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

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4.2 Characterization of SC Stochastic Processes

In this section, spectrally correlated stochastic processes are introduced (Definitions 4.2.4–4.2.8) and characterized (Theorems 4.2.7 and 4.2.9). Moreover, examples of applications where such processes occur are presented.

4.2.1 Second-Order Characterization

Definition 4.2.1 A covariance function img is said to be harmonizable if there exists a spectral covariance function img of bounded variation on img

(4.1) equation

such that

(4.2) equation

where the integral is a Fourier-Stieltjes transform (Loève 1963).

img

Definition 4.2.2 A second-order stochastic process img is said to be (strongly) harmonizable if there exists a second-order stochastic process χ(f) with increments dχ(f) having covariance function with of bounded variation on such that

(4.3)

with probability one ...

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