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1、电子科大课堂讲义课堂版信号10临时Stillwatersrundeep.流静水深流静水深,人静心深人静心深Wherethereislife,thereishope。有生命必有希望。有生命必有希望10.1 The Z-Transform Chapter 10 The Z-TransformEigenfunction特征函数特征函数Eigenvalue (特征值）特征值）Consider a discrete-time LTI system:2 Chapter 10 The Z-TransformZ-planeunit circle3 Chapter 10 The Z-TransformExamp
2、le is right sidedis two sidedis left sided10.2 The Region of Convergence for the Z-Transform4 Chapter 10 The Z-TransformBasic Z-Transform pairs:5 Chapter 10 The Z-Transform10.3 The Inverse Z-Transform6 Chapter 10 The Z-Transform1. Partial-Fraction ExpansionExample 10.9Determine for all possible ROC.
3、Solution 112Solution 27 Chapter 10 The Z-Transform8 Chapter 10 The Z-Transform10.5 Properties of the z-Transform10.5.1 Linearity10.5.2 Time ShiftingConsider z=0 or z=9 Chapter 10 The Z-Transform10.5.3 Scaling in the z-Domain10.5.4 Time Reversal 10 Chapter 10 The Z-Transform10.5.6 Conjugation10.5.7 T
4、he Convolution Property11 Chapter 10 The Z-Transform10.5.8 Differentiation in the z-DomainExample 10.17 12 Chapter 10 The Z-TransformMore generally ,13 Chapter 10 The Z-Transform10.7 Analysis and Characterization of LTI Systems using z-Transforms10.7.1 CausalityA discrete-time system is causalinclud
5、ing infinity.If is rational function,系统因果系统因果分子阶数不大于分母阶数分子阶数不大于分母阶数14 Chapter 10 The Z-TransformExample 10.20This system is not causal.Example 10.21It is a causal system.15 Chapter 10 The Z-Transform10.7.2 StabilityA stable systemA discrete-time system is stableExample 10.21The system is causal but
6、not stable.The system is not causal but stable.The system is anticausal and not stable.16 Chapter 10 The Z-Transform如果如果 为有理函数为有理函数,系统因果、稳定系统因果、稳定的极点均在单位圆内的极点均在单位圆内17 Chapter 10 The Z-Transform10.7.3 Linear Constant-Coefficient Difference EquationsROC18 Chapter 10 The Z-TransformExample 10.26 Suppos
7、e that we are given the following information about an LTI system:2. If ，then the output isDetermine the system function for this system, and deduce the causality and stability of this system.Write the difference equation characterizes the system.19 Chapter 10 The Z-Transform20 Chapter 10 The Z-Tran
8、sformExample 10.27 一具有有理系统函数一具有有理系统函数 的因果、稳定系统，的因果、稳定系统，在在 有一极点，在单位圆上某处有一零点，有一极点，在单位圆上某处有一零点，其余零极点未知，试判断下列说法是否正确。其余零极点未知，试判断下列说法是否正确。1. 收敛。收敛。 2. 对某一对某一值有值有21 Chapter 10 The Z-Transform3. 为有限长序列为有限长序列单位脉冲响应单位脉冲响应5. 是一因果、稳定系统的是一因果、稳定系统的4. 为实信号。为实信号。无法判断。无法判断。22 Chapter 10 The Z-Transform10.8 System Function Algebra and Block Diagram RepresentationsExample 10.31 Consider the causal LTI system(a) direct form(b) cascade form(c) parallel form23Chap.10: 10.2 10.6 10.7 10.9 10.10 10.16 10.18 10.23 10.24 10.27 Chapter 10 The Z-Transform24
