Some Novel Properties of Wiener's Canonical Expansion
- 1 April 1969
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Systems Science and Cybernetics
- Vol. 5 (2) , 140-144
- https://doi.org/10.1109/TSSC.1969.300205
Abstract
An expression of Wiener's orthogonal functionals {Fn} for an arbitrary variance parameter is presented along with some of its salient properties. A necessary and sufficient condition for the convergence of the corresponding Wiener series is given. Introduction of the variance parameter enables us to discuss some interesting algebraic properties of Wiener's canonical networks also. It is shown that they form a Boolean algebra, each element of which represents a whole family of Wiener's canonical networks for a fixed variance parameter. Applicability of the Wiener theory to time-variable systems and to non-Gaussian processes is briefly discussed.Keywords
This publication has 2 references indexed in Scilit:
- Fourier analysis on wiener measure spaceJournal of the Franklin Institute, 1968
- On the Applicability of Wiener's Canonical ExpansionsIEEE Transactions on Systems Science and Cybernetics, 1968