訊號與系統

"Signals and Systems" is the foundation to many fields such as signal processing (e.g., audio/image processing, imaging, machine learning,...etc), communication, control, and biomedical systems. This course will cover all aspects of signal representation, system analysis, time/frequency analysis (i.e., Fourier, Laplace, z-Transform), and sampling theory. All materials (mainly PowerPoint) will be available at e3 where the main reference is based on Haykin's textbook titled Signals and Systems. This course also encourages HANDS-ON practice by employing MATLAB computer assignment for each topic. 為了控制進度，本課程將會搭配自行觀看錄製video以及課程講解並行。

Calculus; MATLAB (Optional)

HW#1 HW#2, Midterm I HW#3 HW#4, Midterm II HW#5 HW#6, Final

Course website: https://sites.google.com/nctu.edu.tw/jeng/ss2023?authuser=0 Recommended Readings: Alan V. Oppenheim and Alan S. Willsky, with S. Hamid Nawab, Signals and Systems, 2nd Ed., Pearson New International Ed., Eurasia Book Co. , 2016. https://mcube.nctu.edu.tw/wiki/core/pmwiki.php?n=Course.SS2015 (陽明交大電子工程系杭學鳴教授)

Midterm I : 25% Midterm II: 30% Final: 35% Others: 10% 最後比例可能會有變動。

• Topic 1- Fundamentals

  What is a signal? What is a system? Classification of signals Basic operations on signals Elementary signals Systems viewed as interconnection of operations Properties of systems Noise Exploring concepts with Matlab

  講授：

  3

  示範：

  0.5

  實作：

  0.5

  備註：HW#1

• Topic 2- Linear Time Invariant Systems

  1. Impulse Response Convolution Sum Convolution Sum Evaluation Procedure Convolutional Integral Convolution Integral Evaluation Procedure Interconnections of LTI Systems Relationships between LTI Systems Properties and Impulse Response 2. Step Response Differential and Difference Equation Representation Differential and Difference Equation Representation of LTI Systems Solving Differential and Difference Equations Characteristics of Systems Described by Differential and Difference Eqns A. Block Diagram Block Diagram Representation B. State-Variable Description State-Variable Description of LTI Systems

  講授：

  5

  實作：

  1

  備註：HW#2, Midterm I

• Topic 3- Fourier Theory

  1. Why Fourier Representations ? Complex Sinusoids and Frequency Response of LTI Systems 2. What Are the Fourier Representations ? Fourier Representations for Four Classes of Signals (Introduction) DT Periodic Signals: The Discrete-Time Fourier Series (DTFS) CT Periodic Signals: The (Continuous-Time) Fourier Series (CTFS) DT Nonperiodic Signals: The Discrete-Time Fourier Transform (DTFT) CT Nonperiodic Signals: The (Continuous-Time) Fourier Transform (CTFT) Properties of Fourier Representations (Summary and Comparison of Four Rep's.) 3. Properties of the Fourier Representations Linearity and Symmetry Properties Scaling Properties Time- and Frequency-Shift Properties Convolution Property Multiplication Property Differentiation and Integration Properties Parseval Relationships Time-Bandwidth Product Duality 4. Computation of Inverse Fourier Transforms Finding Inverse Fourier Transforms by Using Partial-Fraction Expansions

  講授：

  8

  實作：

  1

  備註：HW#3

• Topic 4- Fourier Applications

  Introduction Fourier Transform of Periodic Signals Convolution/Multiplication with Mixed Signals Fourier Transform of Discrete-Time Signals Sampling Reconstruction of Continuous-Time Signals Discrete-Time Processing of Continuous-Time Signals Fourier Series of Finite-Duration Nonperiodic Signals

  講授：

  8

  實作：

  1

  備註：HW#4, Midterm II

• Topic 5- Laplace Transform

  1. Unilateral (One-Sided) LT The Unilateral LT Properties of the Unilateral LT Inverse of Unilateral LT Solving Differential Equations with Initial Conditions LT Methods in Circuit Analysis 2. Bilateral (Two-Sided) LT The Bilateral LT Properties of the Bilateral LT Properties of the Region of Convergence (ROC) Inverse of Bilateral LT The Transfer Function of A CT LTI System Causality and Stability of CT LTI Systems 3. Approximate Sketch of Frequency Responses from Transfer Functions Determining Frequency Response from Poles and Zeros

  講授：

  5

  實作：

  1

  備註：HW#5

• Topic 6- z-Transform

  Introduction The z-Transform Properties of the Region of Convergence (ROC) Properties of z-T Inverse of z-T The Transfer Function Causality and Stability The Unilateral z-T Determining Frequency Response from Poles and Zeros Computational Structure for Implementing DT LTI Systems

  講授：

  5

  實作：

  1

  備註：HW#6, Final

1. Classnote (course website, mainly based on 杭學鳴教授講義) 2. S. Haykin and B. Van Veen, Signals and Systems, 2nd Ed., Wiley, 2003.

地點

ED 609 or in class

時間

By appointment (email) 13:00-15:00 Monday,10:00-12:00 Wednesday

聯絡方式

jeng@nycu.edu.tw