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    FurtherresultsonthesynthesisofPIDcontrollers
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    ThereareseveralwaystocalculatetheDiscreteFourierTransform(DFT),suchassolvingsimultaneouslinearequationsorthecorrelationmethoddescribedinChapter8.TheFastFourierTransform(FFT)isanothermethodforcalculatingtheDFT.Whileitproducesthesameresultastheotherapproaches,itisincrediblymoreefficient,oftenreducingthecomputationtimebyhundreds.Thisisthesameimprovementasflyinginajetaircraftversuswalking!IftheFFTwerenotavailable,manyofthetechniquesdescribedinthisbookwouldnotbepractical.WhiletheFFTonlyrequiresafewdozenlinesofcode,itisoneofthemostcomplicatedalgorithmsinDSP.Butdon'tdespair!YoucaneasilyusepublishedFFTroutineswithoutfullyunderstandingtheinternalworkings.CHAPTERTheFastFourierTransform12ThereareseveralwaystocalculatetheDiscreteFourierTransform(DFT),suchassolvingsimultaneouslinearequationsorthecorrelationmethoddescribedinChapter8.TheFastFourierTransform(FFT)isanothermethodforcalculatingtheDFT.Whileitproducesthesameresultastheotherapproaches,itisincrediblymoreefficient,oftenreducingthecomputationtimebyhundreds.Thisisthesameimprovementasflyinginajetaircraftversuswalking!IftheFFTwerenotavailable,manyofthetechniquesdescribedinthisbookwouldnotbepractical.WhiletheFFTonlyrequiresafewdozenlinesofcode,itisoneofthemostcomplicatedalgorithmsinDSP.Butdon'tdespair!YoucaneasilyusepublishedFFTrou……