Physical significance of Power spectral density of sum of correlated random processes

Asked Oct 23 '18 at 17:00

Active Oct 23 '18 at 22:26

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For two processes $X(t)$ and $Y(t)$, PSD of $Z(t) = X(t) + Y(t)$ is $S_Z(\omega) =S_x(\omega)+ S_Y(\omega) + S_{XY}(\omega)+S_{YX}(\omega) $.

If $X(t)$ and $Y(t)$ are orthogonal, PSD of the sum process is sum of the PSDs of individual processes. However for correlated processes, an additional PSD term comes into picture. What is the physical significance of this behavior? To be more specific, the resulting PSD is greater than the sum of individual of PSDs.How can we explain this behavior qualitatively?

edited Oct 23 '18 at 17:08

asked Oct 23 '18 at 17:00

Ehsa

2

look at the case that $X(t) = Y(t)$ ... – AlexTP Oct 23 '18 at 18:50
Even better: look at $X(t) = -Y(t)$ – Hilmar Oct 23 '18 at 23:28

Physical significance of Power spectral density of sum of correlated random processes

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