Invariant spaces and fast transforms [convolution]

Author

Zhechev, Bozhan Z.

Author_Institution

Dept. of Comput. & Commun. Syst., Bulgarian Acad. of Sci., Sofia, Bulgaria

Volume

46

Issue

2

fYear

1999

fDate

2/1/1999 12:00:00 AM

Firstpage

216

Lastpage

219

Abstract

In this paper a new approach to convolution based on the linear representation of the dihedral group is presented. In the decomposition of this representation, the Fourier operator appears. Some useful properties of the Fourier operator are summarized. Its projectors onto its eigenspaces are expressed with the Hartley operator. An orthogonal basis of the invariant spaces of the dihedral group is defined. A generalized method for analyzing and constructing fast transforms is proposed

Keywords

Hadamard transforms; Hartley transforms; convolution; fast Fourier transforms; wavelet transforms; DFT; FFT; Fourier operator; Hartley operator; Hartley transform; convolution; dihedral group; eigenspaces; fast transforms; invariant spaces; linear representation; orthogonal basis; signal processing; wavelets; Convolution; Discrete Fourier transforms; Discrete transforms; Discrete wavelet transforms; Fast Fourier transforms; Filter bank; Hilbert space; Signal processing; Signal processing algorithms; Wavelet packets;

fLanguage

English

Journal_Title

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

Publisher

ieee

ISSN

1057-7130

Type

jour

DOI

10.1109/82.752957

Filename

752957