Pseudodiagonalization of the autocorrelation of a stochastic process by an over‐complete wavelet system
Fuminori Sakaguchi · Electronics and Communications in Japan (Part III Fundamental Electronic Science) · 1995
Abstract If a stochastic process can be regarded as a superposition of the wavelets which arise randomly and independently of one another, the random‐wavelet picture of a stochastic process is intuitive and convenient. This paper investigates theoretically in what case the picture can be used; i.e., in what case the autocorrelation of the stochastic process can be diagonalized by using the over‐complete wavelet system. A general method for calculating the pseudodiagonal form from an arbitrarily given autocorrelation function using the operator algebra is proposed. Next, some properties of stationary wavelet‐diagonal processes are investigated where it is shown that the power spectra of these processes are related to the spectral estimates under the circumstances in which the number of the time points are constrained to a constant finite number.