Understanding FFT Window

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1、APPLICATIONNOTEAN014UnderstandingFFTWindowsIntroductionTheFastFourierTransform(FFT)istheFourierTransformofablockoftimedatapoints.Itrepre-FFTbasedmeasurementsaresubjecttoerrorsfromsentsthefrequencycompositionofthetimesignal.aneffectknownasleakage.ThiseffectoccurswhenFigure2showsa10Hzsinewaveform(top)

2、andthetheFFTiscomputedfromofablockofdatawhichisFFTofthesinewaveform(bottom).Asinewaveisnotperiodic.Tocorrectthisproblemappropriatewin-composedofonepuretoneindicatedbythesingledis-dowingfunctionsmustbeapplied.TheusermustcretepeakintheFFTwithheightof1.0at10Hz.choosetheappropriatewindowfunctionforthesp

3、ecif-icapplication.Whenwindowingisnotappliedcorrect-ly,thenerrorsmaybeintroducedintheFFTampli-tude,frequencyoroverallshapeofthespectrum.Thisapplicationnotedescribesthephenomenonofleak-age,thevariouswindowingfunctionsandtheirstrengthsandweaknesses,andexamplesaregivenforvariousapplications.FFTBackgrou

4、ndMostdynamicsignalanalyzers(Figure1)computetimeandfrequencymeasurements.Timemeasure-mentsincludecapturingtimetracesofmeasuredsig-Figure1.DactronFocusTM(left)andtheDactronPhotonTM(right)DynamicSignalAnalyzersFigure2.Timewaveformofsinefunction(top)andFFT(bottom).nals,includingfilteringandstatisticalm

5、easures.FrequencymeasurementsthatarecomputedbymostDSAsincludeFastFourierTransform,PowerSpectralLeakageDensity,FrequencyResponseFunctions,CoherenceTheFFTcomputationassumesthatasignalisperiodicinandmanymore.Thesesignalsarecomputedintheeachdatablock,thatis,itrepeatsoverandoveragainDSPfromthedigitizedti

6、medata.Timedataisdigi-anditisidenticaleverytime.NotethiswasthecaseintizedandsampledintotheDSPblockbyblock.AblockFigure2becausethereareanintergernumberofcyclesisafixednumberofdatapointsinthedigitaltimeofthesinewaveinthedatarecord.Anothertypeofsig-record.Mostfrequencyfunctionsarecomputedfromnalthatsat

7、isfiestheperiodicrequirementisatransientoneblockofdataatatime.Ablockofdataisalsosignalthatstartsatzeroatthebeginningofthetimewin-calledatimerecordortimewindow.dowandthenrisestosomemaximumanddecaysagai