See Aperiodic Convolution_Old Kiwi

Formula for Periodic Convolution

$ \begin{align} y[n] &= h[n]\circledast x[n]\\ &= \sum_{m=0}^{N-1}h[(n-m) \bmod N]x[m]\\ \end{align} $

Basic Algorithm in MATLAB

x1 = [1 1 1 1 0 0 0 0 0 0 0 0];
x2 = [3 2 1 0 -1 -2 -3 -2 -1 0 1 2];

N = length(x1);
c = zeros(1,N);

for n = 0:N-1
csum = 0;
for m = 0:N-1
csum = csum + x1(mod((n-m),N)+1)*x2(m+1);
end
c(n+1) = csum;
end

Alumni Liaison

Correspondence Chess Grandmaster and Purdue Alumni

Prof. Dan Fleetwood