Cross spectral density show the relationship between two source singals, during the processing, there may be a little bit of time delay which make a little phase difference in cause.
so CSD not only show the difference between the amplitude and also the phase difference.
Pwoer spectral density contains the content of the frequnecy, it show the pwoer load at a specific freqnecy.
Cross-Spectral Density is the same, but using cross-correlation, so you can find the power shared by a given frequency for the two signals using its squared module, and the phase shift between the two signals at that frequency using its argument.
Cross-Spectral Density can be used to identify the frequency response of a noisy LIT system : if the noise is not correlated to the input or output of the system, its frequency response can be found from the CSD of the input and output.
Power-Spectral Density is the distribution of power along the frequency axis. It is generally used for non-finite energy signals (mostly not limited in time signals), who aren’t square-summable. The signal’s PSD is the autocorrelation of the signal’s Fourier Transform, as stated by the Wiener–Khinchin theorem.