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首页 信号与系统 Chapter6 the Z-Domain Analysis for Discret…

信号与系统 Chapter6 the Z-Domain Analysis for Discrete-Time Signal and System.ppt

信号与系统 Chapter6 the Z-Domain Ana…

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2019-06-20 0人阅读 举报 0 0 暂无简介

简介:本文档为《信号与系统 Chapter6 the Z-Domain Analysis for Discrete-Time Signal and Systemppt》,可适用于综合领域

ChaptertheZDomainAnalysisforDiscreteTimeSignalandSystemξTheZTransformDefinexs(t)fs(t)f(t)∵∴TheRegionofConvergenceExf(k)=ε(k)ε(k)F(z)=ROCResult:ROC:<|Z|<∞Exf(k)=akε(k)F(z)=ROCResult:ROC:|z|>|a|Exf(k)=akε(k)F(z)=ROCResult:ROC:|z|<|a|ExF(z)=ROCResult:ROC:|a|<|z|<|b|ROC:)iff(k)isfiniteduration<|Z|<∞(notincludeZk<|Z|<=∞notincludeZk<=|Z|<∞))f(k)ε(k)|Z|>|a|)f(k)ε(k)|Z|<|b|)f(k)ε(k)f(k)ε(k)|a|<|Z|<|b|SomeCommonZTransformSignalTransformROCδ(k)ALLZε(k)(Z)|Z|>ε(k)|Z|<∞δ(km)m>Zm|Z|≠δ(km)m>Zmakε(k)(aZ)|Z|>|a|akε(k)|Z|<|a|(Z)|Z|<(aZ)ξPropertiesofTheZTransformLinearityTimeShiftingaf(k)bf(k)→aF(Z)bF(Z)Exf(k)=k[ε(k)ε(k)]F(z)=ROCResult:ScalingintheZDomainEx:F(z)=ROCResult:f(k)=kε(k)Zkf(k)TimeReversalEx:f(k)=kε(k)F(z)=ROCResult:TimeExpansionConjugationConvolutionPropertyEx:F(Z)=f(k)=Result:y(k)=f(k)*h(k)|z|>DifferentiationintheZDomainEx:f(k)=k(k)akε(k)F(Z)=Result:|z|>|a|TheInitialValueTheoremIff(k)=k<N(N=)TheFinalValueTheoremIff(k)=k<NROCinclude|Z|=Z{f(k)f(k)}=(Z)F(z)Ex:Result:f()=f()=f(∞),=f(∞)=)|z|>Error)|z|>TheInverseZTransformm=m≠APartialFractionExpansion|Z|>|Zi||Z|<|Zi||Z|<|Zi||Z|>|Zi||Z|>|Zi||Z|<|Zi|Ex:f(k)=Result:Ex:Result:f(k)=Ex:Result:f(k)=PowerSeriesExpansionIff(k)=f(k)ε(k)(|Z|>|a|)Iff(k)=f(k)ε(k)(|Z|<|a|)Iff(k)=f(k)ε(k)f(k)ε(k)(|b|>|Z|>|a|)Ex:|z|>f(k)=Result:f()=f()=f()=…f(k)=(k)ε(k)Ex:|z|<f(k)=Result:f()=f()=f()=…f(k)=(k)ε(k)Ex:Result:f(k)=f()=f()=f()=…f(k)=()kε(k)f()=f()=f()=…f(k)=()kε(k)f(k)=()kε(k)()kε(k)ξGeometricEvaluationoftheFourierTransformfromthePoleZeroPlot|z|>Ex:Result:FirstOrderSystemh(k)=akε(k)|Z|>|a|SecondOrderSystem≤θ≤π<r<ξAnalysisandCharacterizationofLTISystemUsingZTransformLTI:iff(k)=ZkROCinclude|Z|=SystemFrequencyResponseCausalitya)h(n)=ifn<b)H(Z)ifandonlyifROC:|Z|>|a|Exteriorofacircle(includeinfinity)c)H(Z)isRational,ifandonlyifROCisoutsideoutermostpoleandnumerator<=denominatorEx:)|z|>)∞>|z|>CausalResult:)CausalNoncausal)Stabilitya)b)H(Z)ifandonlyifROC:include|Z|=c)H(Z)CausalityandRational,ifandonlyifallpolesinsidetheunitcircleEx:)|z|>)|z|<)<|z|<CausalStableLTISystemsCharacterizedbyLinearConstantCoefficientDifferenceEquationsa)y(k)ay(k)=f(k)bf(k)Y(Z)aZY(Z)=F(Z)bZF(Z)b)y(k)ay(k)ay(k)=f(k)bf(k)bf(k)Ex:y()=,y()=,h(n)=y(n)=Result:x(n)=()nε(n)h(n)=()nε(n)ε(n)yx(n)=C()nC=yf(n)=()nε(n)ε(n)y(n)=()nε(n)ε(n)Ex:LTIf(n)=()nε(n)y(n)=(a()n()n)ε(n)f(n)=()ny(n)=()n)H(Z)=)DifferenceEquationsResult:y(n)=()n=H(z)(z)n|z=H()=a=y(n)y(n)y(n)=f(n)f(n)f(n)ξBlockDiagramRepresentationsa)b)ξTheUnilateralZTransforma)k<k>=b)Ex:y()=,y()=,y(n)=Result:x(n)=()nε(n)Y(z)(zY(z)y())(zY(z)zy()y())=X(z)zX(z)y()==y(n)=()nε(n)

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信号与系统 Chapter6 the Z-Domain Analysis for Discrete-Time Signal and System

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