Nested loops of DFT in matlab

Question

Can someone explain these nested loops of DFT in matlab:

N=length(x);
for k=1:N
  X(k)=0;
  for n=1:N
    X(k)=X(k)+x(n).*exp(-1j.*2.*pi.*(n-1).*(k-1)./N);
  end
end

You probably should look through more simple examples of nested loops, if you don't understand this conception. — Mikhail Genkin, Dec 11 '15 at 18:10

score 4 · Answer 1 · answered Dec 11 '15 at 17:36

4

The inner loop over n is a straightforward implementation of the Discrete Fourier Transform equation for a specific frequency bin k:

adjusted for 1-based indexing (as opposed to the 0-based indexing formula from Wikipedia).

The outer loop over k simply compute the equation for all N frequency bins.

answered Dec 11 '15 at 17:36

SleuthEye

I normally don't upvote answers on downvoted questions, but I've always loved your signal processing answers. This one especially. Short and succinct, and brings up the fact about the indexing. +1. – rayryeng Dec 11 '15 at 19:03
thanku so much for helping...but the equation in the loop is not same as fourier transform equation., it inputs (n-1 )* k(-1) instead of n*k.why is that? – noman saeed Dec 13 '15 at 09:33
As I mentioned, "adjusted for 1-based indexing". Wikipedia equation uses 0 to N-1. With the change the change of variables n = n'-1 and k = k'-1, you can loop over n' and k' from 1 to N and get the same result. Try writing down a few terms if it helps. – SleuthEye Dec 13 '15 at 13:35

1 Answers1