Techniques for smoothing and splitting in the construction of tight frame gabor windows

Abstract

We consider Gabor systems with compactly supported windows and rational sampling rate. Two modification techniques for tight frame Gabor windows, splitting for shorter support and smoothing for better smoothness, are introduced. As an illustration of such techniques, we construct multiwindow tight frame Gabor windows with smaller support and C∞ continuity from certain tight frame Gabor windows. © 2013 World Scientific Publishing Company.