离散周期集上的弱Gabor双框架

Weak Gabor bi-frames on discrete periodic sets

因其在数字信号处理的潜在应用,近年来,离散Gabor分析引起了众多学者的关注.本文研究整数集Z的离散周期子集S上的Gabor分析.众所周知,当S≠Z时, l^2(Z)的Gabor框架到l2(S)上的投影不可能穷尽l^2(S)的所有Gabor框架.本文引入了弱Gabor双框架(weak Gabor bi-frame,WGBF),其推广了Gabor双框架的概念,得到了l^2(S)上WGBF的Zak变换域刻画和时域刻画.所得结果即使S=Z时仍是新的,并给出了一些例子.

Due to its good potential for digital signal processing,discrete Gabor analysis has received broad interests in recent years.This paper addresses Gabor analysis on a general discrete periodic subset S of Z.It is well known that the projections of Gabor frames for l^2(Z)onto l^2(S)cannot cover all Gabor frames for l^2(S) if S ≠Z.In this paper,we introduce the notion of weak Gabor bi-frame (WGBF)which generalizes the one of Gabor bi-frame.We obtain a Zak transform domain characterization and a time domain characterization of WGBF in l^2(S).The obtained results are new even if S =Z.Some examples are provided.