Soner Bekleric Title of Thesis: Nonlinear Prediction via Volterra Ser

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3.3. 1-D SYNTHETIC AND REAL DATA EXAMPLES 43 Samples Samples −4 −2 0 2 0 50 100 (a) Amplitude −4 −2 0 2 0 50 100 (d) Amplitude Samples Samples −4 −2 0 2 0 50 100 (b) Amplitude −4 −2 0 2 0 50 100 (e) Amplitude Samples Samples −4 −2 0 2 0 50 100 (c) Amplitude −4 −2 0 2 0 50 100 (f) Amplitude Figure 3.5: 1-D synthetic data. (a) Original data. (b) Prediction using a thirdorder Volterra series with parameters p = 8, q = 8, and r = 8. (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 = 8, and r = 8). prediction associated to both quadratic and cubic terms (q = 10 and r = 10).
3.3. 1-D SYNTHETIC AND REAL DATA EXAMPLES 44 Samples 0 50 100 (a) (a) (b) (c) Amplitude −2 0 2 Samples Samples 0 50 100 0 50 100 Amplitude −2 0 2 (d) (e) Amplitude −2 0 2 Samples Samples 0 50 100 0 50 100 Amplitude −2 0 2 (e) (f) Amplitude −2 0 2 Figure 3.6: Arctic Oscillation data for standardized nonlinear sea-level pressures for comparison of prediction between linear prediction theory and third order Volterra series. (a) Original data. (b) Prediction using a third-order Volterra series (p = 10, q = 10, and r = 10). (c) The error between the original data and the third-order Volterra prediction. (d) Prediction using the first-order Volterra series, which is equivalent to linear prediction (p = 10). (e) The error between the original data and a linear prediction.
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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 and 10: List of Tables 3.1 Filter length an
Page 11 and 12: 4.4 (a) Prediction of Figure 4.2(b)
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
Page 57: 3.3. 1-D SYNTHETIC AND REAL DATA EX
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
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
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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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