Soner Bekleric Title of Thesis: Nonlinear Prediction via Volterra Ser

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List of Figures 2.1 AR IIR filter representation. . . . . . . . . . . . . . . . . . . . . . . 10 2.2 The trade-off parameter µ estimates the optimum solution. . . . . . 19 2.3 1-D synthetic data for comparison of prediction between linear prediction theories. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.4 Arctic Oscillation data for standardized nonlinear sea-level pressures for comparison of prediction between linear prediction theories. . . . 22 2.5 PSD Estimation of Arctic Oscillation data for standardized nonlinear sea-level pressures. . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.1 Schematic representation of a system characterized by a third-order Volterra series. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.2 Frequency domain Volterra model of a cubic nonlinear system. . . . 29 3.3 Volterra AR diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.4 1-D synthetic data for comparison of prediction between linear prediction theory and third order Volterra series. . . . . . . . . . . . . 42 3.5 1-D synthetic data. . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.6 Arctic Oscillation data for standardized nonlinear sea-level pressures for comparison of prediction between linear prediction theory and third order Volterra series. . . . . . . . . . . . . . . . . . . . . . . . 44 3.7 Arctic Oscillation data for standardized nonlinear sea-level pressures. 45 4.1 Optimum filter length for the data in Figure 4.2. . . . . . . . . . . 52 4.2 Synthetic data example for different filter lengths. . . . . . . . . . 53 4.3 (a) Prediction of Figure 4.2(b) (p = 3). (b) The error between original data and predicted data. . . . . . . . . . . . . . . . . . . . . . . 54 5
4.4 (a) Prediction of Figure 4.2(b) (p = 6). (b) The error between original data and predicted data. . . . . . . . . . . . . . . . . . . . . . . 55 4.5 (a) Prediction of Figure 4.2(b) (p = 15). (b) The error between original data and predicted data. . . . . . . . . . . . . . . . . . . . 56 4.6 Synthetic data example for different filter lengths. . . . . . . . . . 57 4.7 Optimality of filter length for the data in Figure 4.6. . . . . . . . . 58 4.8 (a) Prediction of Figure 4.6(b) (p = 3). (b) Error between original data and predicted data. . . . . . . . . . . . . . . . . . . . . . . . . 59 4.9 (a) Prediction of Figure 4.6(b) (p = 5). (b) Error between original data and predicted data. . . . . . . . . . . . . . . . . . . . . . . . . 60 4.10 (a) Prediction of Figure 4.6(b) (p = 15). (b) Error between original data and predicted data. . . . . . . . . . . . . . . . . . . . . . . . . 61 4.11 Same as the data in Figure 4.6. . . . . . . . . . . . . . . . . . . . . 63 4.12 2-D synthetic data for comparison of prediction between linear prediction theory and third order Volterra series. . . . . . . . . . . . . 65 4.13 2-D synthetic data for comparison of prediction between linear prediction theory and the cubic part of a Volterra series. . . . . . . . . 66 4.14 2-D synthetic data. . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.15 2-D synthetic data for comparison of prediction between linear prediction theory and a third-order Volterra series. . . . . . . . . . . . 68 4.16 2-D synthetic data. . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.17 2-D synthetic data. . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.18 2-D real data for comparison of prediction between linear prediction theory and a third-order Volterra series. . . . . . . . . . . . . . . . 72 4.19 2-D real data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5.1 Multiple types. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 5.2 Synthetic data example. . . . . . . . . . . . . . . . . . . . . . . . . 79 5.3 Synthetic data example with two multiples and one primary. . . . . 80 5.4 Synthetic data example with two multiples and one primary. . . . . 81 5.5 Synthetic data example with two multiples and three primaries. . . 82 5.6 Real Data example. Common offset gather. . . . . . . . . . . . . . . 84 5.7 Real Data example. Common offset gather (closer look). . . . . . . 85
Page 1 and 2: Name of Author: Soner Bekleric Univ
Page 3 and 4: University of Alberta Faculty of Gr
Page 5 and 6: Abstract Linear filter theory has p
Page 7 and 8: Contents 1 Introduction 1 1.1 Appli
Page 9: List of Tables 3.1 Filter length an
Page 13 and 14: List of symbols Symbol Name or desc
Page 15 and 16: List of abbreviations Abbreviation
Page 17 and 18: In applied seismology predictive de
Page 19 and 20: 1.1. APPLICATIONS 4 applied to vide
Page 21 and 22: 1.3. THESIS OUTLINE 6 • Chapter 4
Page 23 and 24: 2.2. LINEAR PROCESS 8 Finally, I pr
Page 25 and 26: 2.3. LINEAR PREDICTION 10 E(z) 1 X(
Page 27 and 28: 2.3. LINEAR PREDICTION 12 In my the
Page 29 and 30: 2.3. LINEAR PREDICTION 14 which can
Page 31 and 32: 2.3. LINEAR PREDICTION 16 ∂ρ fb
Page 33 and 34: 2.3. LINEAR PREDICTION 18 I have an
Page 35 and 36: 2.4. 1-D SYNTHETIC AND REAL DATA EX
Page 39 and 40: 2.6. SUMMARY 24 Relative PSD Relati
Page 41 and 42: Chapter 3 Nonlinear Prediction 3.1
Page 43 and 44: 3.1. NONLINEAR PROCESSES VIA THE VO
Page 45 and 46: 3.1. NONLINEAR PROCESSES VIA THE VO
Page 47 and 48: 3.2. NONLINEAR MODELING OF TIME SER
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3.4. SUMMARY 46 3.4 Summary In this
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4.1. LINEAR PREDICTION IN THE F −
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4.2. ANALYSIS OF OPTIMUM FILTER LEN
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4.2. ANALYSIS OF OPTIMUM FILTER LEN
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4.3. NONLINEAR PREDICTION OF COMPLE
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RMSE 2 4.3. NONLINEAR PREDICTION OF
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4.4. NOISE REMOVAL AND VOLTERRA SER
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4.5. SYNTHETIC AND REAL DATA EXAMPL
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5.1. INTRODUCTION 76 ples remains a
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5.3. SYNTHETIC DATA EXAMPLES 78 Not
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5.3. SYNTHETIC DATA EXAMPLES 80 Tim
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5.3. SYNTHETIC DATA EXAMPLES 82 Tim
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5.4. REAL DATA EXAMPLES 84 Time [s]
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series in this thesis has been trun
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6.1. FUTURE DIRECTIONS 94 Noise red
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BIBLIOGRAPHY 96 Canales, L. L. (198
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BIBLIOGRAPHY 98 Marple, S. L. (1980
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BIBLIOGRAPHY 100 Trad, D. (2003). I
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Soner Bekleric Title of Thesis: Nonlinear Prediction via Volterra Ser

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