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On the Equivalence of the Operator and Kernel Methods for Joint Distributions of Arbitrary Variables

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Title: On the Equivalence of the Operator and Kernel Methods for Joint Distributions of Arbitrary Variables
Author: Sayeed, Akbar M.
Type: Conference Paper
Keywords: Temporary
Citation: A. M. Sayeed,"On the Equivalence of the Operator and Kernel Methods for Joint Distributions of Arbitrary Variables," in IEEE Transactions on Signal Processing,
Abstract: Generalizing the concept of time-frequency representations, Cohen has recently proposed a general method, based on operator correspondence rules, for generating joint distributions of arbitrary variables. As an alternative to considering all such rules, which is a practical impossibility in general, Cohen has proposed the kernel method in which different distributions are generated from a fixed rule via an arbitrary kernel. In this paper, we derive a simple but rather stringent necessary condition, on the underlying operators, for the kernel method (with the kernel functionally independent of the variables) to generate all bilinear distributions. Of the specific pairs of variables that have been studied, essentially only time and frequency satisfy the condition; in particular, the important variables of time and scale do not. The results warrant further study for a systematic characterization of bilinear distributions in Cohen's method.
Date Published: 1997-04-20

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  • ECE Publications [1046 items]
    Publications by Rice University Electrical and Computer Engineering faculty and graduate students