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I obtain the cross power spectra by the following steps:

  1. compute the FFT of signal A and B
  2. Multiply A with the conjugate of B store it in C (cross power spectra)
  3. Now looking at the Phase of this cross power spectra C, what all information can I deduce about the two signals A and B?
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If the two signal show a significant correlation at some frequency $f$ then the phase measured in the cross spectrum gives you the phase lag of the signals at that frequency.

So, take $$ A = \sin(2\pi f t ) $$ and $$ B = \sin(2\pi f t - \phi) $$ then the cross spectral phase at frequency $f$ will give you $\phi$.

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  • $\begingroup$ Do you mean the slope of the phase curve across the bandwidth or the phase of individual frequencies? $\endgroup$ – Vivek V K Jul 31 '14 at 1:00
  • $\begingroup$ @VivekVK - I mean the phase of the individual frequency bins. If your signal spans a bandwidth of frequency bins, you'd have to average the phases of those bins. $\endgroup$ – Michael B. Jul 31 '14 at 6:28

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