Fast algorithms for computing the discrete W transforms

Author

Chan, S.C. ; Ho, K.L.

Author_Institution

Dept. of Electr. & Electron. Eng., Hong Kong Univ., Hong Kong

fYear

1990

fDate

24-27 Sep 1990

Firstpage

183

Abstract

New algorithms for computing the discrete W transform (DWT) of arbitrary lengths are presented. It is found that an odd length type II and III DWT can be mapped to a discrete Hartley transform (DHT) by means of a simple index mapping. The DHT or DWT-I can be computed, for example, by the real-valued fast Fourier transform algorithms such as the real-valued prime factor fast Fourier transform algorithm (RPFA FFT). Using the close relationship between the odd DFTs and the DWTs, it is possible to compute the type II and III DWTs with even lengths by means of the real-valued FFT or the fast Hartley transform (FHT). Similar algorithms are also presented for the DWT-IV

Keywords

fast Fourier transforms; transforms; discrete Hartley transform; discrete W transforms; even lengths; fast Hartley transform; fast algorithms; index mapping; odd length; prime factor fast Fourier transform; real valued FFT algorithms; type II DWT; type III DWT; Arithmetic; Discrete Fourier transforms; Discrete cosine transforms; Discrete transforms; Discrete wavelet transforms; Fast Fourier transforms; Frequency; Hardware; Harmonic analysis; Kernel;

fLanguage

English

Publisher

ieee

Conference_Titel

Computer and Communication Systems, 1990. IEEE TENCON'90., 1990 IEEE Region 10 Conference on

Print_ISBN

0-87942-556-3

Type

conf

DOI

10.1109/TENCON.1990.152594

Filename

152594