The ionosphere is a dynamic and ionized medium. Specification of the ionospheric electron density is important for radio systems operating up to a few GHz. Such systems include communication, navigation and surveillance operations. Computerized Ionospheric Tomography (CIT) is a technique that allows specification of the electron density in the ionosphere. CIT, unlike medical tomography, has geometric limitations such as uneven and sparse distribution of ground-based receivers and limited-angle observations. The inversion is therefore underdetermined and to overcome the geometric limitations of the problem, regularization techniques need to be used. In this thesis the horizontal variation of the ionosphere is represented using wavelet basis functions. Wavelets are chosen because the ground based ionospheric instrumentation is unevenly distributed and hence there is an expectation that the resolution of the tomographic image will change across a large region of interest. Wavelets are able to represent structures with different scale and position efficiently, which is known as Multi Resolution Analysis (MRA). The theory of sparse regularization allows the usage of a small number of basis functions with minimum loss of information. Furthermore, sparsity through wavelets can better differentiate between noise and actual information. This is advantageous because it increases the efficacy to resolve the structures of the ionosphere at different spatial horizontal scale sizes. The basis set is also extended to incorporate time dependence in the tomographic images by means of three-dimensional wavelets. The methods have been tested using both simulated and real observations from the Global Navigation Satellite System (GNSS). The simulation was necessary in order to have a controllable environment where the ability to resolve different scale structures would be tested. The further analysis of the methods required also the use of real observations. They tested the technique under conditions of temporal dynamics that would be more difficult to reproduce with simulations, which often tend to be valid in quiet ionospheric behaviors. Improvements in the detection and reconstruction of ionospheric structures were illustrated with sparse regularization. The comparison was performed against two standard methods. The first one was based on spherical harmonics in space, whilst the second relied on a time-dependent smoothing regularization. In simulation, wavelets showed the possibility to resolve small-scale structures better than spherical harmonics and illustrated the potential of creating ionospheric maps at high resolution. In reality, GNSS satellite orbits allow satellite to receiver datasets that traverse the ionosphere at a few hundred km per second and hence a long time window of typically half an hour may be required to provide observations. The assumption of an unchanging ionosphere is only valid at some locations under very quiet geomagnetic conditions and at certain times of day. For this reason the theory was extended to include time dependence in the wavelet method. This was obtained by considering two approaches: a time-smooth regularization and three-dimensional wavelets. The wavelet method was illustrated on a European dataset and demonstrated some improvements in the reconstructions of the main trough. In conclusion wavelets and sparse regularization were demonstrated to be a valid alternative to more standard methods.

A apneia é um Distúrbio Respiratório do Sono com grande incidência, estimando-se que esteja presente em 13% dos homens e 6% das mulheres nos Estados Unidos. Correlacionados com a apoeia, estão a obesidade, a diabete mellitus e, principalmente, algumas doenças cardíacas. No Brasil ainda há poucas pesquisas, possivelmente pelo difícil acesso e pelo alto custo das Polissonografias. Neste trabalho são analisados alguns sinais de Polissonografia, como o Eletrocardiograma, a Saturação do Oxigênio no Sangue, o Flu.xo Respiratório e o Esforço Respiratório. Mostramos como a Transformada Wavelet Discreta e as Redes Nemais constituem ferramentas matemáticas computacionais que possibilitam a extração de características e a classificação, servindo de suporte ao diagnóstico utilizado at ualmente. / Apnea is a highly incident Sleep-Disordered Breathing, which a icts roughly 13% of men and 6% of the women in the USA. It is also found a few correlations with other diseases, like obesity, diabetes mellitus and, especially, certain cardiac diseases. In Brazil, there are few studies, possibly due to the di cult access and the cost of Polysomnography. In this study, we analyzed some signals of Polysomnography, as the electrocardiogram, the oxygen saturation, the respiratory ow and respiratory e ort. We show how the Discrete Wavelet Transform and Neural Network may be applied as computational mathematical tools that enable feature extraction and classi cation, serving to support the diagnosis currently used.

