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1、EstimatingandInterpretingtheInstantaneousFrequencyofaSignal-Part2:AlgorithmsandApplicationsBOUALEMBOASHASH,SENIORMEMBER,IEEEThispaper,whichaddressestheimportantissueofestimatingtherecursiveleastsquares(RLS)algorithm,phase-lockedtheinstantaneousfrequency(IF)
2、ofasignal,isasequeltothelooptechniques,estimationviatime-frequencydistributionpaperwhichappearsinthisissue,anddealtwiththeconcepts(TFD)momentsorpeaks[20],andmethodsbasedonarelatingtotheIF.InthispapertheconceptofIFisextendedtomodelingofthesignalphaselawasapo
3、lynomial.Onlythebeabletocopewithdiscretetimesignals.ThespecificproblemexploredisthatofestimatingtheIFoffrequencymodulatedsingleFMcomponentcasewillbedealtwithindetail,but(FM)discrete-timesignalsimbeddedinGaussiannoise.Thereashortdescriptionofhowonemayextendt
4、healgorithmsaremanywellestablishedmethodsforestimatingtheIF-thesetomulticomponentsignalswillbeprovided.methodsincludedifferentiationofthephaseandsmoothingthereof;SimulationsareprovidedinSectionIVtocomparetheadaptivefrequencyestimationtechniquessuchasthephas
5、elockedvariousmethodswithoneanotherandwiththetheoreticalloop(PLL),andextractionofthepeakfromtime-varyingspectralrepresentations.Morerecentlymethodsbasedonamodelingofthelowervariancebounds.Finally,somediscussiononthesignalphaseasapolynomialhavebeenintroduced
6、.Allofthesesuitabilityofaparticularmethodforgivensignalclassandmethodsarereviewed,andtheirperformancesarecomparedonSNRrangeispresented.bothsimulatedandrealdata.GuidelinesaregivenastowhichThefollowingmodelisusedthroughoutthetext:estimationmethodshouldbeusedf
7、oragivensignalclassands(n),n=0,...,N-1isalength,N,sequence.Thesignal-to-noiseratio(SNR).analyticsignalassociatedwiths(n)isadiscrete-timesequencegivenbyz,(n)=s(n)+jH[s(n)],whereH[]I.INTRODUCTIONdefinesthediscrete-timeHilberttransformoperation[45].Theestimati
8、onoftheinstantaneousfrequency(IF)isaz(n),n=0,...,N-1isalengthNsequenceofcomplexnaturalprogressionfromsteady-statesinusoidalfrequencydatavaluescorrespondingtotheundistortedanalyticsignal,estimationwhich