信號與系統（雙語）

“信號與系統”這門課，是高等學校電子與信息工程、自動化、微電子、生物醫學工程、計算機及物聯網等專業必修的一門核心基礎課，也可以説是這些專業的啓蒙課，是進行後續課程，比如：“數字信號處理”、“數字圖像處理”、“隨機信號分析”、“通信原理”等課程的基礎準備。

簡單來説，“信號與系統”這門課的主要研究內容，就是藉助於一定的數學工具，對自然界中形態各異的信號與系統的共性部分，也即線性與時不變性等特性，對信號與系統進行表述與分類；同時，在“線性與時不變”特性的基礎上，結合“信號分解”的思想，發展出了一系列基本但又重要的信號與系統的分析方法與處理工具。 ^[1] 

01

Signals and Systems （信號與系統）

In this chapter, students should:(1) Master the definitions and classifications of signals. (2) Master the description, classification and characteristics of the system. (3)Focus on mastering the characteristics of determining signals and linear time-invariant systems. (4) Master the idea of 'Decomposition of signals and systems‘

課時

1.0 Introduction

1.0 引言

1.1 Continuous-Time Signals and Discrete-Time Signals

1.1 連續時間信號與離散時間信號

1.2 Basic Transformations of Signals

1.2 信號的基本運算

1.2.1 Basic Transformations of Dependent Variables

1.2.1 因變量的基本運算

1.2.2 Basic Transformations of Independent Variables

1.2.2 自變量的基本運算

1.3.1 Exponential and Sinusoidal Signals (1)

1.3.1 自然指數信號與正弦信號（1）

1.3.2 Exponential and Sinusoidal Signals (2)

1.3.2 自然指數信號與正弦信號（1）

1.4.1 The Unit Impulse and Unit Step Functions (1)

1.4.1 單位衝激與單位階躍信號（1）

1.4.2 The Unit Impulse and Unit Step Functions (2)

1.4.2 單位衝激與單位階躍信號（2）

1.4.3 The Unit Impulse and Unit Step Functions (3)

1.4.3 單位衝激與單位階躍信號（3）

1.5.1 Continuous-Time and Discrete-Time Systems (1)

1.5.1 連續時間系統與離散時間系統（1）

1.5.2 Continuous-Time and Discrete-Time Systems (2)

1.5.2 連續時間系統與離散時間系統（2）

1.6.1 Basic System Properties (1)

1.6.1 系統的基本性質（1）

1.6.2 Basic System Properties (2)

1.6.2 系統的基本屬性（2）

1.6.3 Basic System Properties (3)

1.6.3 系統的基本屬性（3）

02

Linear Time-Invariant Systems （線性時不變系統）

In this chapter, students should:(1) Master the definition and descriptions of LTI systems. (2) Master the characteristics of the LTI systems. (3) Pay more attention to how to determine the response of LTI systems by Bilingual-Zero method through solving LCCDE; (4) master the method of determining the impulse response of LTI systems.

