Discrete fractional Hartley and Fourier transforms

Author

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

Author_Institution

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

Volume

45

Issue

6

fYear

1998

fDate

6/1/1998 12:00:00 AM

Firstpage

665

Lastpage

675

Abstract

This paper is concerned with the definitions of the discrete fractional Hartley transform (DFRHT) and the discrete fractional Fourier transform (DFRFT). First, the eigenvalues and eigenvectors of the discrete Fourier and Hartley transform matrices are investigated. Then, the results of the eigendecompositions of the transform matrices are used to define DFRHT and DFRFT. Also, an important relationship between DFRHT and DFRFT is described, and 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. Finally, a filtering technique in the fractional Fourier transform domain is applied to remove chirp interference

Keywords

Fourier transforms; Hartley transforms; eigenvalues and eigenfunctions; filtering theory; matrix algebra; chirp interference removal; discrete fractional Fourier transform; discrete fractional Hartley transform; eigendecompositions; eigenvalues; eigenvectors; filtering technique; transform matrices; Chirp; Discrete Fourier transforms; Discrete cosine transforms; Discrete transforms; Eigenvalues and eigenfunctions; Filtering; Fourier transforms; Interference; Optical signal processing; Signal processing;

fLanguage

English

Journal_Title

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

Publisher

ieee

ISSN

1057-7130

Type

jour

DOI

10.1109/82.686685

Filename

686685