**ABSTRACT**
### Approximation of dual Gabor frames, window decay, and
wireless communications

#### Thomas Strohmer

We consider three problems for Gabor frames that have recently
received much attention. The first problem concerns the approximation
of dual Gabor frames in $L_2(R)$ 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 $g$ and its dual $\gamma$. Based on results on
commutative Banach algebras and Laurent operators we derive a general
condition under which the dual $\gamma$ inherits the decay properties
of $g$.
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.

Download the paper as a GNU-ziped postscript file (123625 bytes).