HHT-希尔伯特黄变换

HHTTraditionaldata-analysismethodsareallbasedonlinearandstationaryassumptions.TheHilbert–Huangtransform(HHT)isanempiricallybaseddata-analysismethod.Itsadvantageisadaptive,sothatitcanproducemeaningfulspectralanalysisfromnonlinearandnon-stationaryprocesses.TheHHTconsistsoftwoparts:empiricalmodedecomposition(EMD)andHilbertspectralanalysis(HT).Thismethodisespeciallyfortime-frequency-energyrepresentations.Inallthecasesstudied,theHHTgaveresultsmuchsharperthanthosefromanyofthetraditionalanalysismethodsintime-frequency-energyrepresentations.Additionally,theHHTrevealedtruephysicalmeaningsinmanyofthedataexamined.Powerfulasitis,themethodisentirelyempirical.ThestepsofHHTishere；1findextremalpointsofs(t),andmakethepointslinkedbyinterpolationmethod,andthenwegetenvelopefunctionsup(t)andsdown(t);2calculatedmeanvalueofsup(t)andsdown(t)m(t)=[sup(t)+sdown(t)]/2andcreateanewfunction:c1(t)=s(t)-m(t)intheory,c1(t)isthefirstIMF,wegettheleftsignalfroms(t)r1(t)=s(t)-c1(t)3regardr1(t)astheoriginalsignal,andrepeatthestepsbefore.4bythisway,wecangeteveryIMFfroms(t),thenwecanexpresss(t)By:ninitrtct1)()()(s5wemakeHilberttoeveryIMFandwecangetinstantaneousfrequencyofs(t)})(exp()({e)(s1dttwjtaRtniiiThengivenadiscreteseriesfromlesson,weanalyzeitbyHHTfollowingthestepsshowedbefore.X(t)=[cos(2*pi*0.05*t1)+cos(2*pi*0.20*t1)][u(t)-u(t-100)]+[cos(2*pi*0.25*t2)+cos(2*pi*0.45*t2)][u(t-200)-u(t-300)];AndthenwecalculatetheIMFsofs(t):WemakeHTforeveryIMFandgetinstantaneousfrequencyofx(t):Wecanseethefrequencyofx(t)withtimegoing,whentbelongsto[0:100],thefrequencyishigh,whenitisin[100:200],thefrequencyislow,whenitisin[200:300],thefrequencyrises.Atlast,wecanseethatHHTcananalyzethefrequencyofsignalIneverymoment,inotherwords,localfrequencydistribution.