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1、Tuomo SipolaApplying Hilbert-Huang Transformto Mismatch NegativityMasters Thesisin Information Technology(Mobile Systems)October 27, 2009UNIVERSITY OF JYVSKYLDEPARTMENT OF MATHEMATICAL INFORMATION TECHNOLOGYJyvskylAuthor: Tuomo SipolaContact information: tuomo.s.sipolajyu.fiTitle: Applying Hilbert-H
2、uang Transform to Mismatch NegativityTyn nimi: Hilbert-Huang-muunnoksen soveltaminen aivoshksignaaliinProject: Masters Thesis in Information Technology (Mobile Systems)Page count: 80Abstract: EEG signals can be analyzed with modern mathematical methods in orderto separate the most meaningful compone
3、nts from the rest. Hilbert-Huang trans-form is a new method to construct a sharp and clean time-frequency spectrum ofa nonlinear and nonstationary signal. It consists of empirical mode decomposi-tion (EMD), which decomposes the signal to intrinsic mode functions (IMF), andHilbert transform, which is
4、 used to obtain the spectrum. This method was used onEEG data recorded during an oddball paradigm test. The subjects consisted of chil-dren divided into three groups: attention-deficit hyperactivity disorder (ADHD),reading-disabled (RD) and control group. Hilbert-Huang transform revealed differ-ence
5、s between the groups that could not have been obtained using more conven-tional analysis methods.Suomenkielinen tiivistelm: Aivoshksignaalia voidaan analysoida moderneillamatemaattisillamenetelmillmerkityksellistenkomponenttienerottamiseksi. Hilbert-Huang-muunnos on uusi menetelm, joka tuottaa tervn
6、 ja puhtaan aika-taajuus-spektrin eplineaarisesta ja epstationaarisesta signaalista. Se koostuu empiirisestaaltomuotohajotelmasta, joka hajottaa signaalin ominaisaaltomuotofunktioiksi, jaHilbert-muunnoksesta, jollatuotetaanspektri. Ttmenetelmkytettiinnk. oddball-kokeen aikana saatuihin aivoshkmittau
7、ksiin. Koehenkilt olivat lapsia, joista o-salla oli todettu tarkkaavaisuushiri, osalla lukihiri ja osalla ei kumpaakaan.Hilbert-Huang-muunnos paljasti ryhmien vlill eroja, joita ei olisi voitu havaitaperinteisemmill analysointimenetelmill.Keywords: electroencephalography, EEG, event-related potentia
8、l, ERP, mismatchnegativity, MMN, Hilbert-Huang transform, HHT, empirical mode decomposition,EMD, time-frequency analysisAvainsanat: aivoshk, hertepotentiaali, Hilbert-Huang-muunnos, empiirinenaal-tomuotohajotelma, aika-taajuusanalyysiAbbreviationsADHD attention-deficit hyperactivity disorderANOVA an
9、alysis of varianceBCI brain-computer interfaceDW difference waveEEG electroencephalographyEMD empirical mode decompositionERP event-related potentialFFT fast Fourier transformfMRI functional magnetic resonance imagingGLM general linear modelHHT Hilbert-Huang transformICA independent component analys
10、isIMF intrinsic mode functionMMN mismatch negativityMWT Morlet wavelet transformODF optimal digital filteringRD reading-disabledSAR support-to-absence ratioSNR signal-to-noise ratioSTFT short-time Fourier transformiContentsAbbreviationsiList of Figuresiv1Introduction12Electroencephalography32.1Histo
11、ry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .42.2Brain rhythms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .52.3EEG experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .52.4Mathematical nature of EEG signal . . . . . . . . . . . . . .
12、. . . . . .72.5Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .82.6Traditional analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . .83Event-related potentials113.1Detecting event-related potentials . . . . . . . . . . . . . . . . . . . . .113.2Noise and art
13、ifacts. . . . . . . . . . . . . . . . . . . . . . . . . . . . .123.3Auditory ERP components . . . . . . . . . . . . . . . . . . . . . . . . .133.4Mismatch negativity. . . . . . . . . . . . . . . . . . . . . . . . . . . .144Linear time-frequency analysis174.1Fourier transform . . . . . . . . . . . .
14、. . . . . . . . . . . . . . . . . .174.2Short-time Fourier transform. . . . . . . . . . . . . . . . . . . . . . .194.3Shortcomings of Fourier transform . . . . . . . . . . . . . . . . . . . .204.4Wavelet transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .204.5Wigner-Ville transform
15、 . . . . . . . . . . . . . . . . . . . . . . . . . . .225Empirical mode decomposition245.1Instantaneous frequency . . . . . . . . . . . . . . . . . . . . . . . . . .255.2Intrinsic mode function . . . . . . . . . . . . . . . . . . . . . . . . . . .265.3The sifting process. . . . . . . . . . . . . . .
16、 . . . . . . . . . . . . . .275.4Stopping criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .295.5Extracting rest of the oscillations. . . . . . . . . . . . . . . . . . . . .30ii5.6Problems concerning EMD . . . . . . . . . . . . . . . . . . . . . . . . .316Nonlinear time-frequency analysis and Hilbert transform356.1Cauchy principal value . . . . . . . . . . . . . . . . . . . . . . . . . . .356.2Hilbert transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .366.3An
