Non-Locality Analysis of Critical Sampling Gabor Expansion

薛健; 袁保宗

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Non-Locality Analysis of Critical Sampling Gabor Expansion

更新时间：2025-12-08

- Non-Locality Analysis of Critical Sampling Gabor Expansion
- Acta Electronica Sinica Issue 12, (1996)
- 作者机构：
  
  北京北方交通大学信息所
- 作者简介：
- 基金信息：
- DOI：
  CLC： TN911.1
- Published：1996
- 稿件说明：
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[1]薛健,袁保宗.临界抽样Gabor展开的非局部性分析[J].电子学报,1996(12):100-103.

薛健, 袁保宗. Non-Locality Analysis of Critical Sampling Gabor Expansion[J]. Acta Electronica Sinica, 1996, (12).
[1]薛健,袁保宗.临界抽样Gabor展开的非局部性分析[J].电子学报,1996(12):100-103. DOI：

薛健, 袁保宗. Non-Locality Analysis of Critical Sampling Gabor Expansion[J]. Acta Electronica Sinica, 1996, (12). DOI：

摘要

Ｇａｂｏｒ展开是一在时－频混合空间描述信号的非正交展开。由于展开的非正交性，使得展开系数的计算较为困难。现有的关于Ｇａｂｏｒ展开的文献大都集中在讨论Ｇａｂｏｒ展开的计算，而对临界抽样Ｇａｂｏｒ展开的非局部性问题没有给予足够的重视。本文将证明当临界抽样Ｇａｂｏｒ展开的窗函数为连续或对称函数时，Ｇａｂｏｒ展开不仅存在非局部性问题，而且收敛性也得不到保证。同时我们还将给出临界抽样Ｇａｂｏｒ展开非局部性的例子。

Abstract

Gabor expansion

which represents signal in time-frequency space

is a non-or-thogonal expansion. The nonorthogonality of the expansion causes some difficulties in the calculation of the expansion. There exist many papers concentrating on the computation aspect of the expansion. It seem that the non-locality of critical sampling Gabor expansion has not been received enough attention yet. In this paper we will show that when the window function of critical sampling Gabor expansion is continuous or symmetric

the critical sampling Gabor expansion not only can’t always truly reflect the local properties of signals

but exists convergence as well. Examples are also given.

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School of Electronics ＆ Inf，Xi’an Jiaotong University

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