by Chan Chung-Kei, Thomas. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 125-[129]). / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Semiconductor Device Physics --- p.5 / Chapter 2.1 --- IC Design Methodology --- p.6 / Chapter 2.1.1 --- System Level --- p.7 / Chapter 2.1.2 --- Circuit Level --- p.7 / Chapter 2.1.3 --- Device Level --- p.8 / Chapter 2.1.4 --- Process Level --- p.8 / Chapter 2.2 --- Classification of Device Models --- p.8 / Chapter 2.2.1 --- Circuit Models --- p.9 / Chapter 2.2.2 --- Physical Models --- p.10 / Chapter 2.3 --- Classical Drift-Diffusion model --- p.13 / Chapter 2.3.1 --- Basic Governing Equations in Semiconductors --- p.13 / Chapter 2.3.2 --- Shockley-Read-Hall Recombination Statics --- p.15 / Chapter 2.3.3 --- Boundary Conditions --- p.18 / Chapter 2.4 --- pn Junction at equilibrium --- p.20 / Chapter 2.4.1 --- The depletion approximation --- p.23 / Chapter 2.4.2 --- Current-voltage Characteristics --- p.26 / Chapter 3 --- Iteration Scheme --- p.30 / Chapter 3.1 --- Gummel's iteration scheme --- p.31 / Chapter 3.2 --- Modified Gummel's iteration scheme --- p.35 / Chapter 3.3 --- Solution of Differential Equation --- p.38 / Chapter 3.3.1 --- Finite Difference Method --- p.38 / Chapter 3.3.2 --- Moment Method --- p.39 / Chapter 4 --- Theory of Wavelets --- p.43 / Chapter 4.1 --- Multi-resolution Analysis --- p.43 / Chapter 4.1.1 --- Example of MRA with Haar Wavelet --- p.46 / Chapter 4.2 --- Orthonormal basis of Wavelets --- p.52 / Chapter 4.3 --- Fast Wavelet Transform --- p.56 / Chapter 4.4 --- Wavelets on the interval --- p.62 / Chapter 5 --- Galerkin-Wavelet Method --- p.66 / Chapter 5.1 --- Wavelet-based Moment Methods --- p.67 / Chapter 5.1.1 --- Wavelet transform on the stiffness matrix --- p.67 / Chapter 5.1.2 --- Wavelets as basis functions --- p.68 / Chapter 5.2 --- Galerkin-Wavelet method --- p.69 / Chapter 5.2.1 --- Boundary Conditions --- p.73 / Chapter 5.2.2 --- Adaptive Scheme --- p.74 / Chapter 5.2.3 --- The Choice of Classes of Wavelet Bases --- p.76 / Chapter 6 --- Numerical Results --- p.80 / Chapter 6.1 --- Steady State Solution --- p.81 / Chapter 6.1.1 --- Daubechies Wavelet N = 2 --- p.82 / Chapter 6.1.2 --- Daubechies Wavelet N=5 --- p.84 / Chapter 6.1.3 --- Discussion on Daubechies wavelets N = 2 and N=5 --- p.86 / Chapter 6.2 --- Transient Solution --- p.91 / Chapter 6.3 --- Convergence --- p.99 / Chapter 7 --- Conclusion --- p.103 / Chapter A --- Derivation for steady state --- p.107 / Chapter A.1 --- Generalized Moll-Ross Relation --- p.107 / Chapter A.2 --- Linearization of PDEs --- p.110 / Chapter B --- Derivation for transient state --- p.113 / Chapter C --- Notation --- p.119 / Chapter D --- Elements in the Stiffness Matrix --- p.122 / Bibliography --- p.125

Made available in DSpace on 2014-06-12T17:39:28Z (GMT). No. of bitstreams: 2 arquivo6902_1.pdf: 3068620 bytes, checksum: eb2722910d045ddc14f0488856268b0c (MD5) license.txt: 1748 bytes, checksum: 8a4605be74aa9ea9d79846c1fba20a33 (MD5) Previous issue date: 2007 / Esta dissertação se propõe a investigar a representação de sinais no plano tempofreq üência e, mais especificamente, os problemas relativos à resolução de sinais. O princípio da incerteza de Gabor-Heisenberg para sinais e wavelets é analisado criteriosamente. Versões de Gnedenko-Kolmogorov do tipo Teorema Central do Limite são avaliadas, procurando elucidar sua relevância no contexto da resolução de sinais. Finalmente, o conceito de derivada Blur é usado para propor uma nova família de wavelets - as wavelets beta - construídas a partir de distribuições beta de probabilidade. Essas wavelets são atrativas por terem suporte compacto, são monocíclicas, possuem descrição analítica e podem ser consideradas como uma generalização suavizada das wavelets de Haar. Sua relevância decorre do Teorema Central do Limite aplicado a wavelets de suporte compacto. Campos promissores para aplicação destas wavelets são mencionado

No description available.

