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1、PROCEEDINGSOFTHEIEEE,VOL.66,NO.1,JANUARY197851OntheUseofWindowsforHarmonicAnalysiswiththeDiscreteFourierTransformFREDRICJ.HARRIS,MEMBER,IEEEAhmw-ThisPw!rmak=availableaconcisereviewofdatawin-compromiseconsistsofapplyingwindowstothesampleddawspadthe^affectOntheOfinthedataset,orequivalent
2、ly,smoothingthespectralsamples.'7ofaoise9mtheptesenceofsdroagbar-Thetwooperationstowhichwesubjectthedataaremomcmterference.Wedmcallattentiontoanumberofcommon-=inberp~crhofwindowsdenusedwiththefdF~-samplingandwindowing.Theseoperationscanbeperformedtransform.Thispaperincludesacomprehensi
3、vecatdogofdatawin-ineitherorder.Samplingiswellunderstood,windowingislessrelatedtosampledwindowsforDFT's.I.INTRODUCTION11.HARMONICANALYSISOFFINITE-EXTENTHEREISMUCHsignalprocessingdevotedtodetectionDATAANDTHEDFTandestimation.DetectionisthetaskofdeterminingifHarmonicanalysisoffinite-exten
4、tdataentailstheprojectionaspecificsignalsetispresentinanobservation,whileoftheobservedsignalonabasissetspanningtheobservationestimationisthetaskofobtainingthevaluesoftheparametersinterval[1I,[3I.Anticipatingthenextparagraph,wedefinedescribingthesignal.Oftenthesignaliscomplicatedoriscor
5、ruptedbyinterferingsignalsornoise.TofacilitatetheTsecondsasaconvenienttimeintervalandNTsecondsastheobservationinterval.Thesinesandcosineswithperiodsequaldetectionandestimationofsignalsets,theobservationisdecomposedbyabasissetwhichspansthesignalspace[11.toanintegersubmultipleofNTseconds
6、formanorthogonalbasissetforcontinuoussignalsextendingoverNTseconds.Formanyproblemsofengineeringinterest,theclassofsignalsThesearedefinedasbeingsoughtareperiodicwhichleadsquitenaturallytoadecompositionbyabasisconsistingofsimpleperiodicfunc-tions,thesinesandcosines.TheclassicFouriertrans
7、formisthemechanismbywhichweareabletoperformthisdecom-position.Bynecessity,everyobservedsignalweprocessmustbeofsin[%kt]O
