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

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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) equation

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

(5.180) equation

Let

(5.181) equation

(5.182) equation

Without lack of generality, the functions img and img in (4.209a) and (4.209b) can be chosen such that both img and img 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) ...

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