NDLI: Discrete Fractional Fourier Transform Based on New Nearly Tridiagonal Commuting Matrices

Content Provider	IEEE Xplore Digital Library
Author	Soo-Chang Pei Wen-Liang Hsue Jian-Jiun Ding
Copyright Year	1991
Abstract	Based on discrete Hermite-Gaussian-like functions, a discrete fractional Fourier transform (DFRFT), which provides sample approximations of the continuous fractional Fourier transform, was defined and investigated recently. In this paper, we propose a new nearly tridiagonal matrix, which commutes with the discrete Fourier transform (DFT) matrix. The eigenvectors of the new nearly tridiagonal matrix are shown to be DFT eigenvectors, which are more similar to the continuous Hermite-Gaussian functions than those developed before. Rigorous discussions on the relations between the eigendecomposition of the newly proposed nearly tridiagonal matrix and the DFT matrix are described. Furthermore, by appropriately combining two linearly independent matrices that both commute with the DFT matrix, we develop a method to obtain DFT eigenvectors even more similar to the continuous Hermite-Gaussian functions (HGFs). Then, new versions of DFRFT produce their transform outputs closer to the samples of the continuous fractional Fourier transform, and their applications are described. Related computer experiments are performed to illustrate the validity of the works in this paper
Sponsorship	IEEE Signal Processing Society
Starting Page	3815
Ending Page	3828
Page Count	14
File Size	899695
File Format	PDF
ISSN	1053587X
Volume Number	54
Issue Number	10
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-10-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Fourier transforms Discrete Fourier transforms Application software Optical signal processing Signal analysis Quantum mechanics Time frequency analysis Optical filters Filtering Approximation error Hermite–Gaussian functions Discrete fractional Fourier transform (DFRFT) discrete Fourier transform
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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