Behavior of Observer Performing Discrete Gabor Transform

Abstract

The theory of discrete Gabor transforms provides a constructive and interpretable way of creating biorthogonal transforms. These transforms can achieve a non-uniform frequency resolution and they can be implemented recursively by observers based on Hostetter's approach. The dead-beat property of the observers were previously shown for coherent signals with the help of an adequately chosen conceptual signal model. This paper investigates the properties of the signal modelobserver pair and derives the dead-beat property in the case of noncoherent signals based on a modified signal model.