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 model-observer pair and derives the dead-beat property in the case of noncoherent signals based on a modified signal model.