Generalizations of Cyclostationary Signal Processing: Spectral Analysis and Applications

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

(4.1)

such that

(4.2)

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

Definition 4.2.2 A second-order stochastic process 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 ...