参考文献-因果移序定理及其应用

3222010M40JOURNALOFEEEVol.32No.2Apr.2010yTM#杨忠根,任蕾,陈红亮(上海海事大学电子工程系,上海200135)l:2009-09-15;:2010-02-06:Zg5|d6B190109002-2009;ZZYv5|d(S)vy!6A027206-08Te:(1946-),3,V,q,1VYYda|),E-mail:(1979-),o,pV3,=,1VYYda|),E-mail:(1974-),3,V,=,1VYYda|)L,E-mail:K1:yTMHazZVrT,yTMdHazZs1TbtVrTPdseb,7OQb#bcW=9Vb#,Es3hbM/|d0LlBb1oM:|d;LHMd;yTM;Zsms|:G424.1DSM:AcI|:1008-0686(2010)02-0032-04CausalShiftTheoremwithItsApplicationsYANGZhong-gen,RENLei,CHENHong-liang(Dept.ofElectronicEng.,ShanghaiMaritimeUniv.,Shanghai200135,China)Abstract:Thetime-domain,z-domainandstateequationexpressionsofcausalshifttheoremaregiveninthispaper.Theimpotentroleofcausalshifttheoreminthetime-domainanalysis,z-domainanalysisandstateequationanalysisofadiscretesystemisshowed.Thesystemanalysisbecomesverysimpleandclear.Theirphysicalmeaningsarealsoclearlyexpressed.Therelationshipamongthechaptersofthetextbookisobviouslygiven.Itisveryhelpfuullforstudentstolearnandtounderstand.thestudiedknowledgethatisprovedbyourteachingexperiencesformanyyears.Keywords:signalandsystem;discreteLTIsystem;causalshifttheorem;stateequationanalysis1yTMdHs,pdY5,pNd:ENk=0aky(n-k)=EMr=0brf(n-r)PnE0(1)SHqyTsf+(n)=f(n)E(n)/YyTsy+(n)=y(n)E(n),a0=1b1,/S/+0VUMyTsbV?C,Hs1-3Vd?S,7OzsCbyTM,XtbL=,T(1)NENk=0aky(n-k)+=ENr=0bry(n-k)+(2),y(n-k)+=y(n-k)u(n)y(n)MkyTs,9TN?bVT(2)i1f+(n)y+(n)sZbyN,AT(2)1yTyTsZ,1s|MyTs|yTsMW1,/yTMbyTMMm0H,y(n-m)+=y+(n-m)+Emk=1y(-k)Dn-(m-k)(3),D(n)b:y(n)MmH,y(-m)y(-1)M0m-1,y(-k)Mm-k,yT19byN,T(3)b+y,m=1,2H,y(n-1)+=y+(n-1)+y(-1)D(n)y(n-2)+=y+(n-2)+y(-1)D(n-1)+y(-2)D(n)(4),PMm0H,y(n+m)+=y+(n+m)-Em-1k=0y(k)D(n+(m-k)(5):y(n)PMmH,y(0)y(m-1)M-m-1,y(k)M-(m-k),yT1byN,T(5)b+y,m=1,2H,y(n+1)+=y+(n+1)-y(0)D(n+1)y(n+2)+=y+(n+2)-y(0)D(n+2)-y(1)D(n+1)(6)yTMyTsMMyTsWsbD41,4?CyTML=1|yTsb2yTMHsT(2)yTM?Sd:ENk=0aky+(n-k)=x(n)(7),x(n)=xzi(n)+xzs(n)(8)xzs(n)=ENr=0brf(n-r)(9)xzi(n)=EMm=1bmEmk=1f(-k)Dn-(m-k)-ENm=1amEmk=1y(-k)Dn-(m-k)(10)TsYrYar,r,byT|H,T(10)Vexzi(n)=-ENm=1amEmk=1y(-k)Dn-(m-k)(11)V,d,Ya,YYsYT(7)VUn?SdYhx(n)r,xzi(n)ar,xzs(n)rYx(n),yzi(n)=hx(n)*xzi(n)yzs(n)=hx(n)*xzs(n)y(n)=hx(n)*x(n)(12)yN,VLTIdrr?Sd),m1Ub,SHqr,xzi(n),|#r,xzs(n),xzi(n)xzs(n)rYx(n)bm1LTIdrr,xzi(n)aibi1,7r,xzs(n)bi1bm1N?SdYhx(n),VT(1)N+Ki|i=1,2,N9hx(n)=Kn1E(n)*Kn2E(n)*,*KnNE(n)(13)T,E(n)b,yTM,/dHsrE:1ENk=0akKN-k=0N+Ki|i=1,2,NT(13)9?SdYhx(n);2T(9)T(10),(11)sY9r,xzs(n)r,xzi(n);3T(12)9,Yyzs(n),Yyzi(n),pYb4?C,rEL=D4332,:yTM#dHsrEb/b3U1pf(n)=E(n)=LTIdy(n)-2.5y(n-1)+y(n-2)=f(n),SHqy(-1)=-1y(-2)=1/,Ya,YYb:d+0.52,yN?SdYhx(n)=0.5nE(n)*2nE(n)=23(2n+1-0.5n+1)E(n)Kn1E(n)*Kn2E(n)=Kn+11-Kn+12K1-K2E(n)xzi(n)=-y(-1)D(n-1)+y(-2)D(n)+2.5y(-1)D(n)=D(n-1)-3.5D(n)xzs(n)=f(n)=E(n),T(12)V,d,Ya,YYsYyzi(n)=hx(n-1)-3.5hx(n)=0.5n+1-2n+2E(n)yzs(n)=E(n)*hx(n)=13(0.5n+2n+3-6)E(n)y(n)=yzi(n)+yzs(n)=23(50.5n-2n+1-3)E(n)2pduC(n+1)UauC(n)+bus(n)(a=1-1/RC,b=1/RC),SuC(0)H,b:d+a,yN?SdYhx(n)=an-1E(n-1),T(6)V,r,xzi(n)=uC(0)D(n+1)b,T(12)V,d,YuC,zi(n)=an-1E(n-1)*uC(0)E(n+1)=anuC(0)E(n)12sYVUMPMf/r,9Vb4yTMzVrT|T(3)T(6)HzM,iy+(n-m)Zz-mY(z),y+(n+m)ZzmY(z),D(n?(m-k)Zz?(m-k),5HzMMy(n-m)+Zz-mY(z)+Emk=1y(-k)z-(m-k)(14)y(n-1)+Zz-1Y(z)+y(-1)y(n-2)+Zz-2Y(z)+z-1y(-1)+y(-2)(15)y(n+m)+ZzmY(z)-Em-1k=0y(k)zm-k(16)y(n+1)+ZzY(z)-zy(0)y(n+2)+Zz2Y(z)-z2y(0)-zy(1)(17)T(14)T(17)yTMzVUTb,Vdzsb5yTMzs3z/s1b:d=sZ|HzM,Y(z)-2.5z-1Y(z)-1+z-2Y(z)-z-1+1=11-z-1PY(z)=Yzi(z)+Yzs(z),Yzs(z)=11-2.5z-1+z-2#11-z-1=1311-0.5z-1+81-2z-1-61-z-1Yzi(z)=z-1-3.51-2.5z-1+z-2=0.51-0.5z-1-41-2z-1|QM,Vd,Y,Y:yzi(n)=(0.5n+1-2n+2)E(n)yzs(n)=13(0.5n+2n+3-6)E(n)MF,VdY:y(n)=23(5#0.5n-2n+1-3)E(n)4A,3zsV1HsVb6yTMsLTIdZZsYX(n+1)=AX(n)+Be(n)(18)r(n)