参考文献-有限长序列卷积和求解法

3012008M20JOURNALOFEEEVol.30No.1Feb.2008KpE李昌利(广东海洋大学信息学院,广东湛江524088)l:2007-08-05;:2007-08-06Te:(1976-),3,V,=,1VY|)T,E-mail:K1:e74ZE9K,S=BtNCdbYBZE,Ocb,L=q31beZE,3T4|Eb1oM:|d;pE;E;|E;TVUEms|:TN911.7DSM:AcI|:1008-0686(2008)01-0045-03MethodsforCalculatingTwoFinitelyLongSeriesLIChang-li(SchoolofInformationEngineering,GuangdongOceanUniversity,Zhanjiang524088,China)Abstract:Afewsimpleandintuitionisticmethodscanbeusedtocalculatetwofinitelylongseries,buttherearenoanysystemicintroductiontotheminsomedomestictextbooks.Afewtextbooksinvovleonemethodbutitisindistinctlydiscussed,soitisdifficultforteacherstoillustrateandforstudentstostudy.Thispaperaimsatconciseandclearintroductiontofourmethodsincludingonebroughtforwardbytheauthor,whichisnamedsumofserialnumbersmatchingmethod.Keywords:signalsandsystems;convolutionsum;columnsummethod;slidingstripmethod;sumofserialnumbersmatchingmethod;polynomialexpressionmethod0pHWLHMdbTXdYh(n),5ie(n)Yr(n)h(n)e(n)()bVnHpHWLHMdYVbx1(n)x2(n)l:x1(n)*x2(n)=Em=-x1(m)x2(n-m)(1)HWB,9KZElTp,6BZEmEbB|d,KZE,b7L=,1)K,ZL7eZEpbS=7,L,9b3M8,W%ZE,9eB3T4ZE)|Eb1K+pE/x1(n)=25|04x2(n)=4|13b1.1pEpE,pBD(n)VU,x1(n)=Emx1(m)D(n-m)(2)InD(n-m)*x2(n)=x2(n-m)(3)V7x1(n)*x2(n)=Emx1(m)D(n-m)*x2(n)=Emx1(m)x2(n-m)(4)Vx1(n)*x2(n)Tx2(n)MFx2(n-m),x1(m)b,x1(n)VVUx1(n)=2D(n+1)+5D(n)+4D(n-2)V7x1(n)*x2(n)=2D(n+1)+5D(n)+4D(n-2)*x2(n)=2x2(n+1)+5x2(n)+4x2(n-2)89VV1VUbx2(n)S|,2x2(n+1)S|-1,VKBS|bH1iM,5x2(n)S|2x2(n+1)v1,H17S;4x2(n-2)S|2x2(n+1)v3,H37SbV3-5MFTpx1(n)*x2(n)=822|1131412V1pEpLx1(n)x2(n)25044132D(n+1)*x2(n)=2x2(n+1)5D(n)*x2(n)=5x2(n)4D(n-2)*x2(n)=4x2(n-2)8262051516412x1(n)*x2(n)=2x2(n+1)+5x2(n)+4x2(n-2)8221131412|-1012341.2EQx2(n)x2(-n),|x2(-n)MPKBx1(n)Sb,x2(-n)BQMB,px1(n),|bEHQiPV%bEL=n9V,Vm1EpLx1(m)x2(n-m)z7S,KsbpV,Mx1(m),x2(n-m)bp,px1(m)x2(n-m)btp,lTmpbNVn,ELlmEbS|,7SH8|n=-1+0=-1,GQ9B|bKTx1(n)*x2(n)=822|11314121.3|EInlT(1),lTmpBx1(m)x2(n-m)b%n,mMH,x1(m)x2(n-m)x1(m)x2(n-m)|(n-m)+m=n,MnOm1,|M,|E?bx1(n)d,|l1=-1012;x2(n)d,|l2=012bx1(n)*x2(n)d,|ll1l2sYMFTblKll1l2Kl,lKvl1l2Kv,S|S|,|bl1l2|MFTk,5y(k)t|b1l10a1a2sYl22a1a0MF2,y(2)=x1(0)x2(2)+x1(1)x2(1)+x1(2)x2(0)=53+01+44=15+16=31V24B9Lb1-2,|=|b3-5l|=|,|MBbVVA,3-5Bx2(n)BGQx1(n)46030,HBGQMBbBKTbV2|pL1.4TVUEKTVU,BKeZE,T,Q|b1,TVUx1(n)x1(z)=2z-1+5+4z2TVUx2(n)x2(z)=4+z+3z25x1(n)*x2(n)TVUx1(z)x2(z),x1(z)x2(z)=8z-1+22+11z+31z2+4z3+12z4TTBT,BQ|bV7x1(n)*x2(n)=822|1131412VUTQ|,pTV|MFa|MiV,NVnZE|ELBb2eK9ZE,34|EbpEBVU,7Bde;ElT,PQMV%,LmE;%n,|ElT|M,|MMFV|n;TpETVU,|TQVU,pTV|MFaMa|MiV,ZE|ELBbS=KpE,eB|EZE,89Vbd+ZE,mbID:1,),.|d(=)M.:,2000.2AshokAmbardar,pVr.|ad|)M.:,2001.3.|dM.:bv,2004.45,1a.|Ld()M.:,1992.5vI.|Lds()M.:,1998.(上接第40页贾君霞文)4|N=210=1024,MatlabI4-5bTV,4yE1.dyEy|2,7H.dyEMbID:1M.Vetterli,0RunningFIRandIIRfilteringusingmultiplybanks,0IEEETrans.Acoust.,Speech,SignalProcess.,vol.34.pp.730-738,May1988.2I.LinandS.K.Mitra,0Overlappedblockdigitalfiltering0,IEEETrans.CircuitsSyst.II,vol.43,no.8,pp.586-596,Aug.1996.3P.P.Vaidyanathan,MultirateSystemsandFilterBanks.F.Cliffs,NJ:Prentice-Hall,1993.4J.W.Cooley,P.A.W.Lewis,andP.D.Welch,0thefastFou-riertransformalgorithm:Programmingconsiderationsinthecalculationofsine,cosine,andLaplacetransforms,0J.SoundVibr.,vol.12.pp315-337,Jul.1970.5L.R.RabinerandC.M.rader,Eds.,0Thefas