An Application of Operator Algebra to the Pseudo-diagonalization Problem of the Auto-correlation Functions of Random Signals by an Over-complete Wavelet System
Fuminori Sakaguchi · International Symposium on Information Theory and its Applications · 1994
The eigenfunction system of an operator is identical to an over-complete wavelet system, as has been shown. In this presentation, the ordering problem among this operator and its Hermitean adjoint is investigated. Then, an application of this ordering problem to the pseudo-diagonalization problem of the autocorrelation function of a stochastic process is proposed.