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.

线性均方（MS）最优滤波器的设计问题是基于典型小波展开（CWE）的。为了模拟一类基本的非平稳随机过程，包括描述冲击效应的过程，本文提出的想法是使用基于正交二维小波展开的协方差函数系数的CWE。为了估计表示为CWE的观测过程，构造了一组形式规则的线性MS最优算子，该形式描述了算子对基本小波函数的响应。推导了用于计算信号的MS最优估计和构造的线性MS最优算子质量的MS最优估计的显式。Sintez-VL描述了在MATLAB中开发的软件工具。提供了一个带有增量功能的测试示例。