# Phase difference calculation between two wave files

I am doing comparison between two wave files, How to calculate phase difference between those files? Second wave is generated by making some changes in the first one .I have tried calculating phase like this:-

y, sr = librosa.load('first.wav')
D = librosa.stft(y)
magnitude, phase1 = librosa.magphase(D)
D1 = librosa.stft(y1)
magnitude1, phase2 = librosa.magphase(D1)

than

calculated the difference(phase1-phase2).


Is this the correct way?

Is this the correct way?

This may be technically correct but won't give you any useful information. The reasons for this are actually quite simple. The phase between two signals can be computed accurately only if your signals contain pure sine tones. You basically have only 2 scenarios where computing the phase difference between 2 signals makes sense.

• a) the 2 signals both contain the same frequency component but have a phase shift between them
• b) the 2 signals contain each a different frequency component

For case #a, the phase difference will remain the same throughout the entire length of the signals, whereas in #b, the phase difference will change as you traverse the length of the signals (it's assumed that the frequency in signal #2 is not a multiple of the frequency in signal #1 and the signals don't start in phase)

When you have a signal that contains multiple frequency components, the phase calculated by an FFT routine (including librosa.stft, which computes dft on multiple signal frames) is pretty much random (you can think of it as being the average of all frequency components contributing to a particular frequency bin, including noise i.e. undesirable components).

This means that computing the phase difference for the purpose of finding the true phase difference between 2 random signals is not possible and is completely meaningless. Computing the phase difference (within a single signal) can still be useful in other applications where it can be used to more accurately estimate the "true" bin frequencies but here it's the relative phases that we're dealing with so it's different.

In conclusion, if your signals don't fit either case a# or case b#, you won't be able to do what you want and it doesn't even make sense to try to do that in the first place.