Reduction of cross terms in the Wigner-Ville distribution using variational mode decomposition

Abstract

This thesisfocusesontheanalysisofthenon-stationarysignalsusingthe time-frequency distribution(TFD).Thenon-stationarysignalscontain time-varyingparametersandconventionalFouriertransformisnotsuitablefor analysis ofsuchsignals.Forsuchtime-varyingsignals,TFDplaysanimportant role foranalysis.TheTFDsprovideinformationaboutthetime-varyingfrequency componentspresentinthesignal.Inthisthesis,theWigner-Villedistribution (WVD) methodisstudiedtoobtaintheTFDofthesignal.Theoretically,the WVD providesaninfiniteresolutionintimeandfrequencydomains.Dueto bilinear natureoftheWVD,itcontainscrosstermsintime-frequency representation(TFR)fornon-stationarysignals. This thesispresentstwomethodologiestoreducethecrosstermsinWVDfor the analysisofnon-stationarysignals.Theseproposedmethodologiesaresuitable for reducingcrosstermsintheanalysisofnon-stationarysignalswhentheir monocomponentsarewellseparatedinfrequencydomainforlinearandnon-linear frequency modulated(NLFM)signals,respectively.Inthefirstproposedmethod, variationalmodedecomposition(VMD)decomposesamulticomponent, non-stationary signalintoanumberofsub-signals.Thesesub-signalshavebeen convertedintoanalyticsub-signalsusingtheHilberttransform.AfterthisWVD has beencomputedtoobtaintheTFDofeachanalyticsub-signal.Thesummation of thesecomputedTFDofallsub-signalsprovidecrosstermsfreeTFDof non-stationary signals. In signalswherethemonocomponentsareNLFMsignalsincludeintracrossterms in its TFD.To remove these cross terms, we need to introduce another method called time domain decomposition(TDD).TheTDD further segments the modes obtained after decomposition of the NLFM signals using VMD in time domain and after that WVD is applied on each obtained sub-band to obtain the TFD of each component of the segment. At last,thefinalWVDhasbeenobtainedbysummationofallthe obtained WVDs.Now,thisobtainedWVDdoesnotcontaincrossterms. The results of the proposed method imply that cross terms are successfully suppressed in TFD of a multicomponent non-stationary signal. These results are compared withdifferentmethodssuchassmoothedpseudoWigner-Ville distribution (SPWVD),Born-Jordandistribution(BJ),and Choi-Williams distribution (CWD).TheproposedmethodhaveprovidedbetterTFRforthe studied multicomponent non-stationary signals. The result are also presented in terms of Renyi information for the studied signals.