Calculate frequency bins of an audiosignal

Question

I am doing a fft (stft) on a audio-file, which contains voice and music. I took out a range of 1-200 from signal, which i saved in a variable called, for example, frequency_band1. How can i calculate the frequency bins from variable, which stores my specificially chosen signal, on which the fft was applied before.? I think, read somewhere, that i needed to calculate fs/fftpoints. In my case, 44100/4096. Do i multiply it with my variable frequency_band1*(44100/4096)? This is done on matlab, and i need to do it, with a stft.

The output values of a DFT (FFT) are at frequencies `[0:n-1]/n*fs` where `n` is DFT size and `fs` is sample frequency — Luis Mendo, Jan 26 '17 at 22:21
@Lusi Mendo, with "n", do you mean the fft points? I am not quite sure, since i am a newbie at matlab. How is this linked to my question, if you could enlighten me, i would really appreciate it. — CidelFastro, Jan 26 '17 at 22:50
@Luis Mendo Ok, thank you, now i got it. One last question, sorry for being annoying btw, but does "numel" stands for the number of elements from the sinusoid, so that you can create a frequency vector? — CidelFastro, Jan 26 '17 at 23:06
Yes, `numel` is size of the vector `x`. You should actually use the size of the output of `fft`, in case it's different from the size of the input (that is, if you use a second argument to `fft`). I've edited that — Luis Mendo, Jan 26 '17 at 23:10

score 0 · Accepted Answer · edited Jan 27 '17 at 22:48

The output values of a DFT (FFT) are at frequencies (0:n-1)/n*fs where n is DFT size and fs is sample frequency.

Here's an example. This creates a sinusoid at a known frequency, performs the DFT of the whole signal (so n is signal size), and plots the spectrum using the above as frequency values.

fs = 44100; % sample frequency
t = 0:1/fs:.1; % 0.1-second time axis
x = sin(2*pi*300*t); % sinusoid of frequency 220 Hz
X = fft(x); % DFT of x
f = (0:numel(X)-1)/numel(X)*fs; % frequency axis of DFT
plot(f, abs(X)) % plot the spectrum in absolute value
grid % add grid
axis([0 1000 -500 2500])

You can check that the spectral line of this signal is where it should, that is, at 300 (Hz).

Calculate frequency bins of an audiosignal

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