One of the problems in Proakis's signal processing book using Matlab asks to plot the histogram of
x3(n) = x1(n) + x1(n-1)
x1(n) is a random sequence.
x1(n), I do the following:
n1 = 1:100000; a = 0; b = 2; % interval over which to pick random numbers. x1 = a + (b-a)*rand(100000,1); N1 = hist(x1,100); figure, bar(N1);
To generate x3(n), I use a couple of helper-functions defined in Proakis's book.
[x31,n31] = sigshift(x1,n1,1); [x3,n3] = sigadd(x1,n1,x31,n31); N3 = hist(x3,nbins); figure, bar(N3);
Unfortunately, I do not have enough points to post images. However, the histogram of the random sequence
x1(n) just shows that
x1 is uniformly distributed. The
x3(n) however, looks more like a Gaussian distribution.
I don't understand why this happens, and would appreciate if someone could explain this a bit.