220 research outputs found
Approximation of dual Gabor frames, window decay, and wireless communications
We consider three problems for Gabor frames that have recently received much
attention. The first problem concerns the approximation of dual Gabor frames in
by finite-dimensional methods. Utilizing Wexler-Raz type duality
relations we derive a method to approximate the dual Gabor frame, that is much
simpler than previously proposed techniques. Furthermore it enables us to give
estimates for the approximation rate when the dimension of the finite model
approaches infinity. The second problem concerns the relation between the decay
of the window function and its dual . Based on results on
commutative Banach algebras and Laurent operators we derive a general condition
under which the dual inherits the decay properties of . The third
problem concerns the design of pulse shapes for orthogonal frequency division
multiplex (OFDM) systems for time- and frequency dispersive channels. In
particular, we provide a theoretical foundation for a recently proposed
algorithm to construct orthogonal transmission functions that are well
localized in the time-frequency plane
Groups with frames of translates
Let be a locally compact group with left regular representation
We say that admits a frame of translates if there exist a
countable set and such that
is a frame for The present
work aims to characterize locally compact groups having frames of translates,
and to this end, we derive necessary and/or sufficient conditions for the
existence of such frames. Additionally, we exhibit surprisingly large classes
of Lie groups admitting frames of translates
Frame Theory for Signal Processing in Psychoacoustics
This review chapter aims to strengthen the link between frame theory and
signal processing tasks in psychoacoustics. On the one side, the basic concepts
of frame theory are presented and some proofs are provided to explain those
concepts in some detail. The goal is to reveal to hearing scientists how this
mathematical theory could be relevant for their research. In particular, we
focus on frame theory in a filter bank approach, which is probably the most
relevant view-point for audio signal processing. On the other side, basic
psychoacoustic concepts are presented to stimulate mathematicians to apply
their knowledge in this field
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