Fraction-of-time probability for time-series that exhibit cyclostationarity (Q811075)

A nonstochastic alternative to the stochastic process framework for conceptualizing, modeling and analyzing time-series encountered in communications, radar and telemetry systems is proposed. Wold's isomorphism between a single time-series and an ergodic stationary stochastic process is generalized to accommodate time-series with periodic structure and corresponding cycloergodic cyclostationary stochastic processes. This reveals the existence of a nonstochastic theory for single time-series with periodic structure that completely parallels the theory of cycloergodic cyclostationary stochastic processes.