Phase space localization operators: asymptotics of singular values

The Weyl correspondence is a convenient and practical way to define a broad class of time-frequency localization operators. Given a region /spl Omega/ in the time-frequency (or phase) plane R/sup 2/, and a distribution P(/spl xi/, x) in the Cohen's (1989) class, the Weyl correspondence defines an operator L/sub /spl Omega///sup P/ on L/sup 2/(R) which essentially localizes the signal in the region /spl Omega/ according to the distribution P. Different choices of P allow different interpretations of phase-space localization. Empirically, such localization operators have the following singular value structure: the singular values range between 0 and 1, and when arranged in decreasing order, a finite number of them are close to 1, while the rest fall toward 0 asymptotically. We present a result on the asymptotic structure of the singular values of such phase-space localization operators.<
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