A Generalization of Wiener Optimum Filtering and Prediction

Citation

Beutler, Fredrick Joseph (1957) A Generalization of Wiener Optimum Filtering and Prediction. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/D8FV-4255. https://resolver.caltech.edu/CaltechETD:etd-07082004-135353

Abstract

This work generalizes the Wiener-Kolmogorov theory of optimum linear filtering and prediction of stationary random inputs. It is assumed that signal and noise have passed through a random device before being available for filtering and prediction. A random device is a unit whose behavior depends on an unknown parameter for which an a priori probability distribution is given. Use of representation theorems and a Hilbert space structure make it possible to present the mathematical theory without the ambiguities encountered in engineering derivations. This approach also leads to a proof of the essential identity between the operator solution and a realizable lumped parameter filter. A number of engineering applications are cited. A few of these are worked out in some detail to illustrate the optimization procedure.

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