Filter Design Toolbox

adaptfilt.ufdaf

Construct a Unconstrained frequency-domain (UFDAF) FIR adaptive filter with binned step size normalization

Syntax

ha = adaptfilt.ufdaf(l,step,leakage,delta,lambda,blocklen,offset,c oeffs,states)

Description

ha = adaptfilt.ufdaf(l,step,leakage,delta,lambda,blocklen,offset,c oeffs,states) constructs an unconstrained frequency-domain FIR adaptive filter ha with bin step size normalization.

Input Arguments

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

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	Adaptive filter step size. It must be a nonnegative scalar. You can use maxstep to determine a reasonable range of step size values for the signals being processed. step defaults to 0.
leakage	Leakage parameter of the adaptive filter. When you set this argument to a value between zero and one, you are implementing a leaky version of the UFDAF algorithm. leakage defaults to 1--no leakage.
delta	Initial common value of all of the FFT input signal powers. the initial value of delta should should be positive, and it 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]. For default UFDAF filter objects, 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. This can help you avoid divide by zero conditions, or divide by very small numbers conditions, when any of the FFT input signal powers become very small. Default value is zero.
coeffs	Initial time-domain coefficients of the adaptive filter. It should be a length l vector. The 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 blocklen.
states	Adaptive filter states. states defaults to a zero vector with length equal to l.

adaptfilt.ufdaf Object Properties

Since your adaptfilt.ufdaf 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.ufdaf 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		Adaptive filter step size. It must be a nonnegative scalar. You can use maxstep to determine a reasonable range of step size values for the signals being processed. step defaults to 0.
Leakage		Leakage parameter of the adaptive filter. When you set this argument to a value between zero and one, you are implementing a leaky version of the UFDAF algorithm. leakage defaults to 1--no leakage.
Power	2*l element vector	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		Specifies the averaging factor used to compute the exponentially-windowed FFT input signal powers for the coefficient updates. AvgFactor should lie in the range (0,1]. For default UFDAF filter objects, AvgFactor defaults to 0.9. Note that AvgFactor and lambda are the same thing--lambda is an input argument and AvgFactor a property of the object.
BlockLength		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. This can help you avoid divide by zero conditions, or divide by very small numbers conditions, when any of the FFT input signal powers become very small. Default value is 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

Show an example of Quadrature Phase Shift Keying (QPSK) adaptive equalization using a 32-coefficient adaptive filter. For fidelity, use 1024 iterations.

• 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.ufdaf(32,mu,1,del,lam);
  [y,e] = filter(ha,x,d); 
  subplot(2,2,1); 
  plot(1:1000,real([d(1:1000);y(1:1000);e(1:1000)]));
  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.blms, adaptfilt.blmsfft

References

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

adaptfilt.tdafdct

allpassbpc2bpc