# Phase Spectrum 0 Phase

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,

• It looks like you are seeing the effect of a very large delay (each sample delay will linearly go from 0 to -2 pi as you sweep from DC to the sampling rate) Apr 22, 2022 at 19:37
• Thank you very much for your comment. How can I solve that problem? Apr 22, 2022 at 22:59
• If you want to make it zero phase, multiply the result by the opposite phase versus frequency (using e^{j omega T}) where omega is your frequency axis and adjust T to match the opposite of your phase slope. Apr 22, 2022 at 23:47

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.
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 $$e^{j2\pi \frac{N}{2} \frac{k}{N_{FFT}}}$$