Dissertations / Theses on the topic 'Wavelets'
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Gussin, Sara. "Wavelets and Wavelet Sets." Scholarship @ Claremont, 2008. https://scholarship.claremont.edu/hmc_theses/206.
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Wavelets are functions that are useful for representing signals and approximating other functions. Wavelets sets are defined in terms of Fourier transforms of certain wavelet functions. In this paper, we provide an introduction to wavelets and wavelets sets, examine the preexisting literature on the subject, and investigate an algorithm for creating wavelet sets. This algorithm creates single wavelets, which can be used to create bases for L2(Rn) through dilation and translation. We investigate the convergence properties of the algorithm, and implement the algorithm in Matlab.
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Kutyniok, Gitta. "Affine density in wavelet analysis /." Berlin [u.a.] : Springer, 2007. http://www.gbv.de/dms/ilmenau/toc/529512874.PDF.
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Alnasser, Mais. "PHASE-SHIFTING HAAR WAVELETS FOR IMAGE-BASED RENDERING APPLICATIONS." Doctoral diss., University of Central Florida, 2008. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/4181.
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In this thesis, we establish the underlying research background necessary for tackling the problem of phase-shifting in the wavelet transform domain. Solving this problem is the key to reducing the redundancy and huge storage requirement in Image-Based Rendering (IBR) applications, which utilize wavelets. Image-based methods for rendering of dynamic glossy objects do not truly scale to all possible frequencies and high sampling rates without trading storage, glossiness, or computational time, while varying both lighting and viewpoint. This is due to the fact that current approaches are limited to precomputed radiance transfer (PRT), which is prohibitively expensive in terms of memory requirements when both lighting and viewpoint variation are required together with high sampling rates for high frequency lighting of glossy material. At the root of the above problem is the lack of a closed-form run-time solution to the nontrivial problem of rotating wavelets, which we solve in this thesis. We specifically target Haar wavelets, which provide the most efficient solution to solving the tripleproduct integral, which in turn is fundamental to solving the environment lighting problem. The problem is divided into three main steps, each of which provides several key theoretical contributions. First, we derive closed-form expressions for linear phase-shifting in the Haar domain for one-dimensional signals, which can be generalized to N-dimensional signals due to separability. Second, we derive closed-form expressions for linear phase-shifting for two-dimensional signals that are projected using the non-separable Haar transform. For both cases, we show that the coefficients of the shifted data can be computed solely by using the coefficients of the original data. We also derive closed-form expressions for non-integer shifts, which has not been reported before. As an application example of these results, we apply the new formulae to image shifting, rotation and interpolation, and demonstrate the superiority of the proposed solutions to existing methods. In the third step, we establish a solution for non-linear phase-shifting of two-dimensional non-separable Haar-transformed signals, which is directly applicable to the original problem of image-based rendering. Our solution is the first attempt to provide an analytic solution to the difficult problem of rotating wavelets in the transform domain.Ph.D.
School of Electrical Engineering and Computer Science
Engineering and Computer Science
Computer Science PhD
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Colthurst, Thomas. "Multidimensional wavelets." Thesis, Massachusetts Institute of Technology, 1997. http://hdl.handle.net/1721.1/43934.
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Piché, Daniel Guy. "IFSM, wavelets and fractal-wavelets, three methods of approximation." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp04/mq21538.pdf.
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Pich??, Daniel Guy. "IFSM, wavelets and fractal-wavelets, three methods of approximation." Thesis, National Library of Canada = Biblioth??que nationale du Canada, 1997. http://hdl.handle.net/10012/29.
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Ebert, Svend. "Wavelets on Lie groups and homogeneous spaces." Doctoral thesis, Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2011. http://nbn-resolving.de/urn:nbn:de:bsz:105-qucosa-78988.
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Within the past decades, wavelets and associated wavelet transforms have been intensively investigated in both applied and pure mathematics. They and the related multi-scale analysis provide essential tools to describe, analyse and modify signals, images or, in rather abstract concepts, functions, function spaces and associated operators. We introduce the concept of diffusive wavelets where the dilation operator is provided by an evolution like process that comes from an approximate identity. The translation operator is naturally defined by a regular representation of the Lie group where we want to construct wavelets. For compact Lie groups the theory can be formulated in a very elegant way and also for homogeneous spaces of those groups we formulate the theory in the theory of non-commutative harmonic analysis. Explicit realisation are given for the Rotation group SO(3), the k-Torus, the Spin group and the n-sphere as homogeneous space. As non compact example we discuss diffusive wavelets on the Heisenberg group, where the construction succeeds thanks to existence of the Plancherel measure for this group. The last chapter is devoted to the Radon transform on SO(3), where the application on diffusive wavelets can be used for its inversion. The discussion of a variational spline approach provides criteria for the choice of points for measurements in concrete applications.
