% Pick a length of signal
x = zeros(512,1);

% Set the number of pixels to average
W = 50;

%Put a pulse in the middle of the signal
x(length(x)/4:3*(length(x)/4)) = ones(length(length(x)/4:(3*(length(x)/4))),1);

% Smooth the pulse
s = zeros(1,length(x)/2);
s = exp(-(([1:length(s)])/(0.2*W)).^2);
S = circul(s,1);
f = S * x;
x = x ./max(abs(x));
f = f ./max(abs(f));

% generate the filter h
h = zeros(1,length(x)/2);
h = exp(-(([1:length(h)])/W).^2);

% generate the white noise w
w = 10*rand(512, 1);