Generalizations of Cyclostationary Signal Processing: Spectral Analysis and Applications

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

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be the discrete-time processes obtained by uniformly sampling with period T_s = 1/f_s 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 y_d(n) and x_d(n) at cycle frequency is defined as

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