Soner Bekleric Title of Thesis: Nonlinear Prediction via Volterra Ser

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4.5. SYNTHETIC AND REAL DATA EXAMPLES 71 Time (s) Time (s) 0 0.5 1.0 0 0.5 1.0 Traces 20 40 (a) Traces 20 40 (d) 0 0.5 1.0 0 0.5 1.0 Traces 20 40 (b) Traces 20 40 (e) 0 0.5 1.0 0 0.5 1.0 Traces 20 40 (c) Traces 20 40 Figure 4.17: 2-D synthetic data. (a) Original data. (b) Prediction using a thirdorder Volterra series with parameters p = 7, q = 7, and r = 7. (c) Contribution from the linear part. (d) Contribution from the quadratic part. (e) Contribution from the cubic part. (f) Contribution from both quadratic and cubic parts (q = 7, and r = 7). diffractions and apexes of events properly with parameters q = 9 and r = 9 (Figure 4.19(f)). It is clear that this particular data set requires both linear and nonlinear components to properly model the complex waveforms. (f)
4.5. SYNTHETIC AND REAL DATA EXAMPLES 72 Time (s) 0 0.5 1.0 Traces 20 40 60 Time (s) (a) (b) Time (s) 0 0.5 1.0 0 0.5 1.0 Traces 20 40 60 Traces 20 40 60 (e) (d) Time (s) Time (s) 0 0.5 1.0 0 0.5 1.0 Traces 20 40 60 (c) Traces 20 40 60 Figure 4.18: 2-D real data for comparison of prediction between linear prediction theory and a third-order Volterra series. (a) Original data. (b) Prediction using a third order Volterra series with parameters p = 9, q = 9, and r = 9. (c) Error between the original data and predicted data via a third-order Volterra series. (d) Prediction using linear prediction theory with parameter p = 9. (e) Error between original data and predicted data via linear prediction theory. (f) (e)
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Name of Author: Soner Bekleric Univ
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University of Alberta Faculty of Gr
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Abstract Linear filter theory has p
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Contents 1 Introduction 1 1.1 Appli
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List of Tables 3.1 Filter length an
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4.4 (a) Prediction of Figure 4.2(b)
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List of symbols Symbol Name or desc
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List of abbreviations Abbreviation
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In applied seismology predictive de
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1.1. APPLICATIONS 4 applied to vide
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1.3. THESIS OUTLINE 6 • Chapter 4
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2.2. LINEAR PROCESS 8 Finally, I pr
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2.3. LINEAR PREDICTION 10 E(z) 1 X(
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2.3. LINEAR PREDICTION 12 In my the
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2.3. LINEAR PREDICTION 14 which can
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2.3. LINEAR PREDICTION 16 ∂ρ fb
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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
Page 61 and 62: 3.4. SUMMARY 46 3.4 Summary In this
Page 63 and 64: 4.1. LINEAR PREDICTION IN THE F −
Page 65 and 66: 4.2. ANALYSIS OF OPTIMUM FILTER LEN
Page 67 and 68: 4.2. ANALYSIS OF OPTIMUM FILTER LEN
Page 69 and 70: 4.3. NONLINEAR PREDICTION OF COMPLE
Page 73 and 74: RMSE 2 4.3. NONLINEAR PREDICTION OF
Page 77 and 78: 4.4. NOISE REMOVAL AND VOLTERRA SER
Page 79 and 80: 4.5. SYNTHETIC AND REAL DATA EXAMPL
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Page 91 and 92: 5.1. INTRODUCTION 76 ples remains a
Page 93 and 94: 5.3. SYNTHETIC DATA EXAMPLES 78 Not
Page 95 and 96: 5.3. SYNTHETIC DATA EXAMPLES 80 Tim
Page 97 and 98: 5.3. SYNTHETIC DATA EXAMPLES 82 Tim
Page 99 and 100: 5.4. REAL DATA EXAMPLES 84 Time [s]
Page 107 and 108: series in this thesis has been trun
Page 109 and 110: 6.1. FUTURE DIRECTIONS 94 Noise red
Page 111 and 112: BIBLIOGRAPHY 96 Canales, L. L. (198
Page 113 and 114: BIBLIOGRAPHY 98 Marple, S. L. (1980
Page 115 and 116: BIBLIOGRAPHY 100 Trad, D. (2003). I
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Soner Bekleric Title of Thesis: Nonlinear Prediction via Volterra Ser

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