Generalizations of Cyclostationary Signal Processing: Spectral Analysis and Applications

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

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

(3.155)

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

(3.156)

Let us consider first the case .

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

(3.157)

Let us consider now the case , ν > 0.

For every the function is Riemann integrable and we have

(3.158)

that is, ∀₁ > 0 such that for ...