If auto- or cross- correlation function decreases with t rapidly, it means the process changes fast with time. On the other hand, if the correlation function decreases with t slowly, it means the process changes with time slowly.
Correlation function, slow and rapid responce
This concept give us an idea that the correlation function has strong relationship between spectrum (frequency contents). For stationary process, there is an important relation known as Wiener-Khinchin relation.
Wiener-Khinchin relation
Here, autospectral density function and cross spectral density function are follows (from above list).
Autospectral density function
Cross spectral density function
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