Discrete multi-Gabor expansions

A discrete multi-Gabor expansion (DMGE) is developed to meet the requiremen ts of localized and refined time-frequency (TP) representation of signals. DMGE uses multiple windows and their translations and complex modulations a s synthesis (or analysis) waveforms. It includes and generalizes the metapl ectic (translation, modulation, and dilation) representations which are use ful in signal analysis. Uniform, nonuniform, and proportional time sampling schemes are analyzed. Fundamental features and importance of DMGE are disc ussed, We focus on the construction of DMGE and deriving fast algorithms fo r the computation of related multi-analysis sequences. With the matrix alge bra, the algorithms derived apply to both multi-Gabor expansions and uni-(w indow) Gabor expansions. Another useful feature of DMGE lies in the fact th at the multi-Gabor transform can be realized in a parallel FFT-based implem entation structure. Examples of DMGE and their applications to TF analysis are also discussed.