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Generalizations of Cyclostationary Signal Processing: Spectral Analysis and Applications by Antonio Napolitano

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2.5 Sampling of GACS Processes

In this section, the problem of uniformly sampling GACS processes is addressed. Aliasing formulas for second-order cyclic cross-moments are derived. It is shown that uniformly sampling a continuous-time GACS process leads to a discrete-time ACS process. Moreover, it is shown that continuous-time GACS processes do not have a discrete-time counterpart, that is, discrete-time GACS processes do not exist.

Let

(2.172) equation

be the discrete-time processes obtained by uniformly sampling with period Ts = 1/fs the continuous-time (jointly) GACS processes x(t) and y(t).

Definition 2.5.1 The cyclic cross-correlation function of the discrete-time sequences yd(n) and xd(n) at cycle frequency img is defined as

(2.173) equation

img

The magnitude and phase of img are the amplitude and phase of the finite-strength additive complex sinewave component at frequency img contained in the discrete-time cross-correlation ...

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