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FIR adaptive filter that uses sign-error algorithm will be removed in a future release. Use dsp.LMSFilter instead.


ha =,step,leakage,coeffs,states)


ha =,step,leakage,coeffs,states) constructs an FIR sign-error adaptive filter ha.

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

Input Argument



Adaptive filter length (the number of coefficients or taps) and it must be a positive integer. l defaults to 10.


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


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


Vector of initial filter coefficients. it must be a length l vector. coeffs defaults to length l vector with elements equal to zero.


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.


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.


Default Value




Defines the adaptive filter algorithm the object uses during adaptation



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.



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



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.


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.



Vector of the adaptive filter states. states defaults to a vector of zeros which has length equal to (l -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.


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
ha =,mu);
[y,e] = filter(ha,x,d);
axis([ntr-100 ntr -3 3]);
title('Adaptive Line Enhancement of Noisy Sinusoid');
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');
xlabel('Normalized Frequency (\times \pi rad/sample)');
ylabel('Power Spectral Density'); grid on;

Compare the figure shown here to the ones for and to see how the variants perform on the same example.


Gersho, A, "Adaptive Filtering With Binary Reinforcement," IEEE® Trans. Information Theory, vol. IT-30, pp. 191-199, March 1984.

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

Introduced in R2011a

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