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Numerical techniques for solving differential equations have been vigorously studied, and various techniques have been proposed and investigated for particular problems. Maxwell's equations are the system of partial differential equations which describe the behavior of electromagnetic fields. The methods for solving the equations should be properly chosen depending on the purpose of the analysis and the available computational resources. In this thesis, we propose a time-domain electromagnetic field modeling technique based on Haar wavelets. The multiresolution nature of the wavelets was used in the formulation, and a time stepping algorithm that is similar to the conventional finite-difference time-domain (FDTD) method was obtained. The proposed technique effectively models realistic structures by virtue of the multi-resolution property; the computational time is reduced approximately by half compared to the conventional FDTD method. In order to provide a comprehensive understanding of the proposed method, algorithms for one, two and three space dimensions were formulated, validated in terms of the accuracy, and actually applied to various realistic problems. Various boundary conditions have been formulated and implemented, and in addition, the following applications are addressed: S-parameter extraction for two-dimensional waveguide problems, combined with field singularity correction at metal edges and corners, resonant cavity analyses for validation purposes, and analyses of microwave passive devices with open boundaries such as microstrip low-pass filters and spiral inductors. An algorithm that needs half the computational effort is equivalent to hardware that is twice as fast. The purpose of this thesis is to make a contribution to the improvement of computational speed in electromagnetic time domain solutions. / Graduate

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by Chan, Kin Pong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 100-105). / Abstracts in English and Chinese. / Acknowledgments --- p.ii / Abstract --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Wavelet Transform --- p.4 / Chapter 1.2 --- Time Warping --- p.5 / Chapter 1.3 --- Outline of the Thesis --- p.6 / Chapter 2 --- Related Work --- p.8 / Chapter 2.1 --- Similarity Models for Time Series --- p.8 / Chapter 2.2 --- Dimensionality Reduction --- p.11 / Chapter 2.3 --- Wavelet Transform --- p.15 / Chapter 2.4 --- Similarity Search under Time Warping --- p.16 / Chapter 3 --- Dimension Reduction by Wavelets --- p.21 / Chapter 3.1 --- The Proposed Approach --- p.21 / Chapter 3.1.1 --- Haar Wavelets --- p.23 / Chapter 3.1.2 --- DFT versus Haar Transform --- p.27 / Chapter 3.1.3 --- Guarantee of no False Dismissal --- p.29 / Chapter 3.2 --- The Overall Strategy --- p.34 / Chapter 3.2.1 --- Pre-processing --- p.35 / Chapter 3.2.2 --- Range Query --- p.35 / Chapter 3.2.3 --- Nearest Neighbor Query --- p.36 / Chapter 3.3 --- Performance Evaluation --- p.39 / Chapter 3.3.1 --- Stock Data --- p.39 / Chapter 3.3.2 --- Synthetic Random Walk Data --- p.45 / Chapter 3.3.3 --- Scalability Test --- p.51 / Chapter 3.3.4 --- Other Wavelets --- p.52 / Chapter 4 --- Time Warping --- p.55 / Chapter 4.1 --- Similarity Search based on K-L Transform --- p.60 / Chapter 4.2 --- Low Resolution Time Warping --- p.63 / Chapter 4.2.1 --- Resolution Reduction of Sequences --- p.63 / Chapter 4.2.2 --- Distance Compensation --- p.67 / Chapter 4.2.3 --- Time Complexity --- p.73 / Chapter 4.3 --- Adaptive Time Warping --- p.77 / Chapter 4.3.1 --- Time Complexity --- p.79 / Chapter 4.4 --- Performance Evaluation --- p.80 / Chapter 4.4.1 --- Accuracy versus Runtime --- p.80 / Chapter 4.4.2 --- Precision versus Recall --- p.85 / Chapter 4.4.3 --- Overall Runtime --- p.91 / Chapter 4.4.4 --- Starting Up Evaluation --- p.93 / Chapter 5 --- Conclusion and Future Work --- p.95 / Chapter 5.1 --- Conclusion --- p.95 / Chapter 5.2 --- Future Work --- p.96 / Chapter 5.2.1 --- Application of Wavelets on Biomedical Signals --- p.96 / Chapter 5.2.2 --- Moving Average Similarity --- p.98 / Chapter 5.2.3 --- Clusters-based Matching in Time Warping --- p.98 / Bibliography --- p.99

