Z Transform(数字信号处理Z变换).pdf

ThThe z-TTransfform 李富才李富才(F(Fucaii Li)Li) ContentContent  IntroductionIntroduction  z-Transform  Zeros and Poles  RegionRegion ofof ConvergenceConvergence  Important z-Transform Pairs  InverseInverse zz-TransformTransform  z-Transform Theorems and Properties  System Function ThThe z-TTransfform IntroductionIntroduction PierrePierre-Simon,Simon, marquismarquis dede LaplaceLaplace Laplace is one of only seventy-two persons to have his name engraved on the Eiffel Tower LaplaceLaplace TransformTransform TheThe LaplaceLaplace transformtransform ofof aa functionfunction xx ((tt):):  X (s)  x (t)est dt 00 Fourier Transform Laplace Transform ExpressesExpresses aa functionfunction oror signalsignal asas aa seriesseries ResolvesResolves aa functionfunction intointo itsits of modes of vibration (frequencies) moments In physics and engineering it is used for analysis of LTI systems such as electricalelectrical circuitscircuits, harmonicharmonic oscillatorsoscillators, opticaloptical devicesdevices, andand mechanicalmechanical systems. In such analyses, the Laplace transform is often interpreted as a transformation from the time-domain to the frequency-domain. The Laplace transform provides an alternative functional description that often simplifies the process of analyzing the behavior of the system TheThe zz TransformTransform TheThe LaplaceLaplace transformtransform ofof aa functionfunction xx ((tt):):  X (s)  x (t)est dt 00 The one-sided z-transform of a function