Orientador: Orlando José Tobias. / Coorientador: Marcelo Grafulha Vanti. / Dissertação (mestrado) - Universidade Regional de Blumenau, Centro de Ciências Tecnológicas, Programa de Pós-Graduação em Engenharia Elétrica.

Qin, Guiming. / "August 2010." / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (p. 72-74). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 1.1 --- B splines and B-splines surfaces --- p.5 / Chapter 1. 2 --- Box spline --- p.6 / Chapter 1. 3 --- Biorthogonal subdivision wavelets based on the lifting scheme --- p.7 / Chapter 1.4 --- Geometrically-constrained subdivision wavelets --- p.9 / Chapter 1.5 --- Contributions --- p.9 / Chapter 2 --- Explicit symbol formulae for B-splines --- p.11 / Chapter 2. 1 --- Explicit formula for a general recursion scheme --- p.11 / Chapter 2. 2 --- Explicit formulae for de Boor algorithms of B-spline curves and their derivatives --- p.14 / Chapter 2.2.1 --- Explicit computation of de Boor Algorithm for Computing B-Spline Curves --- p.14 / Chapter 2.2.2 --- Explicit computation of Derivatives of B-Spline Curves --- p.15 / Chapter 2. 3 --- Explicit power-basis matrix fomula for non-uniform B-spline curves --- p.17 / Chapter 3 --- Biorthogonal subdivision wavelets with geometric constraints --- p.23 / Chapter 3. 1 --- Primal subdivision and dual subdivision --- p.23 / Chapter 3. 2 --- Biorthogonal Loop-subdivision-based wavelets with geometric constraints for triangular meshes --- p.24 / Chapter 3.2.1 --- Loop subdivision surfaces and exact evaluation --- p.24 / Chapter 3.2.2 --- Lifting-based Loop subdivision wavelets --- p.24 / Chapter 3.2.3 --- Biorthogonal Loop-subdivision wavelets with geometric constraints --- p.26 / Chapter 3. 3 --- Biorthogonal subdivision wavelets with geometric constraints for quadrilateral meshes --- p.35 / Chapter 3.3.1 --- Catmull-Clark subdivision and Doo-Sabin subdivision surfaces --- p.35 / Chapter 3.3.1.1 --- Catmull-Clark subdivision --- p.36 / Chapter 3.3.1.2 --- Doo-Sabin subdivision --- p.37 / Chapter 3.3.2 --- Biorthogonal subdivision wavelets with geometric constraints for quadrilateral meshes --- p.38 / Chapter 3.3.2.1 --- Biorthogonal Doo-Sabin subdivision wavelets with geometric constraints --- p.38 / Chapter 3.3.2.2 --- Biorthogonal Catmull-Clark subdivision wavelets with geometric constraints --- p.44 / Chapter 4 --- Experiments and results --- p.49 / Chapter 5 --- Conclusions and future work --- p.60 / Appendix A --- p.62 / Appendix B --- p.67 / Appendix C --- p.69 / Appendix D --- p.71 / References --- p.72

"August, 2003" Bibliography: p. 261-268. In this thesis, wavelet transforms are chosen as the primary analytical tool for texture analysis. Specifically, Dual-Tree Complex Wavelet Transform is applied to the texture segmentation problem. Several possibilities for feature extraction and clustering steps are examined, new schemes being introduced and compared to known techniques.

Includes bibliographical references (leaves 199-214) / xxx, 214 leaves : ill. (some col.), plates (col.) ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Electrical and Electronic Engineering, 2002

"August, 2003" / Bibliography: p. 261-268. / xxvi, 268 p. : ill. (some col.) ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / In this thesis, wavelet transforms are chosen as the primary analytical tool for texture analysis. Specifically, Dual-Tree Complex Wavelet Transform is applied to the texture segmentation problem. Several possibilities for feature extraction and clustering steps are examined, new schemes being introduced and compared to known techniques. / Thesis (Ph.D.)--University of Adelaide, Dept. of Electrical and Electronic Engineering, 2003