Filter Design Toolbox

adaptfilt.sd

Construct an FIR adaptive filter object that uses the sign-data algorithm

Syntax

• ha = adaptfilt.sd(l,step,leakage,coeffs,states)
  

Description

ha = adaptfilt.sd(l,step,leakage,coeffs,states) constructs an FIR sign-data adaptive filter object ha.

Input Arguments

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

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	SD step size. It must be a nonnegative scalar. step defaults to 0.1
leakage	Your SD leakage factor. It must be a scalar between 0 and 1. When leakage is less than one, adaptfilt.sd implements a leaky SD algorithm. When you omit the leakage property in the calling syntax, it defaults to 1 providing no leakage in the adapting algorithm.
coeffs	Vector of initial filter coefficients. it must be a length l vector. coeffs defaults to length l vector with elements equal to zero.
states	Vector of initial filter states for the adaptive filter. It must be a length l-1 vector. states defaults to a length l-1 vector of zeros.

adaptfilt.sd Object Properties

In the syntax for creating the adaptfilt object, the input options are properties of the object you create. This table list all the properties for sign-data objects, their default values, and a brief description of the property.

Property	Default Value	Description
Algorithm	Sign-data	Defines the adaptive filter algorithm the object uses during adaptation
FilterLength	10	Reports the length of the filter, the number of coefficients or taps
Coefficients	zeros(1,l)	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. Should be initialized with the initial coefficients for the FIR filter prior to adapting. You need l entries in coefficients.
States	zeros(l-1,1)	Vector of the adaptive filter states. states defaults to a vector of zeros which has length equal to (l - 1).
StepSize	0.1	Sets the SD algorithm step size used for each iteration of the adapting algorithm. Determines both how quickly and how closely the adaptive filter converges to the filter solution.
Leakage	0	Specifies the leakage parameter. Allows you to implement a leaky algorithm. Including a leakage factor can improve the results of the algorithm by forcing the algorithm to continue to adapt even after it reaches a minimum value. Ranges between 0 and 1. DEFaults to 0
ResetBeforeFiltering	off or on	Determine whether the filter states and coefficients 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 property value that the filter changes during processing. Property values that the filter does not change are not affected. Defaults to 'on'.
NumSamplesProcessed	0	Returns the number of samples processed during filtering. Defaults to zero.

Example

Adaptive line enhancement using a 32-coefficient FIR filter to perform the enhancement. This example runs for 5000 iterations, as you see in property iter.

• d  = 1;                              % Number of samples of delay
  ntr= 5000;                           % Number of iterations
  v  = sin(2*pi*0.05*[1:ntr+d]);       % Sinusoidal signal
  n  = randn(1,ntr+d);                 % Noise signal
  x  = v(1:ntr)+n(1:ntr);              % Input signal (delayed 
  desired                                      % signal)
  d  = v(1+d:ntr+d)+n(1+d:ntr+d);      % Desired signal
  mu = 0.0001;                         % Sign-data step size.
  ha = adaptfilt.sd(32,mu);
  [y,e] = filter(ha,x,d); 
  subplot(2,1,1); plot(1:ntr,[d;y;v(1+d:ntr+d)]);
  axis([ntr-100 ntr -3 3]);
  title('Adaptive Line Enhancement of a Noisy Sinusoidal Signal');
  legend('Observed','Enhanced','Original');
  xlabel('Time Index'); ylabel('Signal Value');
  [pxx,om] = pwelch(x(ntr-1000:ntr));
  pyy = pwelch(y(ntr-1000:ntr));  
  subplot(2,1,2); 
  plot(om/pi,10*log10([pxx/max(pxx),pyy/max(pyy)]));
  axis([0 1 -60 20]);
  legend('Observed','Enhanced'); 
  xlabel('Normalized Frequency (\times \pi rad/sample)');
  ylabel('Power Spectral Density'); grid on;
  

See Also

adaptfilt.lms, adaptfilt.se, adaptfilt.ss

References

Moschner, J.L., "Adaptive Filter with Clipped Input Data," Ph.D. thesis, Stanford Univ., Stanford, CA, June 1970.

Hayes, M., Statistical Digital Signal Processing and Modeling, New York Wiley, 1996.

adaptfilt.rls

adaptfilt.se