On a novel critically-sampled discrete-time real Gabor transform

Abstract

In the generalized discrete-time Gabor transform (DTGT), localization of both the dual sequences is not possible at critical sampling. A novel DTGT is defined for real signals and real symmetric synthesis and analysis sequences. It allows small length dual sequences even at critical sampling. The novel DTGT is similar to a modulated lapped transform or a perfect reconstruction cosine-modulated filter bank structure. The novel DTGT is derived and a method to compute the analysis (synthesis) sequence given the synthesis (analysis) sequence is presented. We computed the dual sequences for various popular windows to demonstrate that they have finite lengths, or can be well-approximated by sequences of finite length. We validated the dual sequences by reconstructing a sequence of normally distributed random numbers and demonstrating low mean-square-error in reconstruction. Based on the results, we make some recommendations on the choice of analysis window or filter.