Signal Processing for Nondifferentiable Data Defined on Cantor Sets: A Local Fractional Fourier Series Approach

Signal Processing for Nondifferentiable Data Defined on Cantor Sets: A Local Fractional Fourier Series Approach

From the signal processing point of view, the nondifferentiable data defined on the Cantor sets are investigated in this paper. The local fractional Fourier series is used to process the signals, which are the local fractional continuous functions. Our results can be observed as significant extensio...

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Main Authors: Zhi-Yong Chen, Carlo Cattani, Wei-Ping Zhong
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2014/561434
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spelling doaj-3c37c728760845f686caa739a3af57022021-07-02T07:02:44ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392014-01-01201410.1155/2014/561434561434Signal Processing for Nondifferentiable Data Defined on Cantor Sets: A Local Fractional Fourier Series ApproachZhi-Yong Chen0Carlo Cattani1Wei-Ping Zhong2School of Electronic Science and Engineering, National University of Defense Technology, Changsha 410073, ChinaDepartment of Mathematics, University of Salerno, Via Giovanni Paolo II, Fisciano, 84084 Salerno, ItalySchool of Mechanics & Civil Engineering, China University of Mining & Technology, Xuzhou 221116, ChinaFrom the signal processing point of view, the nondifferentiable data defined on the Cantor sets are investigated in this paper. The local fractional Fourier series is used to process the signals, which are the local fractional continuous functions. Our results can be observed as significant extensions of the previously known results for the Fourier series in the framework of the local fractional calculus. Some examples are given to illustrate the efficiency and implementation of the present method.http://dx.doi.org/10.1155/2014/561434
collection DOAJ
language English
format Article
sources DOAJ
author Zhi-Yong Chen
Carlo Cattani
Wei-Ping Zhong
spellingShingle Zhi-Yong Chen
Carlo Cattani
Wei-Ping Zhong
Signal Processing for Nondifferentiable Data Defined on Cantor Sets: A Local Fractional Fourier Series Approach
Advances in Mathematical Physics
author_facet Zhi-Yong Chen
Carlo Cattani
Wei-Ping Zhong
author_sort Zhi-Yong Chen
title Signal Processing for Nondifferentiable Data Defined on Cantor Sets: A Local Fractional Fourier Series Approach
title_short Signal Processing for Nondifferentiable Data Defined on Cantor Sets: A Local Fractional Fourier Series Approach
title_full Signal Processing for Nondifferentiable Data Defined on Cantor Sets: A Local Fractional Fourier Series Approach
title_fullStr Signal Processing for Nondifferentiable Data Defined on Cantor Sets: A Local Fractional Fourier Series Approach
title_full_unstemmed Signal Processing for Nondifferentiable Data Defined on Cantor Sets: A Local Fractional Fourier Series Approach
title_sort signal processing for nondifferentiable data defined on cantor sets: a local fractional fourier series approach
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9120
1687-9139
publishDate 2014-01-01
description From the signal processing point of view, the nondifferentiable data defined on the Cantor sets are investigated in this paper. The local fractional Fourier series is used to process the signals, which are the local fractional continuous functions. Our results can be observed as significant extensions of the previously known results for the Fourier series in the framework of the local fractional calculus. Some examples are given to illustrate the efficiency and implementation of the present method.
url http://dx.doi.org/10.1155/2014/561434
work_keys_str_mv AT zhiyongchen signalprocessingfornondifferentiabledatadefinedoncantorsetsalocalfractionalfourierseriesapproach
AT carlocattani signalprocessingfornondifferentiabledatadefinedoncantorsetsalocalfractionalfourierseriesapproach
AT weipingzhong signalprocessingfornondifferentiabledatadefinedoncantorsetsalocalfractionalfourierseriesapproach
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