Some Novel Properties of Wiener´s Canonical Expansion

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.