电子科大课堂讲义课堂版信号 (2)ppt课件

1、 Chapter 9 The Laplace Transform Chapter 9 The Laplace Transform9.1 The Laplace Transform dtethsHstste stesH Defining dtetxsXst Laplace Transform F tetxsX Dirichlet Condition 1 : dtetxt ROC0 jssXjX Chapter 9 The Laplace Transform sDsNsX 0sDPoles: 0sNZeros:1. The direction of signals2. The position o

2、f polesROC of X(s)9.2 The Properties of ROC Chapter 9 The Laplace TransformstuL1 0sRe 1Lt sRe1. stuL1 0sRe2.astueLat1 asRe astueLat1 asRe3.Basic Laplace Transform-Pairs Chapter 9 The Laplace TransformExample 9.8 211sssXj12j21 2Res 1Re2sj12 1Resleft sidedtwo sidedright sided Chapter 9 The Laplace Tra

3、nsform9.3 The Inverse Laplace TransformExample 9.9 211sssXDetermine the inverse Laplace transform for all possible ROC. 1Re s tuetuetxtt2 1Re2 s tuetuetxtt2 2Re s tuetuetxtt2 Chapter 9 The Laplace Transform9.5 Properties of the Laplace Transform9.5.1 Linearity of the Laplace Transform sbXsaXtbxtaxL2

4、121 sXtxL111RRoc sXtxL222RRoc 21RRRoc Chapter 9 The Laplace Transform9.5.2 Time Shifting 0L0stesXttx sXtxLRRoc RRoc Example kTttxk 0 1Lt sRe LskTekTt sRe kTtk 0ksTke0LsTe11Poles:10 , 2,kTkjsk jpole-zero plotTj2Tj2 sXtxL Chapter 9 The Laplace Transform9.5.3 Shifting in s-Domain 0L0ssXetxtsRRoc 0Re sR

5、RocROC的边境平移的边境平移 202L0cos sstut 0Res 2020L0sin stut 0Res Chapter 9 The Laplace Transform9.5.4 Time Scaling sXtxLRRoc asXaatx/1LaRRoc sXtxLRRocWhen 1a asastueLatRe 1 1astueLat 1as as Re Chapter 9 The Laplace Transform9.5.5 Conjugation sXtxLRRoc sXtxLRRoc txtx sXsX9.5.6 Convolution Property sXtxL111RR

6、oc sXtxL222RRoc sXsXtxtxL212121RRRoc Chapter 9 The Laplace Transform9.5.7 Differentiation in the Time Domain sXtxLRRoc RRoc ssXdttdxL 0Re 1sstuL stutLRe 1 Chapter 9 The Laplace Transform10t tx2468Example Determine sX10 tx12t txtxtx21 sXsXsXL210246t1 tx2 222121ssseeX sse 0Res9.5.8 Differentiation in

7、the s-Domain Chapter 9 The Laplace Transform sXtxLRRoc RRoc dssdXttxL 21astuteLat asRe 32121astuetLat asRe Chapter 9 The Laplace TransformExample 11tuettxatDetermine sX 1tuettxatass11 dssdX sassXlnln sassX lnPoles:ass , 0 as, 0maxRe Chapter 9 The Laplace Transform9.7 Analysis and Characterization of

8、 LTI Systems Using the Laplace Transform ty th sH sY tx sX thtxty sHsXsY sHSystem Function or Transfer Function9.7.1 CausalityCausal maxRe sROC Chapter 9 The Laplace TransformFor a system with a rational system function,causal maxRe sROC9.7.2 Stability (稳定性稳定性Stable system: dtth dtetht when0stableax

9、isjROCconverges sH Chapter 9 The Laplace TransformExample 9.20 211ssssHj21j21j21 2Re asCausal , unstable system 2Re1 bs-noncausal , stable system 1Re csanticausal , unstable system反因果反因果系统因果、稳定系统因果、稳定 Chapter 9 The Laplace Transform sH的极点均在的极点均在 轴左侧，轴左侧，且且j maxRes假设假设 为有理函数为有理函数 sHStability of Causa

10、l SystemConsider the following causal systems 11 assHStable 211 bsssHunstable Chapter 9 The Laplace Transform9.7.3 LTI Systems Characterized by Linear Constant-Coefficient Differential Equations sXsbsYsakkMkkkNk 00 kkMkkkkNkkdttxdbdttyda00 ROCkkNkkkMksasb00 sXsYsHA ratio of polynomials in s Chapter

11、9 The Laplace TransformExample 9.25Consider an LTI system with input ,Output , determine the system function. tuet xt 3 tueet ytt 2 312sH sss -s1ReExample Consider a causal LTI system , tbutuethdttdht42 . 2 t-etyt-etxtt 61 . 122bunknown constantDetermine the system function and b. sH Chapter 9 The L

12、aplace Transform 42sssH 0ResThe system is unstable. Chapter 9 The Laplace TransformExample 9.26 An LTI system: 1. The system is causal. 2. is rational and has only two poles: s= - 2 and s=4. 3. 4. Determine 01tytx sH 40h sHExample 9.26 An LTI system: 1. The system is causal. 2. is rational and has o

13、nly two poles: s=-2 and s=-4. 3. 4. Determine 01tytx sH 40h sH 424ssssH 4Res Chapter 9 The Laplace TransformExample 9.27 知一因果稳定系统，知一因果稳定系统， 为有理函数，有一极点为有理函数，有一极点在在s=-2处，原点处，原点s=0处没有零点，其他零极点未知，处没有零点，其他零极点未知，判别以下说法能否正确。判别以下说法能否正确。 sH1. 的傅立叶变换收敛。的傅立叶变换收敛。 teth3 dtetht3 sH在在 收敛收敛3 2. 0dtth 00ssH3. 为一因果稳定

14、系统的单位冲激呼应。为一因果稳定系统的单位冲激呼应。 tth4. 至少有一个极点。至少有一个极点。 dttdh5. 为有限长度信号。为有限长度信号。 th Chapter 9 The Laplace Transform 0, 0tth 0, 0ttth dssdHtthLROC不变不变 ssHdttdhL 21, 0TtTtth ssHLRe Chapter 9 The Laplace Transform6. sHsH在在s=-2处有极点处有极点在在s=+2处有极点处有极点7. 2limsHs无法判别正确与否。无法判别正确与否。9.8 LTI 系统的方框图信号流图表示系统的方框图信号流图表示1

15、 kkkovHgk前向通路的序号前向通路的序号gk第第k条前向通路的增益条前向通路的增益k去掉第去掉第k条前向通路后条前向通路后,余下的子流图的特征行列式余下的子流图的特征行列式信号流图的特征行列式信号流图的特征行列式 Chapter 9 The Laplace Transform一一 Mason 增益公式增益公式Example 9.31 2224632ssH sss sXs/1s/12324 sY6 Chapter 9 The Laplace Transform1L2L Chapter 9 The Laplace Transform二二 系统的方框图信号流图模拟系统的方框图信号流图模拟两个根本商定：两个根本商定：1. 假定一切的环路均相互接触；假定一切的环路均相互接触；iiL12. 假定每一前向通路与一切的环路相互接触；假定每一前向通路与一切的环路相互接触；1kiikkkkkLggHov11 Chapter 9 The Laplace TransformExample Consider the causal LTI system 53142ssssssH 3232/15/23/91/8/6/1sssssssH1. 直接模拟直