課時

2.0 Introduction

2.0 引言

2.1.1 Discrete-Time Linear Time-Invariant Systems (1)

2.1.1離散時間線性時不變系統（1）

2.1.2 Discrete-Time Linear Time-Invariant Systems (2)

2.1.2離散時間線性時不變系統（2）

2.2.1 Continuous-Time Linear Time-Invariant Systems (1)

2.2.1連續時間線性時不變系統（1）

2.2.2 Continuous-Time Linear Time-Invariant Systems (2)

2.2.2 連續時間線性時不變系統（2）

2.3.1 Properties of Linear Time-Invariant Systems (1)

2.3.1 線性時不變系統的性質（1）

2.3.2 Properties of Linear Time-Invariant Systems (2)

2.3.2 線性時不變系統的性質（2）

2.3.3 Properties of Linear Time-Invariant Systems (3)

2.3.3 線性時不變系統的性質（3）

2.4.1 Causal LTI Systems Described by Differential and Difference Equations (1)

2.4.1 用微分和差分方程表述的因果線性時不變系統（1）

2.4.2 Causal LTI Systems Described by Differential and Difference Equations (2)

2.4.2 用微分和差分方程表述的因果線性時不變系統（2）

2.4.3 Determine the Homogeneous Solution and Particular Solution by Solving LCCDE

2.4.3 求解線性常係數微分和差分方程的通解與特解

2.4.4 Determine the complete solution by solving LCCDE

2.4.4 求解線性常係數微分和差分方程的全解

2.4.5 Translation of Initial Conditions by Singularity Functions Balancing Method

2.4.5 利用奇異值函數配平法進行初始條件的轉換

2.4.6 Solving LCCDE by bilingual zero method

2.4.6 利用雙零法求解線性常係數微分和差分方程

2.4.7.1 Determine the Impulse Response of LTI Systems by Solving LCCDE (1)

2.4.7.1 通過解線性常係數微分和差分方程求解系統的單位衝激響應函數（1）

2.4.7.2 Determine the Impulse Response of LTI Systems by Solving LCCDE (2)

2.4.7.2 通過解線性常係數微分和差分方程求解系統的單位衝激響應函數（2）

2.4.8 Diagram Description of LCCDE Described LTI Systems

2.4.8 用線性常係數微分和差分方程表述的LTI系統的框圖表示

03

Fourier Series Representation of Periodic Signals （週期信號的傅里葉級數表示）

In this chapter, students should:(1) Review the idea of decomposition and master the definition of eigenfunction and eigenvalue of LTI systems; (2) Master the development of FS on the basis of signal decomposition; (3) Master the relationship between exponential formed FS and trigonometric formed FS; (4) Master the definition and physical meaning of amplitude spectrum and phase spectrum; (5) Pay more attention to the properties of FS and know how to use them in Fourier analysis.

課時

3.0 Introduction

3.0 引言

3.1.1 Complex Exponential Formed Fourier Series Representation of CT Periodic Signals

3.1.1 連續時間週期信號的復指數形式的傅里葉級數表示

3.1.2 Trigonometric Formed Fourier Series Representation of CT Periodic Signals (1)

3.1.2 連續時間週期信號的三角函數形式的傅里葉級數表示（1）

3.1.3 Trigonometric Formed Fourier Series Representation of CT Periodic Signals (2)

3.1.3 連續時間週期信號的三角函數形式的傅里葉級數表示（2）

3.1.4 Relationship between the Trigonometric and Exponential Formed CTFS

3.1.4 指數函數形式的傅里葉級數與三角函數形式的傅里葉級數之間的關係

3.2.1 Amplitude and Phase Frequency Spectral of CTFS (1)

3.2.1 連續時間傅里葉級數的幅值譜與相位譜（1）

3.2.2 Amplitude and Phase Frequency Spectral of CTFS (2)

3.2.2 連續時間傅里葉級數的幅值譜與相位譜（2）

3.2.3 Amplitude and Phase Frequency Spectral of CTFS (3)

3.2.3 連續時間傅里葉級數的幅值譜與相位譜（3）

3.3 Convergence of the CTFS and Gibbs' Phenomenon

3.3 連續時間傅里葉級數的收斂性與吉布斯現象

3.4.1 Properties of CTFS (1)

3.4.1 連續時間傅里葉級數的性質（1）

3.4.2 Properties of CTFS (2)

3.4.2 連續時間傅里葉級數的性質（2）

3.5.1 Fourier Series Representation of Discrete-Time Periodic Signals

3.5.1 離散時間週期信號的傅里葉級數表示

3.5.2 Properties of DTFS

3.5.2 離散時間傅里葉級數的性質

04

The Continuous -Time Fourier Transform （連續時間傅里葉變換）

In this chapter, students should:(1) know the idea of regarding a aperiodic signal as a special periodic signal with period from minus infinite to plus infinite; (2) Master the development of CTFT from CTFS; (3) Know how to determine periodic signals' CTFT and understand its physical means; (4) Pay more attention to properties of CTFT, especially to multiplication property and convolution property which play important roles in the analysis of LTI systems; (5) know how to analysis LTI systems with the tool of CTFT.

課時

4.1.1 Representation of Aperiodic Signals: The Continuous-Time Fourier Transform (1)

4.1.1 非週期信號的表示：連續時間傅里葉變換（1）

4.1.2 Representation of Aperiodic Signals: The Continuous-Time Fourier Transform (2)

4.1.2 非週期信號的表示：連續時間傅里葉變換（2）

4.2 The Fourier Transform for Periodic Signals

4.2 週期信號的傅里葉變換

4.3.1 Properties of Continuous-Time Fourier Transform (1)

4.3.1 連續時間傅里葉變換的性質（1）

4.3.2 Properties of Continuous-Time Fourier Transform (2)

4.3.2 連續時間傅里葉變換的性質（2）

4.4 The Convolution Property

4.4 卷積特性

4.5 The Multiplication Property

4.5 乘積特性

4.6 The Frequency Response Function of LTI systems Characterized by LCCDEs

4.6 由線性常係數差分方程表述的LTI系統的頻域響應函數

05

The Discrete-Time Fourier Transform （離散時間傅里葉變換）

In this chapter, students should:(1) know the idea of regarding a aperiodic signal as a special periodic signal with period from minus infinite to plus infinite; (2) Master the development of DTFT from DTFS; (3) Know how to determine periodic signals' DTFT and understand its physical means; (4) Pay more attention to properties of DTFT, especially to multiplication property and convolution property which play important roles in the analysis of LTI systems; (5) know how to analysis LTI systems with the tool of DTFT;(6) know the differences between CTFT and DTFT.

