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

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dc.citation.bibtexNameinproceedingsen_US
dc.citation.conferenceNameIEEE Transactions on Signal Processingen_US
dc.contributor.authorSayeed, Akbar M.en_US
dc.contributor.orgDigital Signal Processing (http://dsp.rice.edu/)en_US
dc.date.accessioned2007-10-31T01:04:20Z
dc.date.available2007-10-31T01:04:20Z
dc.date.issued1997-04-20
dc.date.modified2004-01-22en_US
dc.date.note2004-01-09en_US
dc.date.submitted1997-04-20en_US
dc.descriptionConference Paperen_US
dc.description.abstractGeneralizing 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.en_US
dc.identifier.citationA. M. Sayeed, "On the Equivalence of the Operator and Kernel Methods for Joint Distributions of Arbitrary Variables," 1997.
dc.identifier.urihttps://hdl.handle.net/1911/20333
dc.language.isoeng
dc.subjectTemporary*
dc.subject.keywordTemporaryen_US
dc.subject.otherTime Frequency and Spectral Analysisen_US
dc.titleOn the Equivalence of the Operator and Kernel Methods for Joint Distributions of Arbitrary Variablesen_US
dc.typeConference paper
dc.type.dcmiText
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