GABOR SYSTEMS AND COMMUNICATION THEORY

Guido Janssen
Philips Research Laboratories Eindhoven

A Gabor system (g, a, b) for L^2(R) is characterized
by a finite-energy function g and two shift parameters a>0 and
b>0; it consists of all time-frequency translates g_{na, mb} of g
over the lattice {(na, mb)| integer n and m}. Gabor systems are
used in communication theory for the problems of
(i) robust representation of finite-energy signals as linear combi-
nations of the g_{na, mb},
(ii) reliable retrieval of multiple data streams from modulated
signals in which the data are carried by the g_{na, mb}.
In this presentation we focus on the remarkable duality between
these two problems, the main result being that problem (i) is solved
by the system (g, a, b) if and only if problem (ii) is solved by the
system (g, 1/b, 1/a).