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1、NumericalFourierTransformsDFTandFFTLeventSevgiDOGUSUniversity,ElectronicsandCommunicationEngineeringDepartmentZeametSokak,No21,Acıbadem,Istanbul,Turkey,lsevgi@dogus.edu.trAbstract-FrequencyanalysisisoneofthekeyissuesintheIEEESociety.Usingcomputersinnumericalcalculationsmean
2、smovingintoanon-physical,syntheticenvironment.Numerically,discreteorfastFouriertransformations(DFTorFFT)areusedtoobtainthefrequencycontentsofatimesignalandthesearetotallydifferentthanmathematicaldefinitionoftheFouriertransform.ThisarticlesimplereviewsDFTandFFTwithcharacteri
3、sticexamples.1.IntroductionTheanalysisofrealworldsignalsisafundamentalproblemformanyengineersandscientists,especiallyforelectricalengineerssincealmosteveryrealworldsignalischangedintoelectricalsignalsbymeansoftransducers,e.g.,accelerometersinmechanicalengineering,EEGelectro
4、desandbloodpressureprobesinbiomedicalengineering,seismictransducersinEarthSciences,antennasinelectromagnetics,andmicrophonesincommunicationengineering,etc.Traditionalwayofobservingandanalyzingsignalsistoviewthemintimedomain.BaronJeanBaptisteFourier[1],morethanacenturyago,sh
5、owedthatanywaveformthatexistsintherealworldcanberepresented(i.e.,generated)byaddingupsinewaves.Sincethen,wehavebeenabletobuild(breakdown)ourrealworldtimesignalintermsof(into)thesesinewaves.Itisshownthatthecombinationofsinewavesisunique;anyrealworldsignalcanberepresentedbyon
6、lyonecombinationofsinewaves[2].TheFouriertransform(FT)hasbeenwidelyusedincircuitanalysisandsynthesis,fromfilterdesigntosignalprocessing,imagereconstruction,stochasticmodelingtonon-destructivemeasurements.TheFThasalsobeenwidelyusedinelectromagneticsfromantennatheorytoradiowa
7、vepropagationmodeling,radarcross-sectionpredictiontomulti-sensorsystemsystemdesign.Forexample,thesplit-stepparabolicequationmethod(whichisnothingbutthebeampropagationmethodinoptics)hasbeeninusemorethandecadesandisbasedonsequentialFToperationsbetweenthespatialandwavenumberdo
8、mains.Twoandthreedimensionalpropagationproblemswithnon-flatrealisticterrainprofile