《信号与系统(双语)》课程教学大纲》

《信号与系统（双语）》课程教学大纲》
课程编号：17105000 学分：3 参考学时：42 实验学时：
上机学时：12 适用专业：生物医学工程系各专业
大纲执笔人：魏守水课程负责人：魏守水
1 本课程的性质及适用专业Who is available to this course?
本课程是一门专业基础课程，适用于生物医学工程、控制工程、通信工程等专业。

Course Aims and Objectives ：This course is central to the studies in Biomedical Engineering, Control Engineering and communication Engineering.
2 本课程的教学目标Course objectives and tasks
通过本课程的学习，使学生初步认识如何建立信号与系统的数学模型，如何经适当的数学分析求解，并对所得的结果给出物理解释和赋予物理意义。

学生应能掌握信号分析与线性系统的基本理论及分析方法。

Course Focus ：Students will learn how continuous and discrete time signals are modified by systems described in the frequency and time domains. This course will provide students with an understanding of signals and systems. The material is learned via performance, rather than competition with classmates.
3 对先修课程的要求Request to other courses
建议先修高等教学、线性代数、电路理论等课程。

Suggest learning Advanced Mathematics, linear algebra and Circuits Principle first.
4 本课程教学内容及基本要求
Class Syllabus
4.1 信号与系统概述Introduction
教学内容：连续时间与离散时间信号；自变量的变换；指数信号与正弦信号；单位冲激与单位阶跃函数；连续时间与离散时间系统；基本系统性质。

基本要求：掌握连续时间与离散时间信号，自变量的变换，指数信号与正弦信号，单位冲激与单位阶跃函数；熟悉连续时间与离散时间系统，基本系统性质。

能够正确判定信号和系统的类别。

Signals and Systems
Continuous-Time and Discrete-Time Signals; Transformations of the Independent Variable; Exponential and Sinusoidal Signals; The Unit Impulse and Unit Step Functions; Continuous-Time and Discrete-Time Systems; Basic System Properties.
Mastery: Continuous-time and discrete-time signals , Transformations of the Independent Variable, Exponential and Sinusoidal Signals, The Unit Impulse and Unit Step Functions. How to specify the signals and systems by its properties?
Understand: Continuous- Time and Discrete-Time Systems, Basic System Properties.
4.2 线性时不变系统Linear Time-Invariant Systems
教学内容：卷积和与卷积积分；线性时不变系统性质；用微分和差分方程描述的因果线性时不变系统；奇异函数。

基本要求：掌握卷积和与卷积积分计算与性质，线性时不变系统性质，奇异函数及其性质；熟悉用微分和差分方程描述的因果线性时不变系统。

Linear Time-Invariant Systems
Discrete-Time LTI Systems: The Convolution Sum; Continuous-Time LTI Systems: The Convolution Integral; Properties of Linear Time-Invariant Systems; Causal LTI Systems Described by Differential and Difference Equations; Singularity Functions.
Mastery: Discrete- Time LTI Systems: The Convolution Sum, Continuous-Time LTI Systems, The Convolution Integral, Properties of Linear Time-Invariant Systems, Singularity Functions and it’s Properties.
Understand: Causal LTI Systems Described by Differential and Difference Equations.
4.3 周期信号的傅立叶级数表示Fourier Series Representation of Periodic Signals
教学内容：傅立叶级数的历史回顾；线性时不变系统对复指数信号的响应；连续时间周期信号的傅立叶级数表示；傅立叶级数的收敛；连续时间傅立叶级数性质；离散时间周期信号的傅立叶级数表示；离散时间傅立叶级数性质；傅立叶级数与线性时不变系统；用微分方程描述的连续时间滤波器举例；用差分方程描述的离散时间滤波器举例。

