1993_Signal Processing with Fractional Lower Order Moments Stable Processes and Their Applications_PIEEE

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1、SignalProcessingwithFractionalLowerOrderMoments:StableProcessesandTheirApplicationsNon-Gaussianstatisticalsignalprocessingisimportantwhenaccuracy.WhenthelossofresolutionduetotheidealsignalsandornoisedeviatefromtheidealGaussianmodel.StableGaussianassumptioninanon-Gaussianenvi

2、ronmentcandistributionsareamongthemostimportantnon-Gaussianmodels.notbetolerated,morerealisticstatisticalmodelsmustbeTheysharedejningcharacteristicswiththeGaussiandistribution,used.suchasthestabilitypropertyandcentrallimittheorems,andinfactincludetheGaussiandistributionasali

3、mitingcase.TohelpengineersbetterunderstandthestablemodelsanddevelopA.StatisticalModelingwithNon-Gaussianmethodologiesfortheirapplicationsinsignalprocessing,thisStableDistributionspaperpresentsatutorialreviewofthebasiccharacteristicsofstabledistributionsandstablesignalprocess

4、ing.TheemphasisAbroadandincreasinglyimportantclassofnon-Gaussianwillbeonthedifferencesandsimilaritiesbetweenstablesignalphenomenaencounteredinpracticecanbecharacterizedprocessingmethodsbasedonfractionallowerordermomentsbyitsimpulsivenature.SignalsandnoiseinthisclassareandGau

5、ssiansignalprocessingmethodsbasedonsecond-ordermoments.morelikelytoexhibitsharpspikesoroccasionalburstsofoutlyingobservationsthanonewouldexpectfromnormallydistributedsignals.Asaresult,theirdensityfunctionsdecayI.INTRODUCTIONinthetailslessrapidlythantheGaussiandensityfunction

6、.ThesignalprocessingliteraturehastraditionallybeenUnderwateracousticsignals,low-frequencyatmosphericdominatedbytheGaussianassumption.Inmanyinstancesnoiseandmanytypesofman-madenoisehaveallbeentheidealGaussianmodelisreasonableandcanbejustifiedfoundtobelongtothisclass[9],[121-[

7、161.ItisforthistypebytheCentralLimitTheorem.Inaddition,itoftenleadsofsignalsandnoisethatthestabledistributionprovidesatoanalyticallytractablesolutionsforsignalprocessingusefultheoreticaltool.problems.ThestablelawisadirectgeneralizationoftheGaussianUnfortunately,therearealsom

8、anyphenomenainsig-distributionandinfactincludestheGaussianasalimitingnalpro