A new discrete fractional Fourier transform based on constrained eigendecomposition of DFT matrix by Lagrange multiplier method

Author

Pei, Soo-Chang ; Tseng, Chien-Cheng ; Yeh, Min-Hung

Author_Institution

Dept. of Electr. Eng., Nat. Taiwan Univ., Taipei, Taiwan

Volume

46

Issue

9

fYear

1999

fDate

9/1/1999 12:00:00 AM

Firstpage

1240

Lastpage

1245

Abstract

This paper is concerned with the definition of the discrete fractional Fourier transform (DFRFT). First, an eigendecomposition of the discrete Fourier transform (DFT) matrix is derived by sampling the Hermite Gauss functions, which are eigenfunctions of the continuous Fourier transform and by performing a novel error-removal procedure. Then, the result of the eigendecomposition of the DFT matrix is used to define a new DFRFT. Finally, several numerical examples are illustrated to demonstrate that the proposed DFRFT is a better approximation to the continuous fractional Fourier transform than the conventional defined DFRFT

Keywords

discrete Fourier transforms; eigenvalues and eigenfunctions; matrix decomposition; Hermite Gauss function; Lagrange multiplier; discrete Fourier transform matrix; discrete fractional Fourier transform; eigendecomposition; error removal; Chirp; Discrete Fourier transforms; Discrete transforms; Eigenvalues and eigenfunctions; Filtering; Fourier transforms; Optical computing; Optical filters; Optical signal processing; Quantum mechanics;

fLanguage

English

Journal_Title

Circuits and Systems II: Analog and Digital Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1057-7130

Type

jour

DOI

10.1109/82.793715

Filename

793715