Signals and Systems

Overview

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.

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)