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Agulhari, Cristiano Marcos 1983. "Compressão de eletrocardiogramas usando wavelets." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/259213.
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Orientador: Ivanil Sebastião BonattiDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação
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Resumo: A principal contribuição desta dissertação é a proposta de dois métodos de compressão de eletrocardiogramas (ECGs). O primeiro método, chamado Run Length Encoding Adaptativo (RLEA), é baseado nas transformadas wavelet e consiste basicamente em utilizar uma função wavelet, obtida pela resolução de um problema de otimização, que se ajuste ao sinal a ser comprimido. O problema de otimização torna-se irrestrito com a parametrização dos coeficientes do filtro escala, que definem unicamente uma função wavelet. Após a resolução do problema de otimização é aplicado o procedimento de decomposição wavelet no sinal e os coeficientes de representação mais significativos são retidos, sendo que o número de coeficientes retidos é determinado de forma a satisfazer uma medida de distorção pré-especificada. Os coeficientes retidos são então quantizados e compactados, assim como o bitmap que indica as posições dos coeficientes retidos. A quantização é feita de forma adaptativa, utilizando diferentes números de bits de quantização para os diferentes subespaços de decomposição considerados. Tanto os valores dos coeficientes retidos quanto o bitmap são codificados utilizando uma variante do método Run Length Encoding. O segundo método proposto nesta dissertação, chamado Zero Padding Singular Values Decomposition (ZPSVD), consiste em primeiramente detectar os batimentos, equalizá-los pela inserção de zeros (zero padding) e então aplicar a decomposição SVD para obter tanto a base quanto os coeficientes de representação dos batimentos. Alguns componentes da base são retidos e então comprimidos utilizando os mesmos procedimentos aplicados aos coeficientes de decomposição do ECG no método RLEA, enquanto que os coeficientes de projeção dos batimentos nessa base são quantizados utilizando um procedimento de quantização adaptativa. Os dois métodos de compressão propostos são comparados com diversos outros métodos existentes na literatura por meio de experimentos numéricos
Abstract: The main contribution of the present thesis is the proposition of two electrocardiogram (ECG) compression methods. The first method, called Run Length Encoding Adaptativo (RLEA), is based on wavelet transforms and consists of using a wavelet function, obtained by the resolution of an optimization problem, which fits to the signal to be compressed. The optimization problem becomes unconstrained with the parametrization of the coefficients of the scaling filter, that define uniquely a wavelet function. After the resolution of the optimization problem, the wavelet decomposition procedure is applied to the signal and the most significant coefficients of representation are retained, being the number of retained coefficients determined in order to satisfty a pre-specified distortion measure. The retained coefficients are quantized and compressed, likewise the bitmap that informs the positions of the retained coefficients. The quantization is performed in an adaptive way, using different numbers of bits for the different decomposition subspaces considered. Both the values of the retained coefficients and the bitmap are encoded using a modi- fied version of the Run Length Encoding technique. The second method proposed in this dissertation, called Zero Padding Singular Values Decomposition (ZPSVD), consists of detecting the beat pulses of the ECG, equalizing the pulses by inserting zeros (zero padding), and finally applying the SVD to obtain both the basis and the coefficients of representation of the beat pulses. Some components of the basis are retained and then compressed using the same procedures applied to the coefficients of decomposition of the ECG in the RLEA method, while the coefficients of projection of the beat pulses in the basis are quantized using an adaptive quantization procedure. Both proposed compression methods are compared to other techniques by means of numerical experiments
Mestrado
Telecomunicações e Telemática
Mestre em Engenharia Elétrica
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Thielemann, Henning. "Optimally matched wavelets." kostenfrei, 2005. http://deposit.dnb.de/cgi-bin/dokserv?idn=98026684X.
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Rachelli, Janice. "Frames de wavelets." reponame:Repositório Institucional da UFSC, 1995. http://repositorio.ufsc.br/xmlui/handle/123456789/76270.
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Expansões não necessariamente ortogonais de funções no espaço de Hilbert das funções reais quadrado integráveis, através de uma família de funções gerada a partir de uma única função Wavelet. Se a família gera um frame, então para qualquer função f no espaço de Hilbert citado, existe uma expansão semelhante à expansão ortogonal.
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Varanis, Marcus Vinicius Monteiro [UNESP]. "Análise de vibrações em sistemas discretos de massas concentradas e com dois graus de liberdade através da transformada wavelet." Universidade Estadual Paulista (UNESP), 2008. http://hdl.handle.net/11449/91946.
