complex values in Short-time Fourier Transform

Started by feldmanjonm 6 years ago3 replieslatest reply 6 years ago1021 views

I have an audio file as input, and I want to compute a spectrogram using STFT, manipulate magnitude and phase in the frequency domain, and then transform the signal back using the iSTFT.  Right now I am performing a test to see if I can use the STFT followed by the iSTFT with no frequency domain manipulation and get back the original signal.  The only manipulation I am doing is once I have computed the STFT, I convert the complex values from rectangular form into magnitude and phase, and then back into rectangular form.  When I iSTFT this and write out the audio file, the audio is distorted.  

What is wrong the magnitude/phase calculations that I am doing?  Why doesn't W == S?


% convert spectrogram S to magnitude spectrogram M and phase spectrogram T
M = abs(S);
T = atan(imag(S)./real(S))

% convert back from magnitude/phase form to rectangular coordinates
newReal = M .* cos(T);
newImag = M .* sin(T);
W = newReal + j .* newImag;

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Reply by dgshaw6June 1, 2017


I think that you simply need atan2(y,x) for the phase.  I may be wrong.

Remember that atan has a range of only -pi/2 -> pi/2 if you don't have the full values for real and imaginary.

Good luck.


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Reply by Tim WescottJune 1, 2017

atan(0 / 1) = 0.

atan(0 / -1) = 0.

atan(1 / 1) = pi/8

atan(-1 / -1) = pi/8


What David said about atan2 -- you need to capture the whole picture on the phase, and just atan doesn't do that.

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Reply by artmezJune 2, 2017

What do you mean EXACTLY by distorted? A graph would help.

If imag/real is near an arctan asymptote of a pi/2 increment, then math precision gets in the way. Also, since a discrete STFT is a very granular approximation of a "true" FT, that could lead to calculation "noise", not to mention that transcendental function approximationmath quickly eats up floating point guard bits.

Suggestion: Test your calculations using synthetic "data" for ideal case of pi/4 for each angle to see it you still get noise.