Generalizations of Cyclostationary Signal Processing: Spectral Analysis and Applications

5.10 Proofs for Section 4.9 “Sampling of SC Processes”

5.10.1 Proof of Theorem 4.9.2 Strictly Band-Limited Spectrally Correlated Processes

The strictly band-limitedness condition (4.204) considered in the frequency domain implies that

(5.179)

where . In the case of jointly SC processes, replacing (4.209a) into (5.179) leads to

(5.180)

Let

(5.181)

(5.182)

Without lack of generality, the functions and in (4.209a) and (4.209b) can be chosen such that both and are at most countable (Definition 4.2.4 and Theorem 4.2.7). Let us assume that the number of possible accumulation points (cluster points) ...