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# Documentation

FIR adaptive filter that uses sign-error algorithm

## Description

For information on how to run data through your adaptive filter object, see the Adaptive Filter Syntaxes section of the reference page for filter.

### Input Arguments

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

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

SE 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 0.1

leakage

Your SE leakage factor. It must be a scalar between 0 and 1. When leakage is less than one, adaptfilt.se implements a leaky SE 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.

## Properties

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

Property

Default Value

Description

Algorithm

Sign-error

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.

FilterLength

10

Reports the length of the filter, the number of coefficients or taps

Leakage

1

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 one if omitted.

PersistentMemory

false or true

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. PersistentMemory 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 false.

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 SE 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.

Use inspect(ha) to view or change the object properties graphically using the MATLAB Property Inspector.

## Examples

Adaptive line enhancement using a 32-coefficient FIR filter running over 5000 iterations.

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-error step size
[y,e] = filter(ha,x,d);
subplot(2,1,1);
plot(1:ntr,[d;y;v(1:end-1)]);
axis([ntr-100 ntr -3 3]);
title('Adaptive Line Enhancement of Noisy Sinusoid');
legend('Observed','Enhanced','Original');
xlabel('Time Index'); ylabel('Signal Value');
HWelch = spectrum.welch;
InputPsd = psd(HWelch,x(ntr-1000:ntr));
OutputPsd = psd(HWelch,y(ntr-1000:ntr));
CompPsdEst = [InputPsd.Data/max(InputPsd.Data), OutputPsd.Data/max(OutputPsd.Data)];
subplot(2,1,2); plot(InputPsd.Frequencies/pi,10*log10(CompPsdEst));
axis([0 1 -60 20]); legend('Observed','Enhanced');
ylabel('Power Spectral Density'); grid on;