A larger class of wavepacket eigenfunction systems which contains Cauchy wavelets and coherent states

Author

Sakaguchi, Fuminori

Author_Institution

Fac. of Eng., Fukui Univ., Japan

fYear

1996

fDate

24-26 Jun 1996

Firstpage

436

Lastpage

439

Abstract

A larger class of systems of almost localized wavepackets is proposed. This class contains the Cauchy wavelet system and the coherent state system as special cases. The wavepacket systems in this class are the eigenfunction systems of a kind of linear operators, and they are invariant under the time-shift. Moreover, we show that they are `pseudoorthogonal´ over-complete systems in L². An application of them to the diagonalization problem of the autocorrelation functions of stochastic processes via overcomplete wavepacket systems is also proposed

Keywords

correlation theory; eigenvalues and eigenfunctions; mathematical operators; signal processing; stochastic processes; time-frequency analysis; wavelet transforms; Cauchy wavelets; almost localized wavepackets; autocorrelation functions; coherent states; diagonalization problem; linear operators; overcomplete wavepacket systems; pseudoorthogonal over-complete systems; stochastic processes; time-shift; wavepacket eigenfunction systems; Continuous wavelet transforms; Eigenvalues and eigenfunctions; Fourier transforms; Mechanical factors; Niobium; Quantum mechanics; Shape; Stochastic processes; Time frequency analysis; Wavelet analysis;

fLanguage

English

Publisher

ieee

Conference_Titel

Statistical Signal and Array Processing, 1996. Proceedings., 8th IEEE Signal Processing Workshop on (Cat. No.96TB10004

Conference_Location

Corfu

Print_ISBN

0-8186-7576-4

Type

conf

DOI

10.1109/SSAP.1996.534909

Filename

534909