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Proceedings Paper

Relationship between fractional calculus and fractional Fourier transform
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Paper Abstract

The fractional calculus (FC) deals with integrals and derivatives of arbitrary (i.e., non-integer) order, and shares its origins with classical integral and differential calculus. The fractional Fourier transform (FRFT), which has been found having many applications in optics and other areas, is a generalization of the usual Fourier transform. The FC and the FRFT are two of the most interesting and useful fractional areas. In recent years, it appears many papers on the FC and FRFT, however, few of them discuss the connection of the two fractional areas. We study their relationship. The relational expression between them is deduced. The expectation of interdisciplinary cross fertilization is our motivation. For example, we can use the properties of the FC (non-locality, etc.) to solve the problem which is difficult to be solved by the FRFT in optical engineering; we can also through the physical meaning of the FRFT optical implementation to explain the physical meaning of the FC. The FC and FRFT approaches can be transposed each other in the two fractional areas. It makes that the success of the fractional methodology is unquestionable with a lot of applications, namely in nonlinear and complex system dynamics and image processing.

Paper Details

Date Published: 2 September 2015
PDF: 8 pages
Proc. SPIE 9596, Signal and Data Processing of Small Targets 2015, 95960A (2 September 2015); doi: 10.1117/12.2187649
Show Author Affiliations
Yanshan Zhang, Beijing Institute of Technology (China)
Feng Zhang, Beijing Institute of Technology (China)
Mingfeng Lu, Beijing Institute of Technology (China)

Published in SPIE Proceedings Vol. 9596:
Signal and Data Processing of Small Targets 2015
Oliver E. Drummond; Richard D. Teichgraeber, Editor(s)

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