Title :
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
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;
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
DOI :
10.1109/TFSA.1996.546692
