Convolution, filtering, linear systems, the Wiener-Khinchin theorem: generalizations

Leon Cohen

doi:10.1117/12.130944

30 November 1992 Convolution, filtering, linear systems, the Wiener-Khinchin theorem: generalizations

Leon Cohen

Proceedings Volume 1770, Advanced Signal Processing Algorithms, Architectures, and Implementations III; (1992) https://doi.org/10.1117/12.130944
Event: San Diego '92, 1992, San Diego, CA, United States

Abstract

A simple formulation is given for generating convolution theorems in any representation. Using this method we obtain the convolution theorem for the scale representation. We generalize the concept of invariance to any basis set and devise a method for handling linear invariant systems for arbitrary quantities. The Wiener-Khinchin theorem is generalized to arbitrary power energy densities. Also, we show how standard probability theory can be formulated in terms of signals.

Citation Download Citation

Leon Cohen "Convolution, filtering, linear systems, the Wiener-Khinchin theorem: generalizations", Proc. SPIE 1770, Advanced Signal Processing Algorithms, Architectures, and Implementations III, (30 November 1992); https://doi.org/10.1117/12.130944

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