How can I get DFT/FFT output frequencies in Hertz?

Question

I want to develop musical notes detector as my degree project and I want to do it from scratch. I have written code for ".wav" file which extracts all info from that audio music file and gives me amplitude as a result.

Then I have written a code for DFT - it gives me output as a complex number where one of the axis (real/imaginary) is amplitude/magnitude and other is Phase.

Now the question I want the answer in frequency (in Hertz not in vector) so I can check whether my DFT gives me the proper output or not. How can i convert my DFT output into frequency ?

I have to code this in C language and I don't want to use any built-in library

Answer 1

You need to find the peak magnitude then work out the corresponding frequency:

• calculate the magnitude of each DFT output bin: magnitude = sqrt(re*re+im*im)
• find the bin with the largest magnitude, call its index i_max.
• calculate the equivalent frequency of this bin: freq = i_max * Fs / N, here Fs = sample rate (Hz) and N = no of points in FFT.

See this answer for a more detailed explanation of how bin indices and frequency are related.