課時

5.1.1 Representation of Aperiodic Signals: The Continuous-Time Fourier Transform (1)

5.1.1 非週期信號的表示：連續時間傅里葉變換（1）

5.1.2 Representation of Aperiodic Signals: The Continuous-Time Fourier Transform (2)

5.1.2 非週期信號的表示：連續時間傅里葉變換（2）

5.2 The Fourier Transform for Periodic Signals

5.2 週期信號的傅里葉變換

5.3.1 Properties of Continuous-Time Fourier Transform (1)

5.3.1 連續時間傅里葉變換的性質（1）

5.3.2 Properties of Continuous-Time Fourier Transform (2)

5.3.2 連續時間傅里葉變換的性質（2）

5.4 The Convolution Property

5.4 卷積特性

5.5 The Multiplication Property

5.5 乘積特性

5.6 The Frequency Response Function of LTI systems Characterized by LCCDEs

5.6 由線性常係數微分方程表述的LTI系統的頻域響應函數

06

Sampling （採樣）

n this chapter, students should:(1) know the process of periodic sampling and realize the essence of sampling is the discretization of time; (2) know to verify the effectiveness of sampling by tool of CTFT in frequency domain; (3) Know how to recover the sampled signals from their samples by the method of interpolation; (4) know how to sample the narrowband signals; (5) know the effect of under sampling ;(6) More attention should be payed to the sampling of discrete time signals and master the effective of Up-sampling and Down-sampling.

課時

6.0 Introduction

6.0 引言

6.1 Impulse-Train Sampling

6.1 衝激串採樣

6.2 Reconstruction of the Sampled Signals from Its Samplings Using Interpolation

6.2 利用內插基於樣本重構本採樣信號

6.3 The Effect of Under-sampling: Aliasing

6.3 欠採樣的影響：混疊現象

6.4 The Sampling of Narrowband Signals

6.4 窄帶信號的採樣

6.5 The Sampling of Discrete Signals

6.5 離散時間信號的採樣

6.6 Discrete -Time Decimation and Interpolation

6.6 離散時間抽取與插值

07

The Laplace Transform （拉普拉斯變換）

In this chapter, students should:(1) know the how to induce the Laplace transform from the CTFT and realize that CTFT is the special case and Laplace transform is the generalization of CTFT; (2) Master the determining of the ROC of Laplace transform; (3) Pay more attention to properties of LT, especially to multiplication property and convolution property which play important roles in the analysis of LTI systems; (5) know how to analysis LTI systems described by LCCDE with the tools of Laplace transform.

課時

7.0 Introduction

7.0 引言

7.1 The Region of Convergence of Laplace Transform

7.1 拉普拉斯變換的收斂域

7.2 Rational Transforms and Pole-zero Plot

7.2 有理拉普拉斯變換的零-極圖

7.3 Properties of the Region of Convergence for Laplace Transforms

7.3 拉普拉斯變換收斂域的性質

7.4 The Inverse Laplace Transform

7.4 拉普拉斯逆變換

7.5.1 Properties of the Laplace Transform (1)

7.5.1 拉普拉斯變換的性質（1）

7.5.2 Properties of the Laplace Transform (2)

7.5.2 拉普拉斯變換的性質（2）

7.6 Some Laplace Transform Pairs

7.6 一些常用的拉普拉斯變換對

7.7.1 Analysis and Characterization of LTI Systems Using the Laplace Transform (1)

7.7.1 利用拉普拉斯變換分析與表徵LTI系統（1）

7.7.2 Analysis and Characterization of LTI Systems Using the Laplace Transform (2)

7.7.2 利用拉普拉斯變換分析與表徵LTI系統（2）

7.8 System Function Algebra and Block Diagram Representation

7.8 系統函數的代數表述與框圖表述

08

The z-Transform （z-變換）

In this chapter, students should:(1) know the how to induce the z-Transform from the DTFT and realize that DTFT is the special case and z-Transform is the generalization of DTFT; (2) Master the determining of the ROC of z-Transform; (3) Pay more attention to properties of z-Transform, especially to multiplication property and convolution property which play important roles in the analysis of LTI systems; (5) know how to analysis LTI systems described by LCCDE with the tools of z-Transform.

課時

8.0 Introduction

8.0 引言

8.1 The Region of Convergence of z-Transform

8.1 z- 變換的收斂域

8.2 Rational Transforms and Pole-zero Plot

8.2 有理z-變換的零-極圖

8.3 Properties of the Region of Convergence for z-Transforms

8.3 z-變換的收斂域的性質

8.4 The Inverse z-Transform

8.4 z-變換的逆變換

8.5.1 Properties of the z-Transform (1)

8.5.1 z-變換的性質（1）

8.5.2 Properties of the z-Transform (2)

8.5.2 z-變換的性質（2）

8.6 Some z-Transform Pairs

8.6 一些常用的z-變換對

8.7.1 Analysis and Characterization of LTI Systems Using the z-Transform (1)

8.7.1 用z-變換對LTI系統進行分析與表徵（1）

8.7.2 Analysis and Characterization of LTI Systems Using the z-Transform (2)

8.7.2 用z-變換對LTI系統進行分析與表徵（2）

8.8 System Function Algebra and Block Diagram Representation

8.8 系統函數的代數表述與框圖表示 ^[1]