Approximate series representations of second-order stochastic processes: applications to signal detection and estimation

Two distinct approximate series representations are obtained for the entire class of measurable, second-order stochastic processes defined on any interval of the real line. They include as particular cases all earlier approximate representations based on the Rayleigh-Ritz method. It is also shown that each of them converges with a different type of convergence. Finally, two applications in statistical communication theory are presented.

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