## Title:
Operator Identification and Sampling
## Abstract:
Time--invariant communication channels are usually
modelled as convolution with a fixed impulse--response function.
As the name suggests, such a channel is completely determined by
its action on a unit impulse. Time--varying communication channels
are modelled as pseudodifferential operators or superpositions of
time and frequency shifts. The function or distribution weighting
those time and frequency shifts is referred to as the spreading
function of the operator.
In this talk we consider the question of whether such operators are identifiable, that is, whether they are completely determined by their action on a single function or distribution. It turns out that the answer is dependent on the size of the support of the spreading function, and that when the operators are identifiable, the input can be chosen as a distribution supported on an appropriately chosen grid. These results provide a sampling theory for operators that can be thought of as a generalization of the classical sampling formula for bandlimited functions. This is joint work with G. Pfander of Jacobs University, Bremen. |