Proportional Nonuniform Multi-Gabor Expansions

Abstract

A nonuniform multi-Gabor expansion (MGE) scheme is studied under proportional time and frequency (TF) shifts among different window indices. In particular, TF parameters for each are different, but proportional and relevant to windows' TF patterns. The generation of synthesis waveforms for nonuniform MGE is generally difficult. We show constructively that there is a set of basic synthesis MGE waveforms at each window index under proportional parameter settings. Nonuniform MGE adapts to signal frequency dynamics effectively, and eliminates unnecessary overlapping redundancies of a uniform MGE. Examples of the evaluation of synthesis waveforms are provided. Efficiency comparison of TF analysis using nonuniform and uniform MGEs is also discussed.