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	How slow is Shannon's reconstruction for bandlimited signals?
	Han, Guodong ; Li, Yingqi ; Jiang, Ming
	2015
关键词	Shannon&apos Arbitrarily slow convergence Almost arbitrarily slow convergence CONVERGENCE SEQUENCES SERIES s sampling theorem
英文摘要	Shannon's sampling theorem is fundamental in signal processing. It provides the exact reconstruction of a bandlimited signal from its samples at the Nyquist rate by the cardinal series. But this reconstruction formula is not applied widely in practice because of its slow convergence. It is of theoretical interests to find out how slow the convergence of this reconstruction could be. In this work, the convergence rate of Shannon's reconstruction is studied by the theory on the slow convergence of operator sequences. It is proved that the Shannon's reconstruction consists of a sequence of "arbitrarily slow" convergent operators. Specifically, for any positive sequence alpha(n) -> 0, there exists a bandlimited signal f such that the n-th truncation error of its cardinal series is larger than alpha(n) for all n, where the truncation errors are measured in L-P norms, for 1 < p < infinity. It is also shown that the acceleration techniques by over-sampling and convergence factor do not resolve the slowness too much, which only change the convergence rate from "arbitrarily slow" to "almost arbitrarily slow". (C) 2014 Elsevier B.V. All rights reserved.; Engineering, Electrical & Electronic; SCI(E); EI; 0; ARTICLE; gdhan.math@gmail.com; yingqi65@126.com; ming-jiang@ieee.org; 26-30; 111
语种	英语
出处	EI ; SCI
出版者	signal processing
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/206978]
专题	数学科学学院
推荐引用方式 GB/T 7714	Han, Guodong,Li, Yingqi,Jiang, Ming. How slow is Shannon&apos;s reconstruction for bandlimited signals?. 2015-01-01.

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