电子科大讲义课堂信号ch2课件

1、Chapter 2Linear Time-invariant Systems Chapter 2 LTI Systems10 2 4 t1LConsider an linear time-invariant system Example 10 2 t10 1 2 t1L0 2 4 t1-1 Chapter 2 LTI Systems22.1 Discrete-time LTI Systems : The Convolution Sum（卷积和）1. The Representation of Discrete-Time Signalsin Terms of impulsesSifting Pr

2、operty离散时间信号的冲激表示2. The Unit Impulse Responses单位冲激响应 Chapter 2 LTI Systems3Convolution-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 Chapter 2 LTI Systems4Example 3Determine Solution 3142hn215xn1552010314262846524132210y0y1y2y3y4y5yn= 6 , 5 , 24 , 13 ,22 , 10 n=0,1,2,

3、3,4,5 Chapter 2 LTI Systems5 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 Chapter 2 LTI Systems6Example 4Determine xn yn= 6 , 5 , 24 , 13 ,22 , 10 n=0,1,2,3,4,5y(t)0 Chapter 2 LTI Systems72.2 Continuous-Time LTI Systems : The Convolution Integral

4、（卷积积分）1. The Representation of Continuous-Time Signalsin Terms of impulsesSifting Property Chapter 2 LTI SystemsConvolution Integral卷积积分时刻的冲激t 时刻的响应2. The Convolution Integral82.3 卷积的计算一 由定义计算积分例2.6 Chapter 2 LTI Systems二 图解法9 Chapter 2 LTI Systems例2.7 求下列两信号的卷积其余t其余t解：10 Chapter 2 LTI Systems112.3

5、Properties of LTI SystemsLTI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） Chapter 2 LTI Systems122. The Distributive Property (分配律） Chapter 2 LTI Systems13Commutative PropertyAssociative Property3. The Associative Property (结合律） Chapt

6、er 2 LTI Systems144. 含有冲激的卷积 Chapter 2 LTI Systems155. 卷积的微分、积分性质微分积分 Chapter 2 LTI Systems16Example otherwiseotherwiseSolution 10 1 2 3 t0 1 2 3 tIntegral Chapter 2 LTI Systems17Solution 20 1 2 3 t0 1 2 3 t Chapter 2 LTI Systems18Example Consider the convolution of the two signals(1)(1)0 t-1 0 1 t-

7、2 -1 0 1 2 t-2-2 -1 0 1 2 t-2(-2)196 几种典型系统 恒等系统 微分器 积分器 延迟器 累加器 Chapter 2 LTI Systems202.3.4 LTI Systems with and without Memory 1. Discrete-time SystemIt is memorylessAn LTI system without memory2. Continuous-time SystemAn LTI system without memory Chapter 2 LTI Systems212.3.5 Invertibility of LTI

8、 SystemsLTI系统的可逆性System Inverse System identity system (恒等系统） Chapter 2 LTI Systems222.3.6 Causality for LTI SystemsLTI系统的因果性1. Discrete-time System与n时刻以后输入有关 Causal system2. Continuous-time System Causal system Chapter 2 LTI Systems232.3.7 Stability for LTI Systems (稳定性）1. Discrete-time System Stab

9、le SystemabsolutelySummable 绝对可加2. Continuous-time System Stable SystemabsolutelyIntegrable绝对可积 Chapter 2 LTI Systems242.3.8 The Unit Step Response of an LTI SystemsLTI系统的单位阶跃响应Discrete-time SystemContinuous-time SystemUnit Step ResponseUnit Step Response Chapter 2 LTI Systems25作业：2.1 2.5 2.102.7 2.

10、11 2.12 2.22 (a) (c)2.20 2.23 2.40 2.46 2.47 Chapter 2 LTI Systems262.5Determine the value of N. Chapter 2 LTI Systems272.7 A linear system S has the relationshipbetween its input and output(c) S is time-varying. Chapter 2 LTI Systems28 Chapter 2 LTI Systems292.10 Suppose that(a) Determine(b) If con

11、tains only three discontinuities,what is the value of a?Solution ：0 a 1 1+a t Chapter 2 LTI Systems302.12 LetShow that for Determine the value of A. Chapter 2 LTI Systems312.20. Evaluate the following integrals: Chapter 2 LTI Systems322.22(c)one period of Chapter 2 LTI Systems332.23Determine and ske

12、tch for the following value of T:(a) T=4 (b) T=2 (c) T=3/2 (d) T=1 Chapter 2 LTI Systems340 t (c) T=3/2(a) T=4-5 -4 -3 -1 0 1 3 5 t (d) T=10 t -3 -1 0 1 3 t (b) T=2 Chapter 2 LTI Systems352.40 (a) an LTI system:What is the impulse response for this system? (b) Determine the response of Chapter 2 LTI

13、 Systems362.46 Consider an LTI system S and a signal andIf Determine the impulse response of S. Chapter 2 LTI Systems372.47 An LTI system with impulse response 0 2 t In each of these cases,determinewhether or not we have enough Information to determine the output Chapter 2 LTI SystemsWe have not enough information to determine the output 382.24 Find the impulse responseFind the response of the overall system to the input Chapter 2 LTI Syst