SS1001文档格式.docx
- 文档编号:7852811
- 上传时间:2023-05-09
- 格式:DOCX
- 页数:13
- 大小:73.38KB
SS1001文档格式.docx
《SS1001文档格式.docx》由会员分享,可在线阅读,更多相关《SS1001文档格式.docx(13页珍藏版)》请在冰点文库上搜索。
H(z)=h[n]z-nZ-Transform
∙
X(z)=x[n]z-n
x[n]X(z)
∙AGeneralizationofFourierTransform
fromz=ejtoz=rej
X(rej)=x[n](rej)-n={x[n]r-n}e-jn
Im
FourierTransformofx[n]r-n
unitcirclez=rej
r
z=ej
Re
1
X(z)|z=ej=X(ej)reducestoFourierTransform
-X(z)maynotbewelldefined(orconverged)forallz
-X(z)mayconvergeatsomeregionofz-plane,whilex[n]doesn’thaveFourierTransform
-coveringbroaderclassofsignals,performingmoreanalysisforsignals/systems
∙RationalExpressionsandPoles/Zeros
X(z)=
intermsofz,notz-1
-Pole-ZeroPlots
specifyingX(z)exceptforascalefactor
-
GeometricevaluationofFourier/Z-transformfrompole-zeroplots
X(s)=M
eachterm(zi)or(zj)representedbyavectorwithmagnitude/phase
∙Example:
1st-order
h[n]=anu[n]
H[z]==,|z|>
|a|
pole:
z=a,zero:
z=0
SeeExample10.1,pp.743~744oftext
H(ej)=
SeeFig.10.13,p.764oftext
-GeometricevaluationofFourier/Z-transformfrompole-zeroplots
Example:
2nd-order
h[n]=rnu[n]
H(z)=
poles:
z1=rej,z2=re-j
doublezero:
SeeFig.10.14,p.766oftext
-SpecificationofZ-Transformincludestheregionofconvergence(ROC)
Example:
x1[n]=anu[n]
X1(z)==,|z|>
x2[n]=anu[n1]
X2(z)==,|z|<
z=a,zero:
z=0inbothcases
SeeExamples10.1,10.2,pp.743-745oftext
-x[n]=0,n<
0
X(z)involesonlynegativepowersofzinitially
x[n]=0,n>
X(z)involesonlypositivepowersofzinitially
-polesatinfinityif
degreeofN(z)>
degreeofD(z)
zerosatinfinityif
degreeofD(z)>
degreeofN(z)
RegionofConvergence(ROC)
∙Property1:
TheROCofX(z)consistsofaringinthez-planecenteredattheorigin
-fortheFouriertransformofx[n]r-ntoconverge
|x[n]|r-n<
dependingonr
only,noton
-theinnerboundarymayextendtoincludetheorigin,andtheouterboundarymayextendtoinfinity
∙Property2:
TheROCofX(z)doesn’tincludeanypoles
∙Property3:
Ifx[n]isoffiniteduration,theROCistheentirez-plane,exceptpossiblyforz=0and/orz=
N2
n=N1
x[n]=0,n<
N1,n>
-ifN1<
0,N2>
z=0ROC,z=ROC
ifN10,z=ROC
ifN20,z=0ROC
Property4:
Ifx[n]isright-sided,and{z||z|=r0}ROC,then{z|>
|z|>
r0}ROC
|x[n]|r0-n<
ifN1<
0,z=ROC
N2
Property5:
Ifx[n]isleft-sided,and{z||z|=r0}ROC,then{z|0<
|z|<
x[n]r0-n<
ifN2>
0,z=0ROC
∙Property6:
Ifx[n]istwo-sided,and{z||z|=r0}ROC,thenROCconsistsofaringthatincludes{z||z|=r0}
x[n]=xR[n]+xL[n]
-atwo-sidedx[n]maynothaveROC
∙Property7:
IfX(z)isrational,thenROCisboundedbypolesorextendstoinfinity
∙Property8:
IfX(z)isrational,andx[n]isright-sided,thenROCistheregionoutsidetheoutermostpole,possiblyincludesz=.Ifinadditionx[n]=0,n<
0,ROCalsoincludesz=
∙Property9:
IfX(z)isrational,andx[n]isleft-sided,thenROCistheregioninsidetheinnermostpole,possiblyincludesz=0.Ifinadditionx[n]=0,n>
ROCalsoincludesz=0
SeeExample10.8,pp.756-757oftext
Fig.10.12,p.757oftext
InverseZ-Transform
x[n]r1-n=F-1{X(r1ej)}=X(r1ej)ejnd
x[n]=X(r1ej)(r1ej)nd,d→dz
x[n]=∮X(z)zn-1dz
-integrationalongacirclecounterclockwise,
{z||z|=r1}ROC,forafixedr1
m
i=1
Partial-fractionexpansionpracticallyuseful:
X(z)=
foreachterm
-ROCoutsidethepoleatz=ai→Aiainu[n]
ROCinsidethepoleatz=ai→Aiainu[n1]
-Example:
X(z)==+
ROC={z||z|>
}
x[n]=()nu[n]+2()nu[n]
ROC={z|>
x[n]=()nu[n]2()nu[n1]
ROC={z||z|<
x[n]=()nu[n1]()nu[n1]
SeeExamples10.9,10.10,10.11pp.758-760oftext
∙Power-seriesexpansionpracticallyuseful:
X(z)=x[n]z-n
-right-sidedorleft-sidedbasedonROC
X(z)=
ROC={z||z|>
|a|}
=1+az-1+a2z-2+……
x[n]=anu[n]
ROC={z||z|<
=a-1za-2z2……
x[n]=anu[n1]
SeeExamples10.12,10.13,10.14pp.761-763oftext
∙Knownpairs/propertiespracticallyhelpful
- 配套讲稿:
如PPT文件的首页显示word图标,表示该PPT已包含配套word讲稿。双击word图标可打开word文档。
- 特殊限制:
部分文档作品中含有的国旗、国徽等图片,仅作为作品整体效果示例展示,禁止商用。设计者仅对作品中独创性部分享有著作权。
- 关 键 词:
- SS1001