Title :
Invariant spaces and fast transforms [convolution]
Author :
Zhechev, Bozhan Z.
Author_Institution :
Dept. of Comput. & Commun. Syst., Bulgarian Acad. of Sci., Sofia, Bulgaria
fDate :
2/1/1999 12:00:00 AM
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;
Journal_Title :
Circuits and Systems II: Analog and Digital Signal Processing, IEEE Transactions on
