Abstract
Wide-sense stationary stochastic processes are of interest in signal analysis and processing, as well as in physics. Their study rests on Bochner’s representation of characteristic functions, which immediately leads to the fundamental notion of power spectral measure, and on the Doob–Wiener integral that permits a mathematical definition of white noise as well as the obtention of a spectral decomposition of the trajectories of such stochastic processes, the Cram´er–Khinchin decomposition, a fundamental result with importance consequences in signal processing.
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