Super Oblique Gabor Duals of Super Gabor Frames on Discrete Periodic Sets

Abstract

The notion of superframe in general Hilbert spaces was introduced in the context of multiplexing, which has been widely used in mobile communication network, satellite communication network and computer area network. The notion of oblique dual frame is a generalization of conventional dual frame. It has provided us with a frame-like expansion. Using oblique dual frames one can extend frame expansions to include redundant expansions in which the analysis and synthesis frames lie in different spaces. Given positive integers L, M and N , an N -periodic set in , let (g, N , M ) be a frame for l 2 ( , L ), and let (h, N , M ) be a frame for (h, N , M ) (generated by (h, N , M )). This article addresses super Gabor duals of g in (h, N , M ). We obtain a necessary and sufficient condition on h admitting super oblique Gabor duals of g, and present a parametrization expression of all super oblique Gabor duals and all oblique canonical Gabor duals of g. We also characterize the uniqueness of super oblique Gabor dual and oblique canonical Gabor dual of g. Some examples are also provided.

Weak Gabor bi-frames on discrete periodic sets

“…因此, l 2 (Z) 的 Gabor 框 架到 l 2 (S) 上的投影不可能穷尽 l 2 (S) 的所有 Gabor 框架. 读者可以参见文献 [30,[48][49][50][51][52] 查阅关于 l 2 (S) 的 Gabor 框架的相关结果. 本文在下述基本假定下研究 l 2 (S) 的弱 Gabor 双框架: 基本假定:…”