M = 10^5;
z = randn(M, 1); %random vector
%fi = sqrt(2)*sin((k + 1/2)*pi*t);
W = 0;
wdist = zeros(101,1);
for t = 0:0.01:1
    for k = 1:M
       W = W + sqrt(2)/((k+0.5)*pi)  *  sin((k + 0.5)*pi*t) * z(k);

    end
wdist(t*100 + 1) = W;
end
%xl
var(wdist)