《信号与线性系统分析基础 》 课件 第 6 章 离散时间信号与系统的时域分析.ppt

信号与系统SignalsandSystems吉林大学

TheAnalysisofDiscrete-TimeSystemsinthez-Domain

Thez-Transform

Definitionofthez-Transform

Definitionofthez-TransformIntuitionontheRelationbetweenZTandLTLT:Let:

Definitionofthez-TransformDefinitionBilateral(two-sided)z-Transform:Unilateral(one-sided)z-Transform:Thetransformpairnotation:

信号与系统SignalsandSystems吉林大学

Thez-Transform

Commonz-transformpairs

Commonz-transformpairsUnitSampleSequence

Commonz-transformpairsOne-sideExponentialSequencewhereaisarealorcomplexnumber.UnitStepSequence

Commonz-transformpairswhereaisarealorcomplexnumber.

信号与系统SignalsandSystems吉林大学

TheRegionofConvergenceforthez-Transform

DefinitionTheRegionofConvergenceforthez-TransformThesetofallcomplexnumberszsuchthatthesummationontheright-handside convergesiscalledtheregionofconvergence(ROC)ofthez-transformF(z).F(z)converges:f(k)z-kisabsolutelysummable

Finite-durationsequenceTheRegionofConvergenceforthez-Transformf(k)=0,kk1,kk2,k1k2k10，k20： k10，k2?0：k1?0，k20：0|z|?|z|?|z|0Example:

CausalsequenceTheRegionofConvergenceforthez-Transformf(k)=0,k0Example:z-planeak?(k)，aisarealorcomplexnumber.

AnticausalsequenceTheRegionofConvergenceforthez-TransformExample:f(k)=0,k≥0f(k)=-ak?(-k-1)，aisarealorcomplexnumber.

Two-sidedsequenceTheRegionofConvergenceforthez-Transformk=-∞→+∞ 0R1R2?:R1|z|R2 R1R2:ROCdoesnotconverge

TheRegionofConvergenceforthez-TransformROCisboundedbypolesorextendstoinfinity.F(z)isrational:f(k)ROCrightsidedoutsidetheoutermostpole——outsidethecircleofradiusequaltothelargestmagnitudeofthepolesofF(z)leftsidedinsidetheinnermostnonzeropole——insidethecircleofradiusequaltothesmallestmagnitudeofthepolesofF(z)otherthananyatz=0andextendinginwardtoandpossibly