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

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5.2 Proofs for Section 4.4 “The Bifrequency Cross-Periodogram”

In this section, proofs of lemmas and theorems presented in Section 4.4 on bias and covariance of the bifrequency cross-periodogram are reported.

The following Lemma 5.2.1 allows, in the proofs of the subsequent lemmas and theorems, the free interchange of the order of limit and sum operations.

Lemma 5.2.1 (Napolitano 2003, Lemma A.1).

a. Under Assumption 4.4.3a (series regularity), the function series img is uniformly convergent. Moreover, for any function sequence img of uniformly bounded functions img the function series img is uniformly convergent.
b. Under Assumption 4.4.3b (series regularity), the function series

img

is uniformly convergent. Moreover, for any function sequence img of uniformly bounded functions, the function series

img

is ...

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