时域取样定理在工程应用中的关键问题推导  

Derivation of Key Problems of Time Domain Sampling Theorem in Practical Application

作　　者：方敬[1] 卢文锋[2] 乔建苹[1] 王春兴[1] FANG Jing;LU Wenfeng;QIAO Jianping;WANG Chunxing(College of Physics and Electronics,Shandong Normal University,Jinan Shandong 250014;School of Management Engineering,Shandong Jianzhu University,Jinan Shandong 250101)

机构地区：[1]山东师范大学物理与电子科学学院,山东济南250014 [2]山东建筑大学管理工程学院,山东济南250101

出　　处：《首都师范大学学报（自然科学版）》2020年第3期24-27,共4页Journal of Capital Normal University：Natural Science Edition

基　　金：山东师范大学教学改革立项项目(2018M38);山东师范大学实验教学改革立项项目(SYJG040245,SYJG040240);山东师范大学在线开放课程;山东省研究生教育质量提升计划项目(SDYY18064);教育部新工科研究与实践项目。

摘　　要：针对传统教材中关于取样定理的论述不够完整,推导了矩形脉冲取样信号频谱与原始连续信号频谱的关系,以及离散信号频谱与原始连续信号频谱的关系,并对工程应用中的抗混叠滤波器做了分析.理论研究表明:矩形脉冲取样信号的频谱是原始连续信号频谱的周期延拓,同时幅度具有取样函数的包络形式,这与传统的理想取样不同.从连续时间信号到离散时间信号存在一个时间归一化问题,从而对应的频谱密度函数之间也存在着频率归一化问题.这些问题的推导与分析有助于深刻理解取样定理,并对工程应用提供指导.In view of the incomplete discussion on sampling theorem in traditional textbooks,the relationship between the rectangular pulse sampled signal spectrum and the original continuous signal spectrum was deduced,as well as the relationship between the discrete signal spectrum and the original continuous signal spectrum,and the anti-aliasing filter in engineering application was analyzed.The theoretical analysis showed that the spectrum of rectangular pulse sampling signal was a periodic extension of the spectrum of the original continuous signal,and the amplitude had the envelope form of the sampling function,which was different from the traditional ideal sampled signal.There was a time normalization problem from continuous time signal to discrete time signal which would result in the frequency normalization between the corresponding spectrum density functions.The derivation and analysis of these problems are helpful to understand the sampling theorem deeply and provide guidance for engineering application.

关 键 词：取样定理 频谱 抗混叠滤波器 

分 类 号：G642[文化科学—高等教育学]