On the use of windows for harmonic analysis with ...

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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