Local sampling set conditions in weighted shift-invariant signal spaces |
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Authors: | Jun Xian |
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Institution: | 1. Department of Mathematics , Sun Yat-sen (Zhongshan) University , Guangzhou 510275 , China xianjun@mail.sysu.edu.cn |
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Abstract: | How to represent a continuous signal in terms of a discrete sequence is a fundamental problem in sampling theory. Most of the known results concern global sampling in shift-invariant signal spaces. But in fact, the local reconstruction from local samples is one of the most desirable properties for many applications in signal processing, e.g. for implementing real-time reconstruction numerically. However, the local reconstruction problem has not been given much attention. In this article, we find conditions on a finite sampling set X such that at least in principle a continuous signal on a finite interval is uniquely and stably determined by their sampling value on the finite sampling set X in shift-invariant signal spaces. |
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Keywords: | local sampling sampling set shift-invariant space |
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