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In Chapter 1, background material that will be referenced in the subsequent chapters is reviewed. The statistical characterization of persistent (finite-power) nonstationary stochastic processes is presented. Both strict-sense and wide-sense characterization are considered. Harmonizability, and time-frequency representations are treated. A survey of definition and properties of almost-periodic functions is provided. A brief review on almost-cyclostationary processes is also presented. The chapter ends with some properties of cumulants.