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

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3.10 Proofs for Section 2.6.2 “Asymptotic Results as N→ ∞”

Lemma 3.10.1 Let img be given by (2.184) with a(t) as in Assumption 2.4.5. It results that

(3.155) equation

Proof: Since a(t) has finite support [− 1/2, 1/2), to prove (3.155) is equivalent to prove that

(3.156) equation

Let us consider first the case img.

Since a(t) is Riemann integrable (Assumption 2.4.5), we have

(3.157) equation

Let us consider now the case img, ν > 0.

For every img the function img is Riemann integrable and we have

(3.158) equation

that is, ∀img1 > 0 such that for ...

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