一、Introduction

1. Representation of LTI systems

a. Impulse response: response of system to an impulse
b. Frequency response: response of system to a complex exponential exp(jω) for all possible frequencies f (ω).
c. Transfer function: Laplace transform and Z transform of impulse response

2. Significance of unit impulse

二、DT-LTI：Convolution Sum

1. Output

2. Impulse response of LTI system H

系统的输出是系统对时移脉冲的响应的加权和。

3. Convolution sum

4. Convolution Sum Evaluation Procedure

5. Sequence Convolution Algebra

（1）Commutative Property

（2）Associative Property

（3）Distributive Property

6. Properties of DT-LTI Systems

（1）Memoryless

（2）Stability

（3）Causality

三、CT-LTI：Convolution Integral

1. The Convolution Integral

（1）Output

（2）Impulse response of LTI system H

（3）

2. Convolution Integral Evaluation Procedure

a. 变换变量，画图
b. 分区间，求值
c. 求卷积

3. Interconnections of CT-LTI system

（1）Parallel Connection of CT-LTI system

（2）Cascade Connection of CT-LTI system

4. Convolution Algebra

5. Response to a Step Excitation

6. Properties of CT-LTI system

(1) Systems with/without memory

(2) Causality

(3) Stability

四、Differential and Difference Equation Representations of LTI systems

1. The general form of a linear constant-coefficient differential equation

2. Solving Differential and Difference Equations

3. The Homogeneous Solution (通解)