FFT and IFFT: Random Phases

32 vues (au cours des 30 derniers jours)
Nycholas Maia
Nycholas Maia le 21 Mar 2019
Commenté : oloo le 22 Fév 2023
I imported a single audio file to MATLAB workspace.
After I apply the FFT:
Y = fft(signal)
How can I random change the audio phases before apply the Inverse FFT and get the 'new_signal'?
new_signal = ifft(Y)
How can I do it?

Réponse acceptée

Brittany Scheid
Brittany Scheid le 16 Juin 2019
Modifié(e) : Brittany Scheid le 16 Juin 2019
Following the comment by David Goodmanson above, here is what I used to randomize an array of timeseries data:
function randX = phaseRandomize(X)
% Returns a phase-randomized version of the input data X. If X is an array,
% each row is treated as an independant time series, and columns represent
% sample points.
[N,L]=size(X);
Y=fft(X,[],2); % Get spectrum
% Add random phase shifts (negative for conjugates), preserve DC offset
rnd_theta= -pi + (2*pi).*rand(N,L/2-1);
Y(:,2:L/2)=Y(:,2:L/2).*exp(1i*rnd_theta);
Y(:,L/2+2:L)=Y(:,L/2+2:L).*exp(-1i*flip(rnd_theta,2));
% return phase-randomized data
randX =ifft(Y,[],2);
end
  2 commentaires
oloo
oloo le 21 Fév 2023
Could You please provide code to revert phases back to oryginal signal? of course based on same rnd_theta. Thank You very much.
oloo
oloo le 22 Fév 2023
ok i figured it out already

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Plus de réponses (1)

David Goodmanson
David Goodmanson le 22 Mar 2019
Hi Nycholas,
Assuming signal is real and of length n, n even, then
Y(1) is for frequency 0, the DC contribution, and it's real. Don't mess with that point.
Y(2) and Y(n) are complex conjugates. You can multiply one of that pair by exp(i*theta) and the other by exp(-i*theta), where theta is a random angle with 0 <= theta < 2*pi. the new Y(2) and Y(n) remain complex conugates.
In general from k = 2 to n/2, Y(k) and Y(n+2-k) form a complex conjugate pair. For each of those pairs, do the same kind of multiplcation as above, with a different random angle. Each pair remain complex conjugates.
Y(n/2+1) is real. Don't mess with that point either.
ifft back.
Here the random phases are totally uncorrelated from frequency to frequency, which may or may not be physically realistic.
  3 commentaires
David Goodmanson
David Goodmanson le 23 Mar 2019
Hi NM, what have you tried so far?
David Daminelli
David Daminelli le 1 Juin 2019
Hello NM and DG! I'm working on a project that needs this same function, and I've done an algorithm that does that. It is here https://www.mathworks.com/matlabcentral/answers/465112-help-with-sound-function, followed by a question I had during the project, if they can help it would be usefull!

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