訊號與系統
Signals and Systems
| 節 | 週一 | 週三 |
|---|---|---|
2 09:00–09:50 | 訊號與系統 ED303 | |
3 10:10–11:00 | 訊號與系統 ED303 2 節連堂 | |
4 11:10–12:00 |
* 根據陽明交大上課時間表所列
正如本課程名稱所說的,我們將介紹各種信號與系統的分類,說明這兩個概念的關係、涵蓋的廣度及某些應用。我們的重點在線性、非時變(linear and time-invariant,LTI)系統,在闡述這樣的系統可用甚麼樣的數學建模(modeling)來描述,來理解,它的特性是甚麼?我們又如何應用這樣的描述?你可以從課程中了解LTI系統在接收各種信號時的反應,學到如何運用線性的特性來化繁為簡的分析方法以及如何透過不同的轉換(transform),從相異的角度、面向(domain)來看信號與系統。我們將可由因果關係的數學描述來認識如何預測系統反應,設計輸入(因)的信號型態與系統架構以獲得所要的反應(果)或從系統反應推測、分析、理解系統架構或反推造成這樣反應的原因。這門課是所有系統科學的入門。這些系統包括通訊、網路、電路、控制、電力、計算機、生醫、物理、機械、土木、化工、製造、生物、天文、交通運輸等等自然或人為的系統以及各種小自社群、親族、部落,大至社會、政治、經濟、國家及國際關係等等有關人類群體行為的系統。
Calculus, Linear Algebra, and Differential Equations
Quitz and assigned problem sets: 40% Midterm: 30% Final: 30%
| 週次 | 主題 |
|---|---|
| 第 1 週 | Introduction: Basic concepts and definitions Examples of signals and systems |
| 第 2 週 | Linear time-invariant (LTI) systems: 1. Discrete-time LTI systems and convolution sums |
| 第 3 週 | Continuous-time LTI systems and convolution integral |
| 第 4 週 | Property of LTI systems: commutative, distributive, associative, memory, invertibility, causality, stability and unit step response. |
| 第 5 週 | Mathematical description of an LTI system: differential and difference equations. |
| 第 5 週 | Singularity functions: Unit impulse, unit doublets and convolution |
| 第 6 週 | 1. Eigenvalues, eigen-vectors and eigen-functions of a linear transform 2. Linear systems as transforms and eigenunctions of LTI syystems |
| 第 6 週 | Fourier series representation of continuous-time periodic signals |
| 第 7 週 | Properties of Fourier series: convergence, linearity, time-shifting, time reversal, time scaling, multiplication, conjugation and energy conservation |
| 第 8 週 | 1. Fourier series representation of discrete-time periodic signals 2. Fourier series and LTI systems |
| 第 9 週 | Fourier transform of general continuous-time signals and its properties |
| 第 10 週 | Discrete-time Fourier transforms |
| 第 11 週 | Time-frequency analysis of signals and systems: Effects of LTI systems on signals |
| 第 12 週 | 1. Sampling continuous-time signals 2. Signal reconstruction via interpolation 3. Under-sampling and aliasing 4. Discrete-time processing of continuous-time signals |
| 第 13 週 | 1. Sampling of discrete-time signals 2. Discrete-time decimation and interpolation 3. Some applications to communication systems |
| 第 14 週 | Laplace transform: definition, region of convergence, inverse transform, properties and applications |
| 第 15 週 | Z-transform: definition, inverse transform, region of convergence, properties and applications |
| 第 16 週 | State space models: 1. Zero-input response and modal representation 2. Zero-state response and general responses 3. Hidden Markov, reachability and observability |
教科書 A. V. Oppenheim, A. S. Willsky, and S. H. Nawab with adaptor Jian-Jiun Ding, Signals & Systems, 2nd adapted ed., Pearson, 2014. 參考書籍 1. M. N. O. Sadiku and W. A. Ali, Signals and Systems: A PRIMER WITH MATLAB, CRC Press, 2016. 2. S. Haykin and B. Van Veen, Signals and Systems, 2nd edition, Wiley, 2003.
- 地點
- ED803
- 時間
- Monday 11:00-12:00 Wed. 15:30-16:30
- 聯絡方式
- campus phone: 31820 email: ytsu@mail.nctu.edu.tw