DocumentCode :
1385629
Title :
On the equivalence of the operator and kernel methods for joint distributions of arbitrary variables
Author :
Sayeed, Akbar M.
Author_Institution :
Coordinated Sci. Lab., Illinois Univ., Urbana, IL, USA
Volume :
45
Issue :
4
fYear :
1997
fDate :
4/1/1997 12:00:00 AM
Firstpage :
1067
Lastpage :
1070
Abstract :
Generalizing the concept of time-frequency representations, Cohen (see Englewood Cliffs, NJ: Prentice-Hall, 1995) has proposed a 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. 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
Keywords :
bilinear systems; signal representation; statistical analysis; time-frequency analysis; Cohen´s method; arbitrary variables; bilinear distributions; equivalence; fixed rule; joint distributions; kernel method; necessary condition; operator correspondence rules; operator method; time-frequency representations; Acoustic signal detection; Detectors; Fast Fourier transforms; Gaussian distribution; Kernel; Matched filters; Signal detection; Signal processing; Speech processing; Time frequency analysis;
fLanguage :
English
Journal_Title :
Signal Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1053-587X
Type :
jour
DOI :
10.1109/78.564195
Filename :
564195
Link To Document :
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