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
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
