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1、UnderstandingtheFFTATutorialontheAlgorithm&SoftwareforLaymen,Students,Technicians&WorkingEngineersAndersE.ZonstV^itrusTressTitusville,FloridaToShirleyivUnderstandingtheFFTACKNOWLEDGEMENTSAspecialthankstoRenee,HeatherandMaureen.Withouttheirhelpyouwouldhavehadtosuffercountlessinstancesofbadgrammar,aw
2、kwardsyntaxandincorrectspelling.Ofmuchmoreimportance,frommypointofview,theyhavenicepersonalitiesandarefuntobearound.CONTENTSPrologueviiIntroductionix1StartingattheBottom12FourierSeriesandtheDFT273TheDFTAlgorithm534TheInverseTransform71PartII-TheFFT5FourFundamentalTheorems816Speeding-UptheDFT1037The
3、FFT1158AnatomyoftheFFTProgram135Appendix1BASICProgrammingLanguage155Appendix5.1DFT5.1(CoreProgramListing)159Appendix5.2DFT5.2(TheoremRoutinesListing)162Appendix5.3ProofoftheTheorems166Appendix6.1DFT6.01(ProgramListing)171viUnderstandingtheFFTAppendix6.2ModificationtoDFT6.01173Appendix6.3Modificatio
4、ntoDFT6.01173Appendix7.1VectorRotation174Bibliography177Index179PROLOGUE"Consideringhowmanyfoolscancalculate,itissurprisingthatitshouldbethoughteitheradifficultoratedioustaskforanyotherfooltolearnhowtomasterthesametricks.Somecalculus-tricksarequiteeasy.Someareenormouslydifficult.Thefoolswhowritethe
5、textbooksofadvancedmathemat•ics—andtheyaremostlycleverfools—seldomtakethetroubletoshowyouhoweasytheeasycalculationsare.Onthecontrary,theyseemtodesiretoimpressyouwiththeirtremendousclevernessbygoingaboutitinthemostdifficultway.Beingmyselfaremarkablystupidfellow,Ihavehadtounteachmyselfthedifficulties
6、,andnowbegtopresenttomyfellowfoolsthepartsthatarenothard.Masterthesethoroughly,andtherestwillfollow.Whatonefoolcando,anothercan."(ProloguetoCalculusMadeEasybySilvanusP.Thompson,F.R.S.,1910)EventhoughagreatmanyyearshadpassedsinceIfirstobtainedacopyofThompson'smagicallittlebook(twenty-eighthprintingo
7、fthesecondedition,MacmillanPublishingCompany,1959),Inonethelessrecognizedthisprologuewhenapartofitappearedrecentlyonthefrontpageofabook.ThereadershouldunderstandthatProfessorThompsonwasn'tsimplybeingsarcast
