电子科技大学电子工程学院：《信号与系统》课程教学资源（PPT课件讲稿，英文版）Chapter 2 Linear Time-invariant Systems

Chapter 2 Linear Time-invariant Systems

1 Chapter 2 Linear Time-invariant Systems

Chapter 2 LTI SyStems Example 1 an LtI system fl y 2 t 012t ()=(0)-f(-2) y2t)=y()-y1(t-2) L 1 0 t

2 Chapter 2 LTI Systems Example 1 an LTI system 0 2 t f (t) 1 1 ( ) ( 2) = f 1 t − f 1 t − 0 1 2 t y (t) 1 L 1 ( ) ( 2) = y1 t − y1 t − 0 2 4 t 1 -1 0 2 4 t f (t) 2 1 L y (t) 2 −1

Chapter 2 LTI SyStems 52.1 Discrete-time LTI Systems The Convolution Sum 卷积和) 52.1.1 The Representation of Discrete- Time Signals in Terms of impulses Example 2 xn 1012 xkFn-k ...+x 15a+1]+x0]]+x[]n-1 +∞ x=∑xkn-k k=-00

3 Chapter 2 LTI Systems §2.1 Discrete-time LTI Systems : The Convolution Sum （卷积和） §2.1.1 The Representation of Discrete-Time Signals in Terms of impulses xn=+ x−1 n+1+ x0 n+ x1n−1+ xn xk n k k =  − + =−  xk n− k Example 2 −1 0 1 2 1  2  3 xn n

Chapter 2 LTI SyStems 52.1.2 The Discrete- Time Unit Impulse Responses and the Convolution-Sum Representation of LtI Systems 1. The Unit Impulse Responses 单位脉冲响应 L0,6|n 2. Convolution-Sum(卷积和) y]=∑xkhm-k]=xh k k时刻的脉冲在n时刻的响应 系统在n时刻的输出包含所有时刻输入脉冲的影响 4

4 Chapter 2 LTI Systems §2.1.2 The Discrete-Time Unit Impulse Responses and the Convolution-Sum Representation of LTI Systems 1. The Unit Impulse Responses 单位脉冲响应 h n L n   =  0 ,   2. Convolution-Sum （卷积和） yn xkhn k k =  − + =− 系统在n时刻的输出包含所有时刻输入脉冲的影响 k时刻的脉冲在n时刻的响应 = xnhn

Chapter 2 LTI SyStems 3.卷积和的计算 ①利用定义计算 例23x团]=a"以=x=? ②图解法 Example 2.4 1,0<n<4 a",0≤n≤6 h 0<a<1 0. otherwise 0. othe rwise Determine the output signal yl 5

5 Chapter 2 LTI Systems 3. 卷积和的计算 ① 利用定义计算 例2.3 xn a un n = hn= un xnhn= ? ② 图解法 Example 2.4         = 0 , otherwise 1 , 0 n 4 x n         = 0 , otherwise a , 0 6 n n h n 0  a 1 Determine the output signal yn