identifying phase shift between signals

Question

I have generated three identical waves with a phase shift in each. For example:

t = 1:10800; % generate time vector
fs = 1; % sampling frequency (seconds)
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Answer 1

For two sinusoidal signal the phase of the complex correlation coefficient gives you what you want. I can only give you an python example (using scipy) as I don't have a matlab to test it.

x1 = sin( 0.1*arange(1024) )
x2 = sin( 0.1*arange(1024) + 0.456)
x1h = hilbert(x1)
x2h = hilbert(x2)
c = inner( x1h, conj(x2h) ) / sqrt( inner(x1h,conj(x1h)) * inner(x2h,conj(x2h)) )
phase_diff = angle(c)

There is a function corrcoeff in matlab, that should work, too (The python one discard the imaginary part). I.e. c = corrcoeff(x1h,x2h) should work in matlab.