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varanis_mvm_me_rcla.pdf: 4826016 bytes, checksum: ab2c8b052e0a038577280ce930b14260 (MD5)O estudo de vibrações diz respeito aos movimentos oscilatórios de corpos e às forças que lhes são associadas. Todos os corpos dotados de massa e elasticidade são capazes de vibrar. Deste modo, a maior parte das máquinas e estruturas estão sujeitas a certos graus de vibração A maioria das atividades humanas envolve alguma forma de vibração. O estudo do comportamento dinâmico dessas oscilações mecânicas é o objetivo deste trabalho e para isto propomos um sistema de massas concentradas e com dois graus de liberdade. O sistema será excitado por forças externas, entre elas ondas de terremoto. Com simulações numéricas estudamos o sistema, usando a transformada rápida de Fourier, transformada wavelet.
The study of vibration concerns oscillatory movement of bodies and the forces they are associated. All bodies that have mass and elasticity are able to vibrate. Thus, most of the machines and structures are subject to certain degrees of vibration most human activities involve some form of vibration. The study of the dynamic behavior of these mechanical oscillations is the objective of this work and to propose that a system of weights and concentrated with two degrees of freedom. The system will be excited by external forces, including waves of earthquake. With numerical simulations studied the system, using the fast Fourier transform, wavelet transform.
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Gottscheber, Achim. "Multi-dimensional wave digital filters and wavelets Mehrdimensionale Wellendigitalfilter und Wavelets /." [S.l. : s.n.], 1999. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB10605015.
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Reimermendt, Renan Renie Gevisiez. "Wavelets em economia: utilizando wavelets para projetar inflação via curva de Phillips." reponame:Repositório Institucional do FGV, 2017. http://hdl.handle.net/10438/18420.
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Wavelet analysis allows for a much more flexible approach than spectral analysis, being highly utilized in many fields, it is a natural evolution from the Fourier analysis. Unifying both time domain and frequency domain in its analysis, it gives the researcher the ability to observe relations that were previously inaccessible and its flexibility makes it recommended to analyze series with structural changes. This work contains a chronological and theoretical introduction of the technique, focusing on what will be used, presenting some successful applications in economics. Lastly, it is created a measure of economic activity by denoising, in both global and specific scales, the seasonally adjusted GDP series and utilizing this measure in a Phillips curve, as described by the Brazilian Central Bank in theirs semi-structural aggregate small sized models, to forecast future inflation. This forecast is then compared to forecasts using the traditional HP filter and a measure of output gap elaborated by Areosa (2008), which incorporates some economic structure in the output gap.
A análise de wavelet permite uma abordagem muito mais flexível que a análise espectral, sendo bastante utilizada em diversas áreas, ela é uma evolução natural da análise de Fourier. Unificando o domínio do tempo e o da frequência em sua análise, dão ao pesquisador a capacidade de observar relações que antes eram inacessíveis e sua flexibilidade a torna recomendada para analisar séries onde ocorram mudanças estruturais. Este trabalho faz uma introdução cronológica e teórica da técnica, focando no que será utilizado, apresentando algumas aplicações bem-sucedidas em economia. Por fim, é criado uma medida de atividade econômica ao extrair ruídos, globais e em escalas específicas, da série de PIB dessazonalizado e utilizado esta medida numa curva de Phillips, como descrita pelo Banco Central do Brasil em seus modelos agregados semiestruturais de pequeno porte, para projetar inflação futura. Estas projeções também são comparadas com projeções utilizando o tradicional filtro HP e uma medida de hiato elaborada por Areosa (2008), que incorpora uma estrutura econômica ao hiato do produto.
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Policardi, Helena. "La Teoria delle Wavelets." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/14718/.
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La tesi è un'esamina della teoria delle wavelets. Dal sistema di Haar (la cui peculiarità è essere un sistema di basi ortonormali) si passa all' analisi in multirisoluzione e la definizione di Wavelet che ne consegue. Infine si esamina la costruzione di Daubechies (relativa alle wavelets a supporto compatto).
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Rocha, Pitta Jorge Antonio Fernandes da. "Transient detection using wavelets." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 1995. http://handle.dtic.mil/100.2/ADA297697.
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Thesis (M.S. in Electrical Engineering) Naval Postgraduate School, March 1995."March 1995." Thesis advisor(s): Ralph D. Hippenstiel, Monique P. Fargues. Includes bibliographical references. Also available online.
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Hua, Xinhou. "Dynamical systems and wavelets." Thesis, University of Ottawa (Canada), 2002. http://hdl.handle.net/10393/6143.