基本要求：掌握线性时不变系统对复指数信号的响应，连续时间周期信号的傅立叶级数表示，周期信号表示为傅立叶级数的方法及性质，离散时间周期信号的傅立叶级数表示，离散时间傅立叶级数性质；熟悉傅立叶级数的收敛，滤波的概念和用微分方程描述的连续时间滤波器以及用差分方程描述的连续时间滤波器；了解傅立叶级数的历史。

Fourier Series Representation of Periodic Signals
A Historical Perspective ; The Response of LTI Systems to Complex Exponentials; Fourier Series Representation of Continuous-Time Periodic Signals; Convergence of the Fourier Series; Properties of Continuous-Time Fourier Series; Fourier Series Representation of Discrete-Time Periodic Signals; Properties of Discrete-Time Fourier Series; Fourier Series and LTI Systems; Filtering; Examples of Continuous-Time Filters Described by Differential Equations; Examples of Discrete-Time Filters Described by Difference Equations.
Mastery: The Response of LTI Systems to Complex Exponentials, Fourier Series Representation of Continuous-Time Periodic Signals, Properties of Continuous-Time Fourier Series, Fourier Series Representation of Discrete-Time Periodic Signals, Properties of
Discrete-Time Fourier Series, Fourier Series and LTI Systems.
Understand: . Convergence of the Fourier Series, Filtering, Continuous-Time Filters Described by Differential Equations, Discrete-Time Filters Described by Difference Equations.
Know about: A Historical Perspective of Fourier series.
4.4 连续信号的傅立叶变换The Continuous-Time Fourier Transform
教学内容：连续时间傅立叶变换；周期信号傅立叶变换；连续时间傅立叶变换性质；卷积性质；相乘性质；由线性常系数微分方程表征的系统。

基本要求：掌握连续时间傅立叶变换，周期信号傅立叶变换，连续时间傅立叶变换性质，线性常系数微分方程表征的系统；熟悉卷积性质和相乘性质。

The Continuous-Time Fourier Transform
Representation of Aperiodic Signals: The Continuous-Time Fourier Transform; The Fourier Transform for Periodic Signals; Properties of the Continuous-Time Fourier Transform; The Convolution Property; The Multiplication Property; Tables of Fourier Properties and of Basic Fourier Transform Paris; Systems Characterized by Linear Constant-Coefficient Differential Equations.
Mastery: The Continuous -Time Fourier Transform, The Fourier Transform for Periodic Signals, Properties of the Continuous-Time Fourier Transform, The Convolution Property, Systems Characterized by Linear Constant-Coefficient Differential Equations.
Understand: The Convolution Property and the Multiplication Property.
4.5 离散信号的傅立叶变换The Discrete-Time Fourier Transform
教学内容：离散时间傅立叶变换；周期信号傅立叶变换；离散时间傅立叶变换性质；卷积性质；相乘性质；对偶性；由线性常系数差分方程表征的系统。

基本要求：掌握离散时间傅立叶变换，周期信号傅立叶变换，离散时间傅立叶变换性质，线性常系数差分方程表征的系统；熟悉卷积性质和相乘性质以及对偶性质。

The Discrete-Time Fourier Transform
Representation of Aperiodic Signals: The Discrete-Time Fourier Transform; The Fourier Transform for Periodic Signals; Properties of the Discrete-Time Fourier Transform; The Convolution Property; The Multiplication Property; Tables of Fourier Transform Properties and of Basic Fourier Transform Paris; Duality; Systems Characterized by Linear Constant-Coefficient Difference Equations.
Mastery: The Discrete- Time Fourier Transform, The Fourier Transform for Periodic Signals, Properties of the Discrete-Time Fourier Transform, The Convolution Property, Systems Characterized by Linear Constant-Coefficient Difference Equations.
Understand: The Convolution Property, the Multiplication Property and Duality.
4.6 采样定理及调制解调原理The Sampling Theorem
教学内容：采样定理；利用内插由样本重建信号；混叠现象；连续时间信号的离散时间处理；离散时间信号采样。

