Sayeed, Akbar M.2007-10-312007-10-311997-04-201997-04-20A. M. Sayeed, "On the Equivalence of the Operator and Kernel Methods for Joint Distributions of Arbitrary Variables," 1997.https://hdl.handle.net/1911/20333Conference PaperGeneralizing 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.engTemporaryTime Frequency and Spectral AnalysisConference paperTemporary