Chan Chun Ping. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 134-137). / Text in English; abstracts in English and Chinese. / Chan Chun Ping. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Automatic Speech Recognition --- p.1 / Chapter 1.2 --- Review of Speech Recognition Techniques --- p.2 / Chapter 1.3 --- Review of Signal Representation --- p.4 / Chapter 1.4 --- Review of Wavelet Transform --- p.7 / Chapter 1.5 --- Objective of Thesis --- p.11 / Chapter 1.6 --- Thesis Outline --- p.11 / References --- p.13 / Chapter 2 --- Baseline Speech Recognition System --- p.17 / Chapter 2.1 --- Intoduction --- p.17 / Chapter 2.2 --- Feature Extraction --- p.18 / Chapter 2.3 --- Hidden Markov Model for Speech Recognition --- p.24 / Chapter 2.3.1 --- The Principle of Using HMM in Speech Recognition --- p.24 / Chapter 2.3.2 --- Elements of an HMM --- p.27 / Chapter 2.3.3 --- Parameters Estimation and Recognition Algorithm --- p.30 / Chapter 2.3.4 --- Summary of HMM based Speech Recognition --- p.31 / Chapter 2.4 --- TIMIT Continuous Speech Corpus --- p.32 / Chapter 2.5 --- Baseline Speech Recognition Experiments --- p.36 / Chapter 2.6 --- Summary --- p.39 / References --- p.40 / Chapter 3 --- Multi-Resolution Based Acoustic Features --- p.42 / Chapter 3.1 --- Introduction --- p.42 / Chapter 3.2 --- Discrete Wavelet Transform --- p.43 / Chapter 3.3 --- Periodic Discrete Wavelet Transform --- p.47 / Chapter 3.4 --- Multi-Resolution Analysis on STFT Spectrum --- p.49 / Chapter 3.5 --- Principal Component Analysis --- p.52 / Chapter 3.5.1 --- Related Work --- p.52 / Chapter 3.5.2 --- Theoretical Background of PCA --- p.53 / Chapter 3.5.3 --- Examples of Basis Vectors Found by PCA --- p.57 / Chapter 3.6 --- Experiments for Multi-Resolution Based Feature --- p.60 / Chapter 3.6.1 --- Experiments with Clean Speech --- p.60 / Chapter 3.6.2 --- Experiments with Noisy Speech --- p.64 / Chapter 3.7 --- Summary --- p.69 / References --- p.70 / Chapter 4 --- Wavelet Packet Based Acoustic Features --- p.72 / Chapter 4.1 --- Introduction --- p.72 / Chapter 4.2 --- Wavelet Packet Filter-Bank --- p.74 / Chapter 4.3 --- Dimensionality Reduction --- p.76 / Chapter 4.4 --- Filter-Bank Parameters --- p.77 / Chapter 4.4.1 --- Mel-Scale Wavelet Packet Filter-Bank --- p.77 / Chapter 4.4.2 --- Effect of Down-Sampling --- p.78 / Chapter 4.4.3 --- Mel-Scale Wavelet Packet Tree --- p.81 / Chapter 4.4.4 --- Wavelet Filters --- p.84 / Chapter 4.5 --- Experiments Using Wavelet Packet Based Acoustic Features --- p.86 / Chapter 4.6 --- Broad Phonetic Class Analysis --- p.89 / Chapter 4.7 --- Discussion --- p.92 / Chapter 4.8 --- Summary --- p.99 / References --- p.100 / Chapter 5 --- De-Noising by Wavelet Transform --- p.101 / Chapter 5.1 --- Introduction --- p.101 / Chapter 5.2 --- De-Noising Capability of Wavelet Transform --- p.103 / Chapter 5.3 --- Wavelet Transform Based Wiener Filtering --- p.105 / Chapter 5.3.1 --- Sub-Band Position for Wiener Filtering --- p.107 / Chapter 5.3.2 --- Estimation of Short-Time Speech and Noise Power --- p.109 / Chapter 5.4 --- De-Noising Embedded in Wavelet Packet Filter-Bank --- p.115 / Chapter 5.5 --- Experiments Using Wavelet Build-in De-Noising Properties --- p.118 / Chapter 5.6 --- Discussion --- p.120 / Chapter 5.6.1 --- Broad Phonetic Class Analysis --- p.122 / Chapter 5.6.2 --- Distortion Measure --- p.124 / Chapter 5.7 --- Summary --- p.132 / References --- p.134 / Chapter 6 --- Conclusions and Future Work --- p.138 / Chapter 6.1 --- Conclusions --- p.138 / Chapter 6.2 --- Future Work --- p.140 / References --- p.142 / Appendix 1 Jacobi's Method --- p.143 / Appendix 2 Broad Phonetic Class --- p.148

