Construct phase spectrum before IFFT

Prashant Kumar answered . 2025-03-30 21:01:03

Hi,

I see that what I said about dividing your angles by a factor of 2*length(...) was incorrect because that factor was inside the argument of the angle function. So I will start over. [1] I believe your time array has one too many points. For true periodicity, the value of T_addition should not be the same at the end point as at the first point. Going with something like

N  = 1000;
dt = .01
Max_t = N*dt;
df = 1/Max_t;
t = (0:N-1)*dt
f = (0:N-1)*df

gives single-point amplitudes at the desired frequencies, zero everywhere else. The extra time point messes that up. If you try plotting the fft either way you will see a significant difference. [2] Sometimes phase variations make good sense, such as with filters, but there is not exactly such a thing as a phase spectrum in all cases. If you have tiny amplitudes between peaks, down around 1e-10 or whatever, you will still get phase angles, which are basically meaningless. [3] Point 1 in the freq array is zero frequency, point 2 matches up with the end point, 3 with end-2 etc. Your code is close but in the last for loop the the -2 terms should be +2. [4] For the fourier transform or fft of a real function, the phase angle at negative frequency is minus the phase angle at positive frequency. So in the last line of the last for loop the = phase should be = - phase. Once those changes are made the plots are reasonably good. The phases from the fft look like noise but almost all those phases belong to minuscule amplitudes; I believe the phases at the actual signal points are correct.

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