# What Information does the phase of a cross power spectra give me?

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?

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 $\phi$.