调制解调的工程应用。

基本要求：掌握采样定理，熟悉利用内插由样本重建信号，混叠现象，离散时间信号采样；了解连续时间信号的离散时间处理。

理解调制解调在现代通讯中的作用。

Sampling
Representation of Continuous -Time Signal by Its Samples: The Sampling Theorem; Reconstruction of a Signal from Its Samples Using Interpolation; The Effect of Undersampling: Aliasing; Discrete-Time Processing of Continuous-Time Signals; Sampling of Discrete-Time Signals. Applications of modulation and demodulation.
Mastery: The Sampling Theorem.
Understand: Reconstruction of a Signal from Its Samples Using Interpolation, The Effect of Undersampling: Aliasing, Sampling of Discrete-Time Signals.
Know about: Discrete-Time Processing of Continuous -Time Signals. The roles of modulation and demodulation in modern communication.
4.7 Z 变换The Z-Transform
教学内容：Z 变换；Z 变换收敛域；逆Z 变换；由零极点图对傅立叶变换进行几何求值；Z 变换性质；几个常用Z 变换对；利用Z 变换分析和表征线性时不变系统；系统函数的代数属性与方框图表示；单边Z 变换。

基本要求：掌握Z 变换，Z 变换收敛域，逆Z 变换，Z 变换性质，系统函数的代数属性与方框图表示；熟悉几个常用Z 变换对，利用Z 变换分析和表征线性时不变系统，单边Z 变换；了解由零极点图对傅立叶变换进行几何求值。

The Z-Transform
The Z-Transform; The Region of Convergence for the Z-Transform; The Inverse Z-Transform; Geometric Evaluation of the Fourier Transform from the Pole-Zero Plot; Properties of the
Z-Transform; Some Common Z-Transform Pairs; Analysis and Characterization of LTI Systems Using the Z-Transform; System Function Algebra and Block Diagram Representations; The Unilateral Z-Transform.
Mastery: The Z-Transform, The Region of Convergence for the Z-Transform, The Inverse
Z-Transform, Properties of the Z-Transform, System Function Algebra and Block Diagram Representations.
Understand: Some Common Z- Transform Pairs, Analysis and Characterization of LTI Systems Using the Z-Transform, The Unilateral Z-Transform.
Know about: Geometric Evaluation of the Fourier Transform from the Pole-Zero Plot.
5 建议使用教材Recommending book
Alan V.Oppenheim, Alan S.Willsky, S.Hamid Nawab . Signals and Systems . 2 nd Edition . 北京：电子工业出版社，2002.8
6 本课程学时分配
Class Syllabus Schedule
7 其它说明Others
7.1 教学参考资料Reference
1 ．郑君里等. 信号与系统. 第2版. 北京：高等教育出版社，2000.5
2 ．J. R. Buck, M. M. Daniel, A. C. Singer, ‘Computer Explorations in Signals and Systems using MATLAB, Prentice-Hall, l997: Exercises, companion to Oppenheim above.
7.2 教学方法和手段Teaching tools
采用多媒体和网络辅助教学，课堂讲授，课下辅导。

Multimedia tools: PPT lecture plus Internet Justifications.
7.3 考核方法Evaluating system
考试+平时测验+作业。

Exam plus quizzes plus homework.
7.4 对实践教学的建议advice to experiments
本课程教学实验采用Matlab 软件作为平台工具，通过对Matlab 软件在信号与信号处理等一些特定函数与工具箱的了解与熟悉的基础上，能应用Matlab 软件进行信号与系统单元模块的分析与仿真，最终基本掌握使用Matlab 软件对给定的信号与线性系统进行初步设计与分析。

The tool of Matlab is used with the experiments of the course. From using the functions of the toolboxes of Matlab, the students will master some simulations analysis methods on signals and LTI systems.
8 制订人：魏守水控制科学与工程学院
Author：Wei Shoushui Control science and Engineering。