Partitioned Block Frequency Domain Adaptive Filter (PBFDAF) For Long Acoustic Echo Cancellation," Signal Processing, vol. 27, no. 3, pp. 301-315, June 1992

adaptfilt.nlms

adaptfilt.pbufdaf