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信号与系统(Signals and Systems)

Beijing Jiaotong University via XuetangX

Overview

信号与系统课程是电子信息类专业本科生必选的专业基础课程,也是以信息化、网络化、智能化为主要特征的新工科专业的核心课程。本课程主要讨论确定性信号的时域分析和变换域分析,线性时不变系统的描述与特性,以及信号通过线性时不变系统的时域分析与变换域分析,重点建立“信号表示”与“系统描述”的基本概念。简要介绍信号与系统的基本理论在轨道交通、通信系统和生物系统中的应用。选用教材为陈后金教授主编的国家级“十二五”规划教材《信号与系统》第3版,2020,高等教育出版社(图1)。

图1 信号与系统教材及其主要教学内容

    北京交通大学信号与系统英文MOOC由国家级电工电子教学团队信号处理课程组教师精心打造,国家级教学名师陈后金教授领衔主讲。课程包括信号与系统分析导论、信号的时域分析、系统的时域分析、信号的频域分析、系统的频域分析、连续信号与系统的复频域分析、离散信号与系统的复频域分析、系统的状态变量分析八章内容,每个视频约10分钟左右,视频累计约800分钟。

    北京交通大学信号与系统课程具有深厚积淀,课程教学效果得到师生普遍好评,课程建设成果得到同行专家的高度认可,获得了6项国家级课程称号(图2)。该课程2021年被评为首批国家级课程思政示范课程、2018年被评为首批国家精品在线开放课程(国家线上一流课程)、2012年被评为首批国家精品资源共享课程、2007被评为首批国家双语教学示范课程、2003被评为首批国家精品课程等。

图2 “信号与系统”获得的国家级课程称号

    “信号与系统”课程已经开设50多年,一直沿袭最初的“信号变换、系统响应”的教学体系,其难以适应当今信息技术的发展。北京交通大学课程组扬弃了传统的信号与系统课程教学体系,建立了“信号表示、系统描述”的教学体系,其教学内涵更加清晰,更加适应新一代信息技术的发展和新工科专业建设(图3)。

图3 信号与系统课程的教学体系

课程的知识点围绕信号分析与系统分析两部分进行组织,准确地反映了“信号表示、系统描述”的教学体系,强调了知识点之间的内在联系和对应关系,有机地串联了课程的教学内容,让学生能够更好地把握住课程的主要脉络,构建了课程知识点图谱(图4)。

图4 课程知识点图谱

在教学内容更新上,提出知识没有“有用与无用”之分,但有“有用与更加有用”之别。根据课程教学内涵,剖析课程的教学重点与难点:为何介绍基本信号与基本运算?如何诠释信号的卷积与卷积和?为何要引入信号与系统的频域分析?如何介绍三大变换及其性质? 抽样定理的本质内容是什么?为何引入系统的复频域分析?等等。结合学科应用开展案例教学,将信号与系统课程的基本理论应用于生物神经网络、主体机车信号识别、音阶频谱分析等,拓展学生的视野,激发学生的学习兴趣。


Syllabus

  • Chapter 1 Overview
    • 1.1 Introduction to signals and sytems
    • 1.2 Classification of signals
    • 1.3 Classification of systems
    • Exercise
  • Chapter 2 Signal Analysis in the Time Domain
    • 2.1 Elementary continuous-time signals
    • 2.2 Basic operations on continuous-time signals
    • 2.3 Elementary discrete-time signals
    • 2.4 Basic operations on discrete-time signals
    • 2.5 Signal decomposition
    • 2.6 Tutorial
    • 2.7 Signal analysis in time with MATLAB
    • Exercise
  • Chapter 3 System Analysis in the Time Domain
    • 3.1 Description of linear time-invariant systems in the time domain
    • 3.2 Response analysis of continuous-time LTI systems in the time domain
    • 3.3 Response evaluation of continuous-time LTI systems
    • 3.4 Impulse response for continuous-time LTI system characterization
    • 3.5 Tutorial for response evaluation of continuous-time LTI systems
    • 3.6 Response analysis of discrete-time LTI systems in the time domain
    • 3.7 Response evaluation of discrete-time LTI systems
    • 3.8 Impulse response of discrete-time LTI system characterization
    • 3.9 Tutorial for response evaluation of discrete-time LTI systems
    • 3.10 Analysis of systems in the time domain with MATLAB
    • Exercise
  • Midterm Exam: Chapters 1-3
    • Chapter 4 Signal Analysis in the Frequency Domain
      • 4.1 Fourier analysis of periodic C-T signals
      • 4.2 Frequency analysis of nonperiodic C-T signals
      • 4.3 Fourier analysis of periodic D-T sequences
      • 4.4 Fourier analysis of nonperiodic D-T sequences
      • 4.5 Sampling of signals in the time domain
      • 4.6 An example of signal analysis in the frequency domain
      • 4.7 Frequency analysis of signals with MATLAB
    • Chapter 5 System Analysis in the Frequency Domain
      • 5.1 Frequency response of a C-T LTI system
      • 5.2 Evaluation of the frequency response of a C-T LTI systems
      • 5.3 Zero-state response of a C-T LTI system to signals
      • 5.4 Ideal analog filters
      • 5.5 Frequency response of a D-T LTI system
      • 5.6 Ideal digital filters
      • 5.7 Amplitude modulation and demodulation
      • 5.8 Frequency response analysis of systems in MATLAB
    • Midterm Exam: Chapters 4-5
      • Chapter 6 Complex Frequency Analysis of Continuous-Time Signals and Systems
        • 6.1 C-T signal representation in the complex frequency domain
        • 6.2 Unilateral Laplace transform of common C-T signals
        • 6.3 Properties of unilateral Laplace transform
        • 6.4 Evaluation of inverse Laplace transform
        • 6.5 Bilateral Laplace transform and its inverse
        • 6.6 Description of C-T LTI systems in the complex frequency domain
        • 6.7 Transfer function and system properties
        • 6.8 Implementation of C-T LTI systems
        • 6.9 Complex frequency analysis of C-T LTI system response
        • 6.10 Complex frequency analysis of signals and systems in MATLAB
      • Chapter 7 Complex Frequency Analysis of Discrete-Time Signals and Systems
        • 7.1 Representation of D-T signals in z-domain
        • 7.2 Unilateral z-transform of common D-T sequences
        • 7.3 Properties of unilateral z-transform
        • 7.4 Evaluation of unilateral z-transform
        • 7.5 Bilateral z-transform and its inverse
        • 7.6 Description of D-T LTI systems in z-domain
        • 7.7 Transfer function and system properties
        • 7.8 Implementation of D-T LTI systems
        • 7.9 z-domain analysis of system's responses
        • 7.10 Complex analysis of D-T signals and systems in MATLAB
      • Final Exam: Chapters 6-7

        Taught by

        Chen Houjin, Yahui Peng, Yanfeng Li, Li Jupeng, and Vivian

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