full_tdlms.m

System identification with adaptive filter using full and partial-update Transform-Domain Least-Mean

function [e,w] = full_tdlms(x,d,N,w0,mu,lambda,epsilon)
%[e,w] = full_tdlms(x,d,N,w0,mu,lambda,epsilon) implements the full-update
%transform-domain LMS algorithm using DCT and single-division power normalization.    
%   ----------------
%   input parameters
%   ----------------
%   x : Lx1 input signal
%   d : Lx1 desired response 
%   N : filter length
%   w0 : Nx1 initialization
%   mu : step-size parameter
%   lambda : exponential forgetting factor for power estimation
%   epsilon : initialization for power estimate
%   ----------------
%   function outputs
%   ----------------
%   w : LxN evolution of coefficients
%   e : Lx1 error vector

x = x(:);
d = d(:);
w0 = w0(:);

L = length(x);
w = zeros(L,N);
e = zeros(L,1);

w(1,:) = w0';
xvec = zeros(N,1);

rpk = (1/epsilon)*ones(N,1);    %initial inv power estimate for single-division power normalization

invlambda = 1/lambda;

for i = 1:L-1
    xvec = [x(i);xvec(1:N-1)];
    vvec = dct(xvec);
    e(i) = d(i) - w(i,:)*vvec;
    
    bk = invlambda*rpk;
    ck = bk.*vvec; 
    upd = mu * e(i) * ck ;          %delayed normalized v
    ck = ck.* vvec;
    dk = bk.*ck;
    rpk = bk - dk/(1+sum(ck));      %update reciprocal power estimate
    
    w(i+1,:) = w(i,:) + upd';       %update coefficients
end

xvec = [x(L);xvec(1:N-1)];
vvec = dct(xvec);
e(L) = d(L)-w(L,:)*vvec;