How do I obtain the frequencies of each value in an FFT?

Question

I have an FFT result. These are stored in two double arrays: a real part array and an imaginary part array. How do I determine the frequencies that correspond t

Answer 1

The FFT output coefficients (for complex input of size N) are from 0 to N - 1 grouped as [LOW,MID,HI,HI,MID,LOW] frequency.

I would consider that the element at k has the same frequency as the element at N-k since for real data, FFT[N-k] = complex conjugate of FFT[k].

The order of scanning from LOW to HIGH frequency is

0,

 1,
 N-1,

 2,
 N-2

 ...

 [N/2] - 1,
 N - ([N/2] - 1) = [N/2]+1,

 [N/2]

There are [N/2]+1 groups of frequency from index i = 0 to [N/2], each having the frequency = i * SamplingFrequency / N

So the frequency at bin FFT[k] is:

if k <= [N/2] then k * SamplingFrequency / N
if k >= [N/2] then (N-k) * SamplingFrequency / N