An elucidating proof that a matched filter is optimum

作     者：Bazdresch, Miguel 

作者机构：Electrical Computer & Telecommunications Engineering Technology Department Rochester Institute of Technology RochesterNY United States 

出 版 物：《International Journal of Electrical Engineering and Education》 (Int J Electr Eng Educ)

年 卷 期：2022年第59卷第1期

页      面：60-70页

核心收录：

学科分类：0810[工学-信息与通信工程] 0711[理学-系统科学] 0808[工学-电气工程] 0809[工学-电子科学与技术（可授工学、理学学位）] 08[工学] 

基　　金：The author(s) received no financial support for the research  authorship  and/or publication of this article 

主　　题：Linear systems 

摘      要：A matched filter is an essential element in digital communications receivers. It is known that it is optimal, in the sense of producing sufficient statistics of maximum signal-to-noise ratio;a proof is presented in many undergraduate textbooks. Recent research in mathematics education suggests that the purpose of a proof is not merely to convince students that a theorem is true by pure logic;rather, a proof should be explanatory, with semantic content that elucidates the relationship between the concepts involved. In this paper, a time-domain proof that the matched filter is optimal is presented, and it is argued that it has larger explanatory value than alternative proofs. © The Author(s) 2018.