Probabilities, signals, and noise

Probabilistic techniques are developed to model the behavior of signals and associated noise during signal propagation through various media. The material is presented in textbook form, with exercises provided. Probability spaces are defined for random signals, along with a review of the underlying mathematical principles. Random vectors and random variables are explored in terms of their general properties and techniques for repartitioning them. Deterministic signals are defined, and attention is devoted to complex spectra, linear filtering, and deterministic signal sampling. Consideration is directed toward random signals, their stationarity, and to random signals with finite average power. Weakly stationary random signals are analyzed, together with elements of a theory of measurement that includes measureable spaces, functions, and positive measurements.