# Calculating PSD, Cross PSD by using FFT outputs

I am having the FFT results of two distinct voice signals. Let's say the FFT results of these two signals are of the form (a+ib) and (c+id). Now, I want to calculate the PSD of each signal and also the Cross PSD between them. I'm calculating PSD and Cross PSD as follows.

PSD of signal 1 = a * a + b * b;

PSD of signal 2 = c * c + d * d;

Cross PSD between signal1 and signal2 = (ac - bd) + (ad + bc). I also want to know whether this equation represents cross-correlation or cross PSD?

And also, I have ambiguity about the importance of cross PSD. I know that cross PSD is obtained by taking the Fourier transform of the cross-correlation results. I know that from PSD, we can get an idea of the power for different frequencies present in the signal. How does cross PSD differ from PSD? I found out that by using cross PSD, we can find the power shared by a given frequency for the two signals. How do we know how much power is shared between the two signals from a single constant power value per frequency? Please help me out in understanding what the cross PSD means and what is its importance?

Cross PSD (fourier transform of cross-correlation) is $$X(f)^*Y(f)$$, so it will $$(a-ib)(c+id)=(ac+bd)+i(ad-bc)$$. I think you missed to take conjugate like you previous question (Calculating Cross Power Spectral density between two complex signals).
Cross PSD tells a lot about correlation between two different signals. If Cross PSD is white (meaning near flat at all frequencies) with very low value implies both signals are uncorrelated. If $$x$$ and $$y$$ are input and output of a system, you can measure the coherence between $$x$$ and $$y$$. The relationship between PSD of $$x$$ and $$y$$ for the LTI system $$h$$ is $$G_{yy}(f)=|H(f)|^2G_{xx}(f)$$. You can read more at https://en.wikipedia.org/wiki/Coherence_(signal_processing)