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1、1,CHAPTER 10THE Z-TRANSFORM,2,10.1 The Z-Transform,Eigenfunction特征函数,Eigenvalue(特征值）,Consider a discrete-time LTI system:,3,4,Example,is right sided,is two sided,is left sided,10.2 The Region of Convergence for the Z-Transform,5,Basic Z-Transform pairs:,6,10.3 The Inverse Z-Transform,7,1.Partial-Fra
2、ction Expansion,Solution 1,1,2,Solution 2,8,9,10.5 Properties of the z-Transform,10.5.1 Linearity,10.5.2 Time Shifting,Consider z=0 or z=,10,10.5.3 Scaling in the z-Domain,10.5.4 Time Reversal,11,10.5.6 Conjugation,10.5.7 The Convolution Property,12,10.5.8 Differentiation in the z-Domain,Example 10.
3、17,13,More generally,14,10.7 Analysis and Characterization of LTI Systems using z-Transforms,10.7.1 Causality,A discrete-time system is causal,including infinity.,If is rational function,分子阶数不大于分母阶数,15,Example 10.20,This system is not causal.,Example 10.21,It is a causal system.,16,10.7.2 Stability,
4、A stable system,Example 10.21,The system is causal but not stable.,The system is not causal but stable.,The system is anticausal and not stable.,17,如果 为有理函数,18,10.7.3 Linear Constant-Coefficient Difference Equations,ROC,19,20,21,1.收敛。,2.对某一值有,22,3.为有限长序列,4.为实信号。,无法判断。,23,10.8 System Function Algebra and Block Diagram Representations,Example 10.31 Consider the causal LTI system,(a)direct form,(b)cascade form,(c)parallel form,24,Chap.10:10.2 10.6 10.7 10.9 10.10 10.16 10.18 10.23 10.24 10.27,
