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

Take a look at my answer here.

Answer to comment:

The FFT actually calculates the cross-correlation of the input signal with sine and cosine functions (basis functions) at a range of equally spaced frequencies. For a given FFT output, there is a corresponding frequency (F) as given by the answer I posted. The real part of the output sample is the cross-correlation of the input signal with cos(2*pi*F*t) and the imaginary part is the cross-correlation of the input signal with sin(2*pi*F*t). The reason the input signal is correlated with sin and cos functions is to account for phase differences between the input signal and basis functions.

By taking the magnitude of the complex FFT output, you get a measure of how well the input signal correlates with sinusoids at a set of frequencies regardless of the input signal phase. If you are just analyzing frequency content of a signal, you will almost always take the magnitude or magnitude squared of the complex output of the FFT.