Generalizations of Cyclostationary Signal Processing: Spectral Analysis and Applications

4.9 Sampling of SC Processes

In this section, a sampling theorem for SC processes is stated to link the Loève bifrequency spectrum of the sampled discrete-time process with that of the continuous-time process. An analogous result is established in terms of densities. Furthermore, in the case of strictly band-limited continuous-time SC processes, sufficient conditions on the sampling frequency to avoid aliasing effects are provided (Napolitano 2011).

For a WSS process, two equivalent conditions describe the absence of aliasing in the Loève bifrequency spectrum of the sampled signal. The former is the non overlap of replicas in the power spectrum of the sampled signal (Lloyd 1959). The latter is that the mappings ν_i = f_i/f_s, i = 1, 2, between frequencies f_i [− f_s/2, f_s/2] of the density of Loève bifrequency spectrum of the continuous-time process and frequencies ν_i of the density of Loève bifrequency spectrum of the discrete-time process hold ∀ν₁ [− 1/2, 1/2], on the main diagonal ν₂ = ν₁. In fact, on the main diagonal the density of Loève bifrequency spectrum is coincident with the power spectrum. It is well known that both conditions are satisfied provided that the sampling frequency is equal to or greater than twice the process bandwidth. In this section it is shown that for SC ...