Quantitative analysis of EEG signals: Time-frequency methods and ...

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agation time. They applied this procedure to study ERPs in central and parietal locations, nding lower values in non-target than in target stimulus, without signicant dierences between electrodes. In the central location (Cz) they report a value of =0:397 0:18 for non-target stimulus and of =0:794 0:44 for the target ones. Although there is a great variance in the results of dierent groups, there is a general agreement that EEG signals have at least one positive Lyapunov exponent, implying that EEGs (in case of having a deterministic origin) reect a chaotic activity. 5.5 Application to scalp recorded EEGs 5.5.1 Material and Methods EEG recordings of 6 subjects were studied. Recordings were performed in a \no-task" awake state with eyes closed. Three of these subjects had normal EEG recordings ( N1, N2, N3 ) and other three had abnormal ones (A1,A2,A3). The main abnormalities of these last ones were: slow waves, increases in theta rhythms, very low alpha reactivity and important decrease in the alpha/theta ratio. EEGs were digitized using a 8 bits analog-to-digital (A/D) converter. 20 electrodes were disposed according to the 10 ; 20 system with earlobe references. The data was sampled with a frequency of 256 Hz, and ltered with a high-pass lter at 0.5 Hz and alow-pass lter at 32 Hz. We chose for our analysis the central electrodes because they were the ones less contaminated by artifacts. 5.5.2 Results and Discussion The objective of this section is to establish some criteria for the analysis of EEG signals previous to any calculation with Chaos methods. This is done in order to avoid spurious results due to unfortunate selections of the segments of data to be analyzed. The rst step is to choose data segments without artifacts. Then, after selecting proper zones free of artifacts or with very few interruptions, the stationarity of the data can be veried by applying the criteria described in sec. x5.3. In this case, the length of the data bins was 1000 data points (about 4 seconds of digitized EEG signal). In Fig. 26 and Fig. 27 the mean and variance for the time series denoted by N1 are showed. In this case, mean and variance were considered stable when their changes were in a range of 20% (see sec. 5.3). From these gures it can be concluded that the stationarity criterion previously proposed is satised between bins 9 and 26. Note that in this case, the variance does not give any restriction about selected bins to be used in the following analysis. 79
Figure 26: Mean values for bins of 1000 data points for the EEG data N1. Figure 27: Standard deviation for bins of 1000 data points for the EEG data N1. Fig. 28 shows that the histogram for this selected segment ofN1 has approximately a normal distribution (at least, no higher order moments seem to be relevant). The algorithm for the calculation of Correlation Dimension assumed stationarity and noise free time series. Since EEGs are usually contaminated by noise it is convenient prior to the calculation of the Correlation Dimension to apply noise reduction techniques as the Singular Value Decomposition (SVD) (Albano et al., 1988 Broomhead and King, 1986)(see sec. x5.2.3). The SVD has the advantage of reducing the embedding dimension of the system and of partially eliminating the noiseofthesignal. In Table 4 the total length of the series, the stationary portions and the results of the calculations of D 2 and are presented. The time lag was chosen as the rst zero of the autocorrelation function and the embedding dimension by satisfying the Takens 80
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Quantitative analysis of EEG signal
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1. Berichterstatter: Prof. Dr.-Ing.
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an okzipitalen Positionen und (c) d
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To my family: Mama, Consuelo, Hugui
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Preface In this work, I will descri
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I would certainly like to remember
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Contents Zusammenfassung Preface Ac
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5.2.6 Calculating Lyapunov Exponent
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Summary Since the rsts recordings i
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1 Outline of Neurophysiology: Brain
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Figure 2: Normal 20 channels (10-20
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1.1.2 EEG in Epilepsy One important
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Figure 3: Scalp EEG of 18 channels
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Figure 4: Averaged responses upon N
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2 Fourier Transform 2.1 Introductio
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I xx (k) =jX(k)j 2 = X(k) X (k) (
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17 Figure 5: Topographical mapping
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1987) is that coherence gives the c
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3 Gabor Transform (Short Time Fouri
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where k g D k= R 1 ;1 jg D(t 0 )j 2
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and the band maximum peak frequency
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Figure 7: Intracraneal seizure reco
Page 46 and 47: Figure 10: Mean (soft line) and max
Page 48 and 49: EEG as the one with least amount of
Page 50 and 51: Figure 11: Scalp EEG of the right c
Page 52 and 53: 3.5 Conclusion In this chapter I de
Page 54 and 55: Original signal FOURIER TRANSFORM G
Page 56 and 57: 4.2.3 Multiresolution Analysis Cont
Page 58 and 59: Original signal -15 0 15 -1sec 0 1s
Page 60 and 61: 4.2.5 Wavelet Packets In the approa
Page 62 and 63: marked decrease in computational ti
Page 64 and 65: ain activity during an epileptic se
Page 66 and 67: 3 2 3 3 3 3.2 Hz 3.6 Hz 4.0 Hz 4.4
Page 68 and 69: Silva et al.,1973a,1973b Lopes da S
Page 70 and 71: sweep #1 sweep #2 sweep #3 sweep #4
Page 72 and 73: VEP non-target target F3 F4 F3 F4 F
Page 74 and 75: VEP non-target target F3 F4 F3 F4 F
Page 76 and 77: Electrode F3 F4 Cz P3 P4 O1 O2 Dela
Page 78 and 79: In conclusion, our results point to
Page 80 and 81: 63 Figure 22: Gamma responses for a
Page 82 and 83: Figure 24: T-test comparison of the
Page 84 and 85: wavelet coecients allowed an easy d
Page 86 and 87: the position vs. the linear momentu
Page 88 and 89: unknown topology it is necessary to
Page 90 and 91: the sum of the positive exponents (
Page 92 and 93: performed. On one hand, must be lar
Page 94 and 95: Duke (1992) and Elbert et al. (1994
Page 98 and 99: Figure 28: Histogram for the EEG da
Page 100 and 101: Figure 29: Attractors corresponding
Page 102 and 103: able for automatic detection proces
Page 104 and 105: ENTROPY Thermodynamics Signal analy
Page 106 and 107: 6.3 Application to visual event-rel
Page 108 and 109: VEP Non Target Target F3 -20 -10 0
Page 110 and 111: 1 VEP NON-TARGET TARGET 1 1 F3 F3 0
Page 112 and 113: 1 VEP NON-TARGET TARGET 1 1 F3 F3 0
Page 114 and 115: and the Lorenz equations (a model o
Page 116 and 117: P300 deection. Due to the relation
Page 118 and 119: 7 General Discussion In this chapte
Page 120 and 121: Wavelet analysis was also applied t
Page 122 and 123: aect the whole spectrum and for thi
Page 124 and 125: peaks. 7.2.3 Wavelet Transform vs.
Page 126 and 127: the ones having wide peaks (being t
Page 128 and 129: A Time-frequency resolution and the
Page 130 and 131: Z 1 ;1 tx(t) d dt x(t) dt = 1 2 Z 1
Page 132 and 133: Figure 37: Time-frequency resolutio
Page 134 and 135: References Abarbanel HDI, Brown R,
Page 136 and 137: Berger, H. Uber das Elektrenkephalo
Page 138 and 139: Gastaut H and Broughton R. Epilepti
Page 140 and 141: Lopes da Silva FH, van Lierop THMT,
Page 142 and 143: Pradhan N, Sadasivan P, Chatterji S
Page 144 and 145: Serrano E, Ph.D. Thesis, Department
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Biographical sketch 21.03.1967 born
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