Oversampled Gabor expansion into one-side exponential functions

In this paper we consider the Gabor representation which uses a one-sided exponential window for detection and analysis of transient signals. Earlier results on the critically sampled case are extended to the more practically useful oversampled case. For oversampling by an integer factor we derive an explicit analytical expression for the dual window (dual frame) function required for computing the Gabor representation. Based on this expression we develop an efficient procedure for computing the Gabor coefficients. Finally, we demonstrate the performance of the method by numerical examples