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1、IEEETRANSACTIONSONACOUSTICS.SPEECH.ANDSIGNALPROCESSING,VOL.37.NO12.DECEMBER19891987AFastandAccurateSingleFrequencyEstimatorSTEVENKAYIllIIIIIII.,Abstract-AnewfrequencyestimatorforasinglecomplexsinusoidincomplexwhiteGaussiannoiseisproposed.Theestimatorism
2、ore-0.5.IIicomputationallyefficientthantheoptimalmaximumlikelihoodesti-matoryetattainsasgoodperformanceatmoderatelyhighsignal-to-noiseratios.Also,theestimatorisshowntoberelatedtothelinearpredictionestimator.Thisrelationshipisexploitedtorevealwhythelinea
3、rpredictionestimatordoesnotattaintheCramer-Raoboundevenathighsignal-to-noiseratios.Fig.3.AnexampleofweightingfunctionsforN=3,n=16.I.INTRODUCTIONTheestimationofthefrequencyofasinglecomplexsinusoidinwhiteGaussiannoiseisaprobleminsignalprocessingwhichhasre
4、ceivedmuchattention.See[I]forasummary.Theoptimalmax-imumlikelihoodestimator(MLE)iswellknowntobegivenbythelocationofthepeakofaperiodogram.ThisestimatorattainstheCramer-Raolowerboundonvarianceforahigh-enoughsignal-to-noiseratio(SNR).Inmanyinstances,howeve
5、r,thecomputationisprohibitiveevenwithanFFTimplementation,andsosimplermethodsaredesirable.Inthiscorrespondencewepresentanap-proachwhichisstronglymotivatedbytherecentworkofTretter[2].ItisshownthattheproposedestimatoriscomputationallymuchFig.4.CCF’sform=1.
6、simplerthantheperiodogram,yetattainstheCramer-RaoboundformoderatelyhighSNR’s.Inparticular,considerthereceiveddatatoconsistofasinglenXNweightelementsarethesameabsolutevalue2/&.AndthecomplexsinusoidincomplexwhiteGaussiannoise,orothers,2N(N-1)weightelement
7、swithavalueof0,neednotbeX,=Ael(WOr’+@)+z,t=0,1,2;..,N-l.(1)implementedintheweightedaddersanddonothaveaneffectontheamplitudedistribution.Therefore,theimplementationoftheNTheamplitudeA,frequencyWO,andphase0aredeterministicbutfiltersisveryeasy,andtheamplit
8、udedistributionofeveryrandomunknownconstants.Itisthefrequencywothatweareinterestedinsignalx,(mj)isbestapproximatedtoanormalfromtheviewpointestimating.Theamplitudeandphaseareconsideredtobenuisanceofkurtosis.parameters.Thenoisez,is
