Diagonalization of the auto-correlation functions of random signals in terms of Cauchy wavelets using operator algebra

Author

Sakaguchi, Fuminori

Author_Institution

Fac. of Eng., Fukui Univ., Japan

fYear

1996

fDate

18-21 Jun 1996

Firstpage

85

Lastpage

88

Abstract

The eigenfunction system of a kind of operator is identical to the over-complete Cauchy wavelet system, as has been shown previously. In this presentation, the re-ordering problem among this operator and its adjoint is investigated. Then, an application of this re-ordering problem to the pseudo-diagonalization problem of the autocorrelation function of a stochastic process is proposed

Keywords

algebra; correlation theory; eigenvalues and eigenfunctions; mathematical operators; random processes; signal processing; stochastic processes; wavelet transforms; Cauchy wavelets; adjoint; auto-correlation functions; diagonalization; eigenfunction system; operator algebra; pseudo-diagonalization problem; random signals; re-ordering problem; stochastic process; Algebra; Autocorrelation; Eigenvalues and eigenfunctions; Fourier transforms; Quantum mechanics; Signal generators; Signal processing; Signal processing algorithms; Stochastic processes; Stochastic systems;

fLanguage

English

Publisher

ieee

Conference_Titel

Time-Frequency and Time-Scale Analysis, 1996., Proceedings of the IEEE-SP International Symposium on

Conference_Location

Paris

Print_ISBN

0-7803-3512-0

Type

conf

DOI

10.1109/TFSA.1996.546692

Filename

546692