講義說明教案2012-chapter2ss

1、 2 Linear Time-Invariant SystemsKey points of analysis:Signals postion: basic signal (impulse)Response synthesis: basic response (impuse response)2. Linear Time-Invariant SystemsProblem: 2 Linear Time-Invariant Systems2.1 Discrete-time LTI system: The convolution sum2.1.1 The Representation of Discr

2、ete-time Signals in Terms of ImpulsesIf xn=un, then 2 Linear Time-Invariant Systems 2 Linear Time-Invariant Systems2.1.2 The Discrete-time Unit Impulse Response and the Convolution Sum Representation of LTI Systems(1) Unit Impulse(Sample) Response Unit Impulse Response: hn xn=nyn=hn 2 Linear Time-In

3、variant Systems(2) Convolution Sum of LTI System Solution:Question: n hnn-k hn-kxkn-k xk hn-kxnyn=? 2 Linear Time-Invariant Systems 2 Linear Time-Invariant Systems 2 Linear Time-Invariant Systems( Convolution Sum )Soor yn = xn hn(3) Calculation of Convolution SumTime Inversal: hk h-kTime Shift: h-k

4、hn-kMultiplication: xkhn-kSumming: 2 Linear Time-Invariant SystemsExample 2.2In graphic form, 2 Linear Time-Invariant SystemsIn another form,If 2 Linear Time-Invariant SystemsIn another words,That means ,In tabular form,n: -1 0 1 2 3 -Xn: 3 -2 4 hn: 4 2 -1- 43 4(-2) 44 23 2(-2) 24 -13 -1(-2) -14 -yn

5、= 12 -2 9 10 -4 Xn= 3 -2 4 , hn= 4 2 -1 Example 2.3 2 Linear Time-Invariant SystemsLook at Fig 2.6 “sliding”Example 2 Linear Time-Invariant SystemsSimilar to Ex 2.4Length Length Length 2 Linear Time-Invariant Systems“sliding”“sliding”“sliding” 2 Linear Time-Invariant SystemsSimilar to Ex 2.5 ExampleCongvergence of convolution?Not existedNot existed 2 Linear Time-Invariant SystemsExample 2 Linear Time-Invariant Systems Causal(right-side)Causal(right-side)Causal(right-side)Time-limited Time-limited Time-limited