Discrete Subspace Multiwindow Gabor Frames and Their Duals

Abstract

This paper addresses discrete subspace multiwindow Gabor analysis. Such a scenario can model many practical signals and has potential applications in signal processing. In this paper, using a suitable Zak transform matrix we characterize discrete subspace mixed multi-window Gabor frames (Riesz bases and orthonormal bases) and their duals with Gabor structure. From this characterization, we can easily obtain frames by designing Zak transform matrices. In particular, for usual multi-window Gabor frames (i.e., all windows have the same time-frequency shifts), we characterize the uniqueness of Gabor dual of type I (type II) and also give a class of examples of Gabor frames and an explicit expression of their Gabor duals of type I (type II).