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The first part of this thesis is concerned with Bakers Conjecture (1984) which says that two permutable transcendental entire functions have the same Julia set. To this end, we shall exhibit that two permutable transcendental entire functions of a certain type have the same Julia set. So far, this is the best result to the conjecture. The second part relates to Newton's method to find zeros of functions. We shall look for the locations of the limits of the iterating sequence of the relaxed Newton function on its wandering domains. A relaxed Newton function with corresponding properties is constructed. The third part relates to the dynamics of ordinary differential equations and inverse problems. Given a target solution, we shall construct second-order differential equations with Legendre polynomial basis to approximate the target solution. An algorithm and numerical solutions are provided. Examples show that the approximations we have found are much better than the known results obtained by means of first-order differential equations. We shall also discuss approximation using a wavelet basis. MATLAB is used to compute the numerical results. In the fourth part, we deal with variational problems in signal and image processing. For a given signal or image represented by a function, we shall provide a good approximation to the function, which minimizes a given functional.
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Karoui, Abderrazek. "Multidimensional wavelets and applications." Thesis, University of Ottawa (Canada), 1995. http://hdl.handle.net/10393/9492.
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In this thesis, one- as well as multi-dimensional biorthogonal wavelet filters are designed and used for the construction of compactly supported wavelet bases. In particular, an adaptation of the McClellan transformation is used to design nonseparable 2-D biorthogonal wavelet bases. Some examples of 2-D biorthogonal wavelet filters are given in the case of the quincunx sampling lattice. Some theoretical and technical results known in the one-dimensional case have been generalized to the n-dimensional case. This generalization leads to a better understanding of the theory and design of multidimensional biorthogonal wavelets. An important part of the thesis devoted to the design of fast discrete wavelet transforms. The main ingredient of the algorithms is the use of a one-point quadrature formula for approximating the nest coefficients of the signals together with a suitable design and implementation of symmetric biorthogonal filters. Special attention is given to the case where the signals have sharp transition points. In this case, a smoothing process has been used to obtain an accurate reconstruction of the signal.
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Mandal, Mrinal Kumar. "Wavelets for image compression." Thesis, University of Ottawa (Canada), 1995. http://hdl.handle.net/10393/10277.
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Wavelets are becoming increasingly important in image compression applications because of its flexibility in representing nonstationary signals. To achieve a high compression ratio, the wavelet has to be adapted to the image. Current techniques use exhaustive search procedures which are computationally intensive to find the optimal basis (type/order/tree) for the image to be coded. In this thesis, we have carried out extensive performance analysis of various wavelets on a wide variety of images. Based on the investigation, we propose some guidelines for searching for the optimal wavelet (type/order) based on the overall activity (measured by the spectral flatness) of the image to be coded. These guidelines will provide the degree of improvement that can be achieved by using the "optimal" over "standard" wavelets. The proposed guidelines can be used to find a good initial guess for faster convergence when searching for optimal wavelet is essential. We propose a wave packet decomposition algorithm based on the local transform gain of the wavelet decomposed bands. The proposed algorithm provides good coding performance at significantly reduced complexity. Most practical coders are designed to minimize the mean square error (MSE) between the original and reconstructed image. It is known that at high compression ratio, MSE does not correspond well to the subjective quality of the image. In this thesis, we propose an image adaptive coding algorithm which tries to minimize the MSE weighted by the visual importance of various wavelet bands. It has been observed that the proposed algorithm provides a better coding performance for a wide variety of images.
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Wood, Peter John, and drwoood@gmail com. "Wavelets and C*-algebras." Flinders University. Informatics and Engineering, 2003. http://catalogue.flinders.edu.au./local/adt/public/adt-SFU20070619.120926.
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A wavelet is a function which is used to construct a specific type of orthonormal basis.
We are interested in using C*-algebras and Hilbert C*-modules to study wavelets. A Hilbert C*-module is a generalisation of a Hilbert space for which the inner product takes its values in a C*-algebra instead of the complex numbers. We study wavelets in an arbitrary Hilbert space and construct some Hilbert C*-modules over a group C*-algebra which will be used to study the properties of wavelets.
We study wavelets by constructing Hilbert C*-modules over C*-algebras generated by groups of translations. We shall examine how this construction works in both the Fourier and non-Fourier domains. We also make use of Hilbert C*-modules over the space of essentially bounded functions on tori. We shall use the Hilbert C*-modules mentioned above to study wavelet and scaling filters, the fast wavelet transform, and the cascade algorithm. We shall furthermore use Hilbert C*-modules over matrix C*-algebras to study multiwavelets.
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Suhasini, Subba Rao Tata. "Wavelets and adaptive filters." Thesis, University of Bristol, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.364840.
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Heaton, T. J. "Wavelets and accompanying applilcations." Thesis, University of Bristol, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.422570.
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NIBHANUPUDI, SWATHI. "SIGNAL DENOISING USING WAVELETS." University of Cincinnati / OhioLINK, 2003. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1070577417.
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Bowman, Christopher 1969. "Pattern formation and wavelets." Diss., The University of Arizona, 1997. http://hdl.handle.net/10150/288741.
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This thesis is a collection of results associated with pattern formation, and consists of several novel results. A multi-scale analysis is carried out near the lