Operator Identification and Feichtinger’s Algebra

The goal in channel operator identification is to obtain complete knowledge of an operator modelling a communication channel by observing the image of a finite number of input signals. It was proved by Kozek and Pfander that identifiability can be related to the spreading support of the operator modelling the channel, as was conjectured by Kailath in 1963. The extended result proved in this paper shows that the collection of identifiable operators can be chosen to be a closed subspace of a Banach space, which includes as examples the identity operator, small perturbations of the identity, and convolution operators with compactly supported kernels as examples of identifiable channels. These examples exceed the scope of the results from Kozek and Pfander. The Feichtinger algebra and its dual arise naturally in this extension further illustrating the enduring usefulness of Feichtinger’s work.