See Aperiodic Convolution_OldKiwi
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
