Gabor systems on discrete periodic sets
Gabor systems on discrete periodic sets
复制标题
离散周期集上的 Gabor 系统
DOI：
10.1007/s11425-008-0177-x
复制
发表时间：
2009-08-01
期刊：
影响因子：
--
通讯作者：
Lian QiaoFang
中科院分区：
文献类型：
--
作者：
Li YunZhang;Lian QiaoFang
Due to its good potential for digital signal processing, discrete Gabor analysis has interested some mathematicians. This paper addresses Gabor systems on discrete periodic sets, which can model signals to appear periodically but intermittently. Complete Gabor systems and Gabor frames on discrete periodic sets are characterized; a sufficient and necessary condition on what periodic sets admit complete Gabor systems is obtained; this condition is also proved to be sufficient and necessary for the existence of sets E such that the Gabor systems generated by chi (E) are tight frames on these periodic sets; our proof is constructive, and all tight frames of the above form with a special frame bound can be obtained by our method; periodic sets admitting Gabor Riesz bases are characterized; some examples are also provided to illustrate the general theory.
