By the end of the course, you will learn concepts, principles, analysis and designs of deterministic signals transmitting and processing through linear time-invariant systems. You will also learn ways to analyze signals and systems from various perspectives such as time domain versus transform domain, continuous signals versus discrete signals. This course will emphasize on how to represent and describe signals and systems, and will provide in-depth understanding of properties and applications of Fourier transform, Laplace transform, z-transform and filter design. When completing the course, you will obtain knowledge of analytical theories of signals and systems in both time and frequency domains, and of analyzing system functions and their applications on filter design. All of which will lay solid foundation for future courses. This course is a major prerequisite to entrance tests for graduate study.
Overview
Syllabus
- Chapter 1 Introduction
- Section 1 Signals and Systems
- Section 2 Descriptions and Classifications of Signals (Part 1)
- Section 2 Descriptions and Classifications of Signals (Part 2)
- Section 3 Signals Operations
- Section 4 Singularity Signals (Part 1)
- Section 4 Singularity Signals (Part 2)
- Section 5 Decomposition of Signals
- Section 6 Systems Models and System Classifications
- Section 7 Linear Time-Invariant Systems
- Section 8 System Analysis Methods
- Chapter 2 Time Domain Analysis of Continuous-Time System
- Section 1 Time Domain Analysis Methods of Linear Systems
- Section 2 Traditional Methods to Solve System Differential Equations
- Section 3 Zero-Input Response and Zero-State Response
- Section 4 Equivalent Conversion of Initial State and Excitation Source
- Section 5 Impulse Response and Step Response
- Section 6 Convolution
- Section 7 Properties of Convolution
- Chapter 3 Fourier Transform
- Section 1 Introductions
- Section 2 Fourier Series Analysis of Periodic Signals (Part 1)
- Section 2 Fourier Series Analysis of Periodic Signals (Part 2)
- Section 3 Fourier Series of Common Periodic Signals
- Section 4 Fourier Transform
- Section 5 Fourier Transform of Common Aperiodic Signals
- Section 6 Fourier Transform of Impulse Function and Step Function
- Section 7 Basic Properties of Fourier Transform (Part 1)
- Section 7 Basic Properties of Fourier Transform (Part 2)
- Section 7 Basic Properties of Fourier Transform (Part 3)
- Section 8 Convolution Properties (Convolution Theorem)
- Section 9 Fourier Transform of Periodic Signals
- Section 10 Fourier Transform of Sampling Signals (Part 1)
- Section 10 Fourier Transform of Sampling Signals (Part 2)
- Section 11 The Sampling Theorem
- Section 12 Applications of Fourier Transform
- Chapter 4 The Laplace Transform and the s-Domain Analysis of Continuous-Time Systems
- Section 1 Introductions
- Section 2 Definition of the Laplace Transform and the Region of Convergence
- Section 3 Basic Properties of the Laplace Transform (Part 1)
- Section 3 Basic Properties of the Laplace Transform (Part 2)
- Section 4 The Inverse Laplace Transform
- Section 5 Analyze Circuits Using the Laplace Transform, and s-Domain Element Models
- Section 6 Systems Functions (Network Functions) H(s)
- Section 7 Determine Time Domain Characteristics from Pole-Zero Distribution of System Functions (Part 1)
- Section 7 Determine Time Domain Characteristics from Pole-Zero Distribution of System Functions (Part 2)
- Section 8 Determine Frequency Response Characteristics from Pole-Zero Distributions of System Functions
- Section 9 Pole-Zero Distribution of All-Pass Functions and Minimum Phase Functions
- Section 10 Stability of Linear Systems
- Section 11 The Bilateral Laplace Transform
- Section 12 Relations between Laplace Transform and Fourier Transform
- Chapter 5 Time Domain Analysis of Discrete-Time Systems
- Section 1 Comparisons: Analysis of Discrete-Time Systems and Continuous-Time Systems
- Section 2 Discrete-Time Signals — Sequences (Part 1)
- Section 2 Discrete-Time Signals — Sequences (Part 2)
- Section 2 Discrete-Time Signals — Sequences (Part 3)
- Section 3 Mathematical Models of Discrete-Time System — Difference Equations
- Section 4 Solving Linear Constant-Coefficient Difference Equations (Part 1)
- Section 4 Solving Linear Constant-Coefficient Difference Equations (Part 2)
- Section 5 Unit Sample Response of Discrete-Time System
- Section 6 Convolution (Convolution Sum)
- Section 7 Deconvolution
- Chapter 6 The z-Transform and the z-Domain Analysis of Discrete-Time Systems
- Section 1 Introductions
- Section 2 The Region of Convergence for the z-Transform
- Section 3 Z-Transform and ROCs of Typical Sequences
- Section 4 The Inverse z-Transform
- Section 5 The Basic Properties of the z-Transform (Part 1)
- Section 5 The Basic Properties of the z-Transform (Part 2)
- Section 6 Relationships between the z-Transform and the Laplace Transform
- Section 7 Solving Difference Equations Using the Z-Transform
- Section 8 System Functions of Discrete Systems
- Section 9 The Fourier Transform of Sequences (DTFT)
- Section 10 Frequency Response Characteristics of Discrete-Time Systems
- Chapter 7 The Discrete Fourier Transform
- Section 1 Discreteness and Periodicity of the Fourier Transform
- Section 2 From Discrete Fourier Series (DFS) to Discrete Fourier Transform (DFT)
- Section 3 Properties of the Discrete Fourier Transform (Part 1)
- Section 3 Properties of the Discrete Fourier Transform (Part 2)
- Section 4 Relationship between Discrete Fourier Transform and z-Transform
- Section 5 Fast Fourier Transform (FFT) (Part 1)
- Section 5 Fast Fourier Transform (FFT) (Part 2)
- Chapter 8 Analog and Digital Filter
- Section 1 Basic Concepts of Filters
- Section 2 Design of Analog Low-pass Filters (Part 1)
- Section 2 Design of Analog Low-pass Filters (Part 2)
- Section 2 Design of Analog Low-pass Filters (Part 3)
- Section 3 Design of Analog High-pass, Band-pass, and Band-stop Filters (Part 1)
- Section 3 Design of Analog High-pass, Band-pass, and Band-stop Filters (Part 2)
- Section 3 Design of Analog High-pass, Band-pass, and Band-stop Filters (Part 3)
- Section 4 Design of Digital Filters (Invariant Impulse Response Method)
- Section 5 Design of Digital Filters (Bilinear z-Transform Method)
- Section 6 Design of Digital High-pass, Band-pass and Band-stop filters
- Section 7 Design of FIR DR Using Window Function (Part 1)
- Section 7 Design of FIR DR Using Window Function (Part 2)
- Final Examination for Spring 2023
Taught by
Qin Gong
