Two New Convolutions for the Fractional Fourier Transform

http://repository.vnu.edu.vn/handle/VNU_123/28884

In this paper we introduce two novel convolutions for the fractional Fourier transforms, and prove natural algebraic properties of the corresponding multiplications such as commutativity, associativity and distributivity, which may be useful in signal processing and other types of applications. 

We analyze a consequent comparison with other known convolutions, and establish necessary and sufficient conditions for the solv-ability of associated convolution equations of both the first and second kind inL 1 ðRÞand L 2 ðRÞspaces.

An example satisfying the sufficient and necessary condition for the solv-ability of the equations is given at the end of the paper.

Title:	Two New Convolutions for the Fractional Fourier Transform
Authors:	P. K. Anh L. P. Castro P. T. Thao N. M. Tuan
Keywords:	Convolution Convolution theorem Fractional Fourier transform Convolution equation Filtering
Issue Date:	2017
Publisher:	SPRINGER, 233 SPRING ST, NEW YORK, NY 10013 USA
Citation:	ISIKNOWLEDGE
Abstract:	In this paper we introduce two novel convolutions for the fractional Fourier transforms, and prove natural algebraic properties of the corresponding multiplications such as commutativity, associativity and distributivity, which may be useful in signal processing and other types of applications. We analyze a consequent comparison with other known convolutions, and establish necessary and sufficient conditions for the solv-ability of associated convolution equations of both the first and second kind inL 1 ðRÞand L 2 ðRÞspaces. An example satisfying the sufficient and necessary condition for the solv-ability of the equations is given at the end of the paper.
Description:	TNS07030 ; WIRELESS PERSONAL COMMUNICATIONS Volume: 92 Issue: 2 Pages: 623-637 Published: JAN 2017
URI:	http://repository.vnu.edu.vn/handle/VNU_123/28884 http://link.springer.com/article/10.1007/s11277-016-3567-3
ISSN:	0929-6212 1572-834X
Appears in Collections:	Bài báo của ĐHQGHN trong Web of Science