英文版《信号与系统》第2章讲义（课件）

1,Consider an LTI system whose response to the signal inFigure (a) is the signal illustrated in Figure (b). Determine and sketch carefully the response of the system to the input depicted in Figure (c).,2,3,Sketch the following signals: (a) (b),(a),4,Chapter 2,Linear Time-invariant Systems,5,Consider a linear time-invariant system,Example 1,6,2.1 Discrete-time LTI Systems : The Convolution Sum（卷积和）,1. The Representation of Discrete-Time Signalsin Terms of impulses,Sifting Property,离散时间信号的冲激表示,2. The Unit Impulse Responses单位冲激响应,7,Convolution-Sum （卷积和）,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,3. 卷积和的计算, 图解法,普通乘法因果序列或有限长度序列之间的卷积,8,Example 3,Determine,Solution,3142hn,215xn,1552010,3142,6524132210,yn= 6 , 5 , 24 , 13 ,22 , 10 n=0,1,2,3,4,5,9, 多项式算法（适用于有限长度序列）,yn= 6 , 5 , 24 , 13 ,22 , 10 n=0,1,2,3,4,5,利用多项式算法求卷积和的逆运算,已知 yn 、hn xn已知 yn 、xn hn,10,Example 4,Determine xn,yn= 6 , 5 , 24 , 13 ,22 , 10 n=0,1,2,3,4,5,11,2.2 Continuous-Time LTI Systems : The Convolution Integral （卷积积分）,1. The Representation of Continuous-Time Signalsin Terms of impulses,Sifting Property,For example:,12,Convolution Integral卷积积分,时刻的冲激,t 时刻的响应,2.3 卷积的计算,一 由定义计算积分,2. The Convolution Integral,13,二 图解法,14,15,2.3 Properties of LTI Systems,LTI系统的特性可由单位冲激响应完全描述,2.3.1 Properties of Convolution Integral and Convolution Sum,1. The Commutative Property (交换律）,16,2. The Distributive Property (分配律）,17,3. The Associative Property (结合律）,18,4. 含有冲激的卷积,19,5. 卷积的微分、积分性质,20,Example,Solution 1,21,Solution 2,22,Example Consider the convolution of the two signals,23,6 几种典型系统, 恒等系统, 微分器, 积分器, 延迟器, 累加器,24,2.3.4 LTI Systems with and without Memory,1. Discrete-time System,It is memoryless,An LTI system without memory,2. Continuous-time System,An LTI system without memory,25,2.3.5 Invertibility of LTI SystemsLTI系统的可逆性,26,2.3.6 Causality for LTI SystemsLTI系统的因果性,1. Discrete-time System,Causal system,2. Continuous-time System,27,2.3.7 Stability for LTI Systems (稳定性）,1. Discrete-time System,absolutelySummable 绝对可加,2. Continuous-time System,absolutelyIntegrable绝对可积,28,2.3.8 The Unit Step Response of an LTI SystemsLTI系统的单位阶跃响应,Discrete-time System,Continuous-time System,Unit Step Response,Unit Step Response,29,作业：,2.1 2.5 2.102.7 2.11 2.12 2.22 (a) (c)2.20 2.23 2.40 2.46 2.47,30,31,(c) S is time-varying.,32,33,Solution ：,34,If a=1， contains only threediscontinuities.,35,36,2.20. Evaluate the following integrals:,37,38,Or,39,40,41,42,43,Solution ：,the impulse response,44,45,We have not enough information to determine the output,46,47,Find the i