Title:Timefrequency localization of multiband signals
Abstract:
The classical "Bell Labs" theory considers
spaces of signals that are "essentially" localized
to a bounded interval in time and a bounded interval
in frequency. Some modern communications applications might
benefit from an extension of this theory to cases in which the frequency
localization support is a finite union of intervals (multiband).
Extensions of the Bell Labs theory would entail estimates
of the decay of eigenvalues of compositions of time and frequency
localization operators and descriptions of the eigenvectors
that are "most localized" in time and
frequency. We will pose some of these questions in precise terms
and offer some preliminary results relating decay of eigenvalues
with the distribution of the frequency support. Numerical approximations
of the projections expressed in terms of practical sampling methods
and some connections with compressive sampling will
also be considered.
