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1、ImplementationofFastFourierTransform(FFT)onFPGAusingVerilogHDLAnAdvanced-VLSI-Design-Lab(AVDL)Term-Project,VLSIEngineeringCourse,Autumn2004-05,Deptt.OfElectronics&ElectricalCommunication,IndianInstituteofTechnologyKharagpurUndertheguidanceofProf.Swapn
2、aBanerjeeDeptt.OfElectronics&ElectricalCommunicationEngg.IndianInstituteofTechnologyKharagpur.SubmittedbyAbhishekKesh(02EC1014)ChintanS.Thakkar(02EC3010)RachitGupta(02EC3012)SiddharthS.Seth(02EC1032)T.Anish(02EC3014)1ACKNOWLEDGEMENTSItiswithgreatrever
3、encethatwewishtoexpressourdeepgratitudetowardsourVLSIEngineeringProfessorandFacultyAdvisor,Prof.SwapnaBanerjee,DepartmentofElectronics&ElectricalCommunication,IndianInstituteofTechnologyKharagpur,underwhosesupervisionwecompletedourwork.Herastuteguidan
4、ce,invaluablesuggestions,enlighteningcommentsandconstructivecriticismalwayskeptourspiritsupduringourwork.WewouldbeaccusedofingratitudeifwefailedtomentiontheconsistentencouragementandhelpextendedbyMr.KailashChandraRay,GraduateResearchAssistant,duringou
5、rTerm-Projectwork.ThebrainstormingsessionsatAVDLspentdiscussingvariouspossiblearchitecturesfortheFFTwereveryeducativeforusnoviceVLSIstudents.Ourexperienceinworkingtogetherhasbeenwonderful.Wehopethattheknowledge,practicalandtheoretical,thatwehavegained
6、throughthistermprojectwillhelpusinourfutureendeavoursinthefieldofVLSI.AbhishekKeshChintanS.ThakkarRachitGuptaSiddharthS.SethT.Anish21.FASTFOURIERTRANSFORMSThenumberofcomplexmultiplicationandadditionoperationsrequiredbythesimpleformsboththeDiscreteFour
7、ierTransform(DFT)andInverseDiscreteFourierTransform2(IDFT)isoforderNasthereareNdatapointstocalculate,eachofwhichrequiresNcomplexarithmeticoperations.Forlengthninputvectorx,theDFTisalengthnvectorX,withnelements:2Incomputersciencejargon,wemaysaytheyhave
8、algorithmiccomplexityO(N)andhenceisnotaveryefficientmethod.Ifwecan'tdoanybetterthanthisthentheDFTwillnotbeveryusefulforthemajorityofpracticalDSPapplications.However,thereareanumberofdifferent'FastFourierTransform'(FFT)algorithmsthatenabletheca