Phase Spectrum 0 Phase

Question

I am a beginner in signal processing. I am learning about the Fourier transform. I was working on the zero-phase Ricker wavelet. As I understand If I extract the phase spectrum I should get something similar to that image.

However, my result is totally different.

Does anyone know the reason? Thank you in advance,

Answer 1

I was working on the zero-phase Ricker wavelet.

Chances you were working on the "linear-phase" wavelet. Assuming a real input, zero-phase requires time symmetry, i.e. $x[-n] = x[n]$. If you just take the wavelet (which is centered around $N/2$) and apply an FFT you get a linear phase behavior.

How can I solve that problem? Two suggestions:

1. Circularly shift the time domain wavelet before the DFT. Recall that the DFT is periodic, i.e. $x[-n] = x[n]$ is equivalent to $x[N-n] = x[n]$
2. Apply the the circular shift in the frequency domain after the DFT by multiplying with $e^{j2\pi \frac{N}{2} \frac{k}{N_{FFT}}}$

Exact details depend a bit on whether the length of the wavelet is odd or even.