Generalized convolution theorem associated with fractional Fourier transform. Issue 13 (29th June 2012)

• Record Type: Journal Article
• Authors: Shi, Jun; Sha, Xuejun; Song, Xiaocheng; Zhang, Naitong
• Is Part Of: Wireless communications and mobile computing. Volume 14:Issue 13(2014)
• Page Start: 1340
• Page End: 1351
• Publication Date: 2012-06-29
• Subjects: Wireless communication systems -- Periodicals; Mobile communication systems -- Periodicals; 621.38205
• DOI: 10.1002/wcm.2254
• Languages: English
• ISSNs: 1530-8669

Abstract

<abstract abstract-type="main" id="wcm2254-abs-0001"> <title>ABSTRACT</title> <p id="wcm2254-para-0005">The fractional Fourier transform (FRFT)—a generalization of the well‐known Fourier transform (FT)—is a comparatively new and powerful mathematical tool for signal processing. Many results in Fourier analysis have currently been extended to the FRFT, including the ordinary convolution theorem. However, the extension of the ordinary convolution theorem associated with the FRFT has been developed differently and is still not having a widely accepted closed‐form expression. In this paper, a generalized convolution theorem for the FRFT is proposed, and the dual of it is also presented. The ordinary convolution theorem and some of its existing extensions related to the FRFT are shown to be special cases of the derived results. Moreover, some applications of the derived results are presented. Copyright © 2012 John Wiley &amp; Sons, Ltd.</p> </abstract>