Advances in Signal Processing by Unknown

Author:Unknown
Language: eng
Format: epub
ISBN: 9783030403126
Publisher: Springer International Publishing

(6.11)

that is similar to the one applied to ACF in the time domain for Eq. 6.2, SCD can be rewritten in the functional form depending on two frequencies f1 and f2:

(6.12)

This form reveals the meaning of spectral correlation as the probabilistic expectation:

(6.13)

where X(f) is a random complex measure [10] that can be considered as the spectral density of the random process x(t) via Crámer’s representation [11]:

(6.14)

Then, the one-to-one relationship between ACF Rx(t1, t2) (Eq. 6.1) and the density Sx(f1, f2) is given by means of two-dimensional Fourier transform:

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