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Advances in Mathematical Physics
Volume 2014 (2014), Article ID 561434, 7 pages
http://dx.doi.org/10.1155/2014/561434
Research Article

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

1School of Electronic Science and Engineering, National University of Defense Technology, Changsha 410073, China
2Department of Mathematics, University of Salerno, Via Giovanni Paolo II, Fisciano, 84084 Salerno, Italy
3School of Mechanics & Civil Engineering, China University of Mining & Technology, Xuzhou 221116, China

Received 3 May 2014; Revised 13 May 2014; Accepted 13 May 2014; Published 10 June 2014

Academic Editor: Xiao-Jun Yang

Copyright © 2014 Zhi-Yong Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.