Theory of Filtering
Theory of Filtering
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过滤理论
DOI：
10.1137/0101003
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发表时间：
1953
期刊：
影响因子：
--
通讯作者：
L. Zadeh
中科院分区：
文献类型：
--
作者：
L. Zadeh
1.导论.近年来，过滤器的概念在传播理论中经历了相当大的演变。在维纳的平滑和预测理论出现之前，滤波器通常被认为是一个电网络，它可以自由地通过某些期望的频带，同时高度衰减相邻的不期望的频带。[1]维纳将信号系综的概念引入通信理论，并将滤波理论置于统计基础之上，大大拓宽了滤波器的这种狭隘观点。近年来，随着最佳非线性滤波器设计方法的发展，以及理想滤波器的概念扩展到非线性和时变系统，滤波器的概念得到了进一步的扩展。从数学观点看，滤波理论实质上是对函数空间和序列空间的某些类型的映射的研究。本文的目的是根据这一观点，提出一种统一的滤波器理论方法。理想滤波器和最佳滤波器是有区别的，前者被定义为实现信号和噪声完美分离的滤波器。概述了理想滤波器的三种一般模型，并从对这些模型的研究中推导出理想滤波器的一些基本性质。本文简要地讨论了最佳滤波的各种准则，并给出了一个求幂级数型最佳非线性滤波器的方法。
1. Introduction. The notion of a filter has undergone con-siderable evolution in communication theory in recent years. Prior to the advent of Wiener’s theory of smoothing and prediction, a fil-ter was generally regarded as an electrical network which would pass freely certain desired bands of frequencies, whilehighly attenuat-ing the neighboring undesired bands of frequencies. 1 This narrow view of the filter was greatly broadened byWiener, who introduced the concept of ensemble ofsignals into communication theory and plac-ed the theory of filtering on a statistical basis. More recently, the notion of a filter was further broadened by the development of methods of design of optimum nonlinear filters, and the extension of the concept of an ideal filter to nonlinear and time-variant systems.From the mathematical point of view, the theory of filtering is essentially a study of certaintypes of mappings of function and se-quence spaces. The purpose of this paper is to outline a unified ap-proach to filter theory based on this viewpoint. A distinction is made between ideal and optimum filters, the former being defined as filters which achieve a perfect separationof signal and noise. Three general models of ideal filters are sketched, and some of the basic properties of ideal filters are deduced from a study of these models. Various criteria of optimumfi, ltering are briefly discussed, and a procedure leading to optimum nonlinear filters of the power series type is out1ined.