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

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2.7 Numerical Results

In this section, simulation experiments are carried out, aimed at corroborating the theoretical results of the previous sections.

2.7.1 Aliasing in Cycle-Frequency Domain

In the simulation experiments, a GACS signal is obtained as the output of the Doppler channel existing between a transmitter and a receiver with constant relative radial acceleration, when the input signal is a cyclostationary PAM signal (Section 2.2.6.1). In this case, an analytical condition on the sampling frequency can be deduced, which limits aliasing. Starting from (2.179a) specialized for xy and ACS signals, it follows that aliasing in the cycle-frequency domain can be avoided, provided that fs ≥ 4B, where B is the monolateral bandwidth of x(t) (Theorem 1.3.7), (Izzo and Napolitano 1996). Since 2B is the maximum allowable cycle frequency for an ACS signal with bandwidth B, condition fs ≥ 4B prevents replicas in (2.179a) with p ≠ 0 from contributing to the discrete-time cyclic autocorrelation function in the “principal domain” img. If x(t) is not strictly bandlimited, with approximate monolateral bandwidth B, then 2B is the maximum cycle frequency at which x(t) exhibits a significant degree of cyclostationarity. For the chirp-modulated signal y(t) in (2.99) with x(t) ACS, the effect of the chirp modulation is to rotate by an angle θ, where tan θ = γ, the support lines of the cyclic autocorrelation ...

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