Fast algorithms for computing the discrete cosine transform

Author

Chan, Shing-Chow ; Ho, Ka-Leung

Author_Institution

Dept. of Electron. Eng., City Polytech. of Hong Kong, Kowloon, Hong Kong

Volume

39

Issue

3

fYear

1992

fDate

3/1/1992 12:00:00 AM

Firstpage

185

Lastpage

190

Abstract

Efficient methods for mapping odd-length type-II, type-II, and type-IV DCTS to a real-valued DFT are presented. It is found that odd-length type-II and type-III DCTs can be transformed, by means of an index mapping, to a real-valued DFT of the same length using permutations and sign changes only. The real-valued DFT can then be computed by efficient real-valued FFT algorithms such as the prime factor algorithm. Similar mapping is introduced to convert a type-IV DCT to a real-valued DFT up to a scaling factor and some additions. Methods for computing DCTs with even lengths are also discussed

Keywords

transforms; DCT; discrete cosine transform; index mapping; odd-length type-II; prime factor algorithm; real-valued DFT; real-valued FFT algorithms; scaling factor; type-II; type-IV; Chromium; Circuits; Cities and towns; Digital signal processing; Discrete Fourier transforms; Discrete cosine transforms; Discrete transforms; Fast Fourier transforms; Frequency; Matrix decomposition;

fLanguage

English

Journal_Title

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

Publisher

ieee

ISSN

1057-7130

Type

jour

DOI

10.1109/82.127302

Filename

127302