When to use cross spectral density versus cross correlation?

All my life, I've used cross-correlation to analyze the strength of the relationship between an input signal and the output signal. I use this to determine which input signal most closely influences the output signal:

Yesterday, a friend told me that he uses cross spectral density (same as coherence, he say).

To my interpretation, they seem to quantify the same thing.

When would someone use one over the other?

• I believe the difference is the cross-correlation is in the time domain, while the cross spectral density is in the frequency domain. If I wanted to know how signals related to other signals versus time delay, I would use the cross-correlation function. If I wanted to know how signals related to other signals versus frequency, I would use cross spectral density. See this post as well: dsp.stackexchange.com/questions/10369/… – Dan Boschen Feb 26 '17 at 16:28
• I looked at the other source you posted a [link]. The answer by @forsker_for_dsp says "For Fourier who has as basis functions the sinusoid that extends infinite in time, power spectral density is the correct term. For wavelets, who has basis functions as finite in time deflections, we should use 'energy'." This doesn't make sense to me. If you use power for infinite signals, then you'd be dividing by infinity (because power is energy over time). Isn't it the other way around? Don't we want to use power for signals with finite support, and energy for signals with infinite support? – simple Feb 26 '17 at 23:55
• It is because these are "densities" not total power; if you have the power spectral density and it was flat for example, the density is given in dBm/Hz (for a dB quantity of power), and we would need to multiply by the BW to get the total power. – Dan Boschen Feb 26 '17 at 23:59
• If you post this as a well-formed answer, i'll accept. thanks. – simple Mar 2 '17 at 23:30