Optimization of linear stochastic systems based on canonical wavelet expansions

Design problems for linear mean square (MS) optimal filters are considered on the basis of canonical wavelet expansions (CWEs). To simulate the class of essentially non-stationary stochastic processes, including those describing shock effects, the idea put forward in this paper is to use the CWEs based on the coefficients of its covariance function expanded in terms of an orthogonal two-dimensional wavelet basis. To estimate an observed process represented as a CWE, a linear MS optimal operator in the form of a set of formal rules describing the operator's response to basic wavelet functions is constructed. Explicit formulas for calculating the MS optimal estimate of the signal and the MS optimal estimate of the quality of the constructed linear MS optimal operator are derived. Sintez-VL, a software tool developed in MATLAB, is described. A test example with the delta function is provided.