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Filtering And Compression For Infinite Sets Of Stochastic Signals

机译：无限组随机信号的滤波和压缩

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摘要

We present a theory for optimal filtering of infinite sets of random signals. There are several new distinctive features of the proposed approach. First, we provide a single optimal filter for processing any signal from a given infinite signal set. Second, the filter is presented in the special form of a sum with p terms where each term is represented as a combination of three operations. Each operation is a special stage of the filtering aimed at facilitating the associated numerical work. Third, an iterative scheme is implemented into the filter structure to provide an improvement in the filter performance at each step of the scheme. The final step of the scheme concerns signal compression and decompression. This step is based on the solution of a new rank-constrained matrix approximation problem. The solution to the matrix problem is described in this paper. A rigorous error analysis is given for the new filter.
机译：我们提出了一种对无限组随机信号进行最佳滤波的理论。提议的方法有几个新的鲜明特征。首先，我们提供了一个最佳滤波器，用于处理来自给定无限信号集中的任何信号。其次，滤波器以具有p个项的和的特殊形式表示，其中每个项表示为三个运算的组合。每个操作都是过滤的一个特殊阶段，旨在促进相关的数值运算。第三，将迭代方案实施到滤波器结构中以在方案的每个步骤处提供滤波器性能的改进。该方案的最后一步涉及信号压缩和解压缩。此步骤基于新的秩受限矩阵逼近问题的解决方案。本文描述了矩阵问题的解决方案。对新过滤器进行了严格的误差分析。

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