Quickly written based on LMS algorithm at Wikipedia (which I think originate from Haykin's "Adaptive Filter Theory 4th Ed.")
function [w,y,e,W] = LMS(x,d,mu_step,M)
N = length(x); % number of data samples
y = zeros(N,1); % initialize filter output vector
w = zeros(M,1); % initialize filter coefficient vector
e = zeros(N,1); % initialize error vector
W = zeros(M,N); % filter coefficient matrix for coeff. history
for n = 1:N
if n <= M % assume zero-samples for delayed data that isn't available
k = n:-1:1;
x1 = [x(k); zeros(M-numel(k),1)];
else
x1 = x(n:-1:n-M+1); % M samples of x in reverse order
end
y(n) = w'*x1; % filter output
e(n) = d(n) - y(n); % error
w = w + mu_step*e(n)'*x1; % update filter coefficients
W(:,n) = w; % store current filter coefficients in matrix
end
