数字信号处理a(双语)chapter6-ztransforma

Chapter6,z-Transform,Chapter6z-Transform,PartA:z-TransformPartB:TheInversez-Transformandz-TransformTheoremsPartC:Convolution(卷积)PartD:TheTransferFunction,Introduction6.1Definition6.2Rationalz-Transforms(有理z变换)6.3RegionofConvergence（收敛域）ofaRationalz-Transform,PartA:z-Transform,PartA:Introduction,TheDTFTprovidesafrequency-domain(频域)representationofdiscrete-timesignalsandLTI（线性时不变）discrete-timesystems.Becauseoftheconvergencecondition,inmanycases,theDTFTofasequencemaynotexist.Asaresult,itisnotpossibletomakeuseofsuchfrequency-domaincharacterizationinthesecases.,PartA:Introduction,Ingeneral,ZTcanbethoughtofasageneralizationoftheDTFT.ZTismorecomplexthanDTFT(bothliterallyandfiguratively),butprovidesagreatdealofinsightintosystemdesignandbehavior.Fordiscrete-timesystems,ZTplaysthesameroleofLaplace-transformdoesincontinuoustimesystems.ZTcharacterizessignalsorLTIsystemsincomplexfrequencydomain（复频域）.,6.1Definitionofz-Transform,6.1Definitionofz-Transform,6.1Definitionofz-Transform,6.1Definitionofz-Transform,6.1Definitionofz-Transform,6.1Definitionofz-Transform,6.1Definitionofz-Transform,6.1Definitionofz-Transform,6.1Definitionofz-Transform,6.1Definitionofz-Transform,6.1Definitionofz-Transform,6.1Definitionofz-Transform,6.1Definitionofz-Transform,6.1Definitionofz-Transform,Table6.1Somecommonlyusedz-transformpairs,Introduction6.1Definition6.2Rationalz-Transforms(有理z变换)6.3RegionofConvergence（收敛域）ofaRationalz-Transform,PartA:z-Transform,6.2Rationalz-Transform,6.2Rationalz-Transform,6.2Rationalz-Transform,6.2Rationalz-Transform,6.2Rationalz-Transform,6.2Rationalz-Transform,6.2Rationalz-Transform,6.2Rationalz-Transform,零极点共轭成对出现、收敛域内无极点需注意的是：求解零、极点时，为避免遗漏，需先将Z变换有理分式的分子和分母都转换成Z的正数次幂，再进行求解，详见第26页PPT。,Introduction6.1Definition6.2Rationalz-Transforms(有理z变换)6.3RegionofConvergence（收敛域）ofaRationalz-Transform,PartA:z-Transform,6.3Regionofconvergenceofarationalz-Transform,6.3Regionofconvergenceofarationalz-Transform,6.3Regionofconvergenceofarationalz-Transform,6.3Regionofconvergenceofarationalz-Transform,6.3Regionofconvergenceofarationalz-Transform,有限长序列的Z变换,有限长序列的Z变换,例1：序列x（n）=（n）的Z变换由于n1=n2=0，其收敛域为整个闭域Z平面，0|Z|,例2：矩形序列x（n）=RN（n）有限项等比级数求和,6.3Regionofconvergenceofarationalz-Transform,6.3Regionofconvergenceofarationalz-Transform,Z变换的收敛域包括点是因果序列的特征。,6.3Regionofconvergenceofarationalz-Transform,6.3Regionofconvergenceofarationalz-Transform,6.3Regionofconvergenceofarationalz-Transform,6.3Regionofconvergenceofarationalz-Transform,6.3Regionofconvergenceofarationalz-Transform,Z变换收敛域的特点：收敛域是一个圆环，有时可向内收缩到原点有时可向外扩展到，只有序列(n)的收敛域是整个Z平面收敛域内无极点，X(z)在收敛域内每一点上都是解析函数。Z变换表示法：级数形式、解析表达式（注意:函数收敛域，缺一不可）,6.3Regionofconvergenceofarationalz-Transform,6.3Regionofconvergenceofarationalz-Transform,6.3Regionofconvergenceofarationalz-Transform,6.3Regionofconvergenceofarationalz-Transform,where,6.3