The discrete fractional cosine and sine transforms

Author

Pei, Soo-Chang ; Yeh, Min-Hung

Author_Institution

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

Volume

49

Issue

6

fYear

2001

fDate

6/1/2001 12:00:00 AM

Firstpage

1198

Lastpage

1207

Abstract

This paper is concerned with the definitions of the discrete fractional cosine transform (DFRCT) and the discrete fractional sine transform (DFRST). The definitions of DFRCT and DFRST are based on the eigen decomposition of DCT and DST kernels. This is the same idea as that of the discrete fractional Fourier transform (DFRFT); the eigenvalue and eigenvector relationships between the DFRCT, DFRST, and DFRFT can be established. The computations of DFRFT for even or odd signals can be planted into the half-size DFRCT and DFRST calculations. This will reduce the computational load of the DFRFT by about one half

Keywords

discrete Fourier transforms; discrete cosine transforms; eigenvalues and eigenfunctions; signal processing; DCT kernel; DFRCT; DFRFT; DFRST; DST kernel; computational load reduction; discrete fractional Fourier transform; discrete fractional cosine transform; discrete fractional sine transform; eigen decomposition; eigenvalue; eigenvector; signal analysis; Discrete Fourier transforms; Discrete cosine transforms; Discrete transforms; Eigenvalues and eigenfunctions; Fourier transforms; Frequency; Helium; Image coding; Kernel; Signal analysis;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.923302

Filename

923302