Shea Yuen Cheuk. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 91-94). / Abstracts in English and Chinese. / Introduction --- p.5 / Chapter 1 --- Prelimaries --- p.9 / Chapter 1.1 --- Basic Notations --- p.9 / Chapter 1.2 --- Multiresolution Analysis --- p.12 / Chapter 1.3 --- Orthonormal Wavelets --- p.17 / Chapter 1.4 --- Theory of Frames --- p.24 / Chapter 2 --- Construction of Orthonormal Wavelets --- p.33 / Chapter 2.1 --- Compactly Supported Smooth Orthonormal Wavelet in R --- p.33 / Chapter 2.2 --- Compactly Supported Smooth Orthonormal Wavelet in R2 --- p.40 / Chapter 3 --- Wavelet Frames --- p.51 / Chapter 3.1 --- Basic Properties --- p.51 / Chapter 3.2 --- Dual Wavelet Frame --- p.56 / Chapter 3.3 --- Canonical Dual Frame --- p.66 / Chapter 3.4 --- Oversampling --- p.69 / Chapter 4 --- MRA-Based Wavelet Frames --- p.74 / Chapter 4.1 --- Definitions --- p.74 / Chapter 4.2 --- Tight Frames Constructed by MRA --- p.77 / Chapter 4.3 --- Approximation Order and Vanishing Moments for Wavelet Frames --- p.82 / Chapter 4.4 --- Construction of MRA-Based Wavelet Frames --- p.85 / Bibliography --- p.91

by Pun Kong-Pang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 94-[96]). / Acknowledgement --- p.i / Abstract --- p.iii / List of Tables --- p.vii / List of Figures --- p.viii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Role of Device Simulation --- p.2 / Chapter 1.2 --- Classification of Device Models --- p.3 / Chapter 1.3 --- Sections of a Typical Simulator --- p.6 / Chapter 1.4 --- Arrangement of This Thesis --- p.7 / Chapter 2 --- Classical Physical Model --- p.9 / Chapter 2.1 --- Carrier Densities --- p.12 / Chapter 2.2 --- Space Charge --- p.14 / Chapter 2.3 --- Carrier Mobilities --- p.15 / Chapter 2.4 --- Generation and Recombination --- p.17 / Chapter 2.5 --- Modeling of Device Boundaries --- p.20 / Chapter 2.6 --- Limits of Classical Device Modeling --- p.22 / Chapter 3 --- Computational Aspects --- p.23 / Chapter 3.1 --- Normalization --- p.24 / Chapter 3.2 --- Discretization --- p.26 / Chapter 3.2.1 --- Finite Difference Method --- p.26 / Chapter 3.2.2 --- Finite Element Method --- p.27 / Chapter 3.3 --- Nonlinear Systems --- p.28 / Chapter 3.3.1 --- Newton's Method --- p.28 / Chapter 3.3.2 --- Gummel's Method and its modification --- p.29 / Chapter 3.3.3 --- Comparison and discussion --- p.30 / Chapter 3.4 --- Linear System and Sparse Matrix --- p.32 / Chapter 4 --- Cubic Spline Wavelet Collocation Method for PDEs --- p.34 / Chapter 4.1 --- Cubic spline scaling functions and wavelets --- p.35 / Chapter 4.1.1 --- Approximation for a function in H2(I) --- p.43 / Chapter 4.2 --- Wavelet interpolation --- p.45 / Chapter 4.2.1 --- Interpolant operator Ivo in Vo --- p.45 / Chapter 4.2.2 --- Interpolation operator IWjf in Wj --- p.47 / Chapter 4.3 --- Derivative Matrices --- p.51 / Chapter 4.3.1 --- First derivative matrix --- p.51 / Chapter 4.3.2 --- Second derivative matrix --- p.53 / Chapter 4.4 --- Wavelet Collocation Method for Solving Device Equations --- p.55 / Chapter 4.4.1 --- Steady state solution --- p.57 / Chapter 4.4.2 --- Transient solution --- p.58 / Chapter 4.5 --- Reducing Collocation Points --- p.59 / Chapter 4.5.1 --- Error evaluation --- p.59 / Chapter 4.5.2 --- Deleting collocation points --- p.61 / Chapter 5 --- Numerical Results --- p.64 / Chapter 5.1 --- P-N Junction Diode --- p.64 / Chapter 5.1.1 --- Steady state solution --- p.69 / Chapter 5.1.2 --- Transient solution --- p.76 / Chapter 5.1.3 --- Convergence --- p.79 / Chapter 5.2 --- Bipolar Transistor --- p.81 / Chapter 5.2.1 --- Boundary Model --- p.82 / Chapter 5.2.2 --- DC Solution --- p.83 / Chapter 5.2.3 --- Transient Solution --- p.89 / Chapter 6 --- Conclusions --- p.92 / Bibliography --- p.94

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Thesis (Ph. D.)--University of Missouri-Columbia, 1998. / Typescript. Vita. Includes bibliographical references (leaves 85-87). Also available on the Internet.

Thesis (M. Phil.)--University of Hong Kong, 2001. / Includes bibliographical references (leaves 80-81).