A Practical Approach ToHigher-Order Statistics. AnApplication toElectrical Transients Characterization
Antonio Moreno‐Muñoz · 2007
Inthis paper weperform apractical review onhigher-caseofhigher-order spectra. Thethird-order spectrum iscalled order statistics interpretation. Concretely wefocuss onanunbiased thebi-spectrum andthefourth-order spectrum iscalled thetry- estimate ofthe4th-order time-domain cumulants. Somesynthetics spectrum. They aredefined tobetheFourier transforms orthe involving classical noiseprocesses arecharacterized usingthisspcruthe are-def toube teFuerrasfomt rte unbiased estimate, withthegoal ofchecking its performance andto third andthefourth-order cumulant sequences, respectvely. provide thescientific community withanother result, dealing with theinterpretation ofthis signal processing tool. A real practicalPoly-spectra aredefined asthehigher-order momentspectra example ispresented inthefield ofelectrical powerquality eventandcumulant spectra canbedefined forbothdeterministic analysis. Theworkalsoaimstopresent asetofgeneral advice in signals andrandomprocesses. Momentspectra canbevery ordertosavememoryandgain speed inarealsignal processing useful intheanalysis ofdeterministic signals (transient and frame, dealing withnon-stationary processes. periodic), whereas cumulant spectra areofgreat importance in KeVwords - Electrical transients, Higher-Order statistics, Neuraltheanalysis ofstochastic signals. networks, Powerquality. Themotivation ofthepoly-spectral analysis yields in Gaussian processes arecompletely characterized bythe threeapplications: (a)Tosuppress Gaussian noiseprocesses autocorrelation sequence anditsassociated Fourier transform, ofunknownspectral characteristics; thebi-spectrum also thepowerspectrum. Inthepowerspectrum estimation, the suppress noise withsymmetrical probability distribution, (b)to information regarding thephase ofthefrequency components of reconstruct themagnitude andphaseresponse ofsystems, and thesignal isnotpresent. Theinformation inthepowerspectrum(c)todetect andcharacterize nonlinearities intime-series. isessentially thesameasintheautocorrelation (1). However, there arenumeroussituations wherewe have Inthis paper weshowtheapplication results dealing withthe tolookbeyondtheautocorrelation inordertogetextracharacterization ofrandomprocesses, following theindications information regarding deviations fromtheGaussian behaviorin(1) andin(2). A real example involving powerquality event andnonlinear characterization.