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

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    Author
    Sayeed, Akbar M.
    Date
    2004-01-09
    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 <i>all</i> 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.
    Description
    Conference Paper
    Citation
    A. M. Sayeed, "On the Equivalence of the Operator and Kernel Methods for Joint Distributions of Arbitrary Variables," 1997.
    Keyword
    Temporary; Time Frequency and Spectral Analysis; Temporary
    Type
    Conference paper
    Citable link to this page
    https://hdl.handle.net/1911/20333
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    • ECE Publications [1468]

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    Managed by the Digital Scholarship Services at Fondren Library, Rice University
    Physical Address: 6100 Main Street, Houston, Texas 77005
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    Site Map