Hi BELIEVE,
Here's an example code of a basic implementation of the Least Mean Squares (LMS) algorithm for an adaptive filter in MATLAB assuming a single-input, single-output (SISO) system.
% Define the input signal
inputSignal = randn(1, N); % N is the number of samples
% Define the desired signal (target signal)
desiredSignal = sin(0.1*pi*(1:N));
% Set the filter order and step size (adaptation rate)
filterOrder = 10;
stepSize = 0.01;
% Initialize the filter coefficients
filterCoefficients = zeros(filterOrder, 1);
% Apply the LMS algorithm
outputSignal = zeros(1, N);
errorSignal = zeros(1, N);
for n = 1:N
% Extract the current input signal segment
x = inputSignal(n:-1:n-filterOrder+1);
% Compute the filter output
y = filterCoefficients' * x;
% Compute the error signal
e = desiredSignal(n) - y;
% Update the filter coefficients using the LMS update rule
filterCoefficients = filterCoefficients + stepSize * e * x;
% Store the output and error signals
outputSignal(n) = y;
errorSignal(n) = e;
end
% Plot the results
figure;
subplot(3, 1, 1);
plot(desiredSignal);
title('Desired Signal');
subplot(3, 1, 2);
plot(outputSignal);
title('Output Signal');
subplot(3, 1, 3);
plot(errorSignal);
title('Error Signal');
In this code, we generate a random input signal and a desired signal (target signal). We then initialize the filter coefficients and iterate through each sample of the input signal to update the filter coefficients using the LMS algorithm. The output signal and the error signal are computed at each iteration. Finally, we plot the desired signal, output signal, and error signal for visualization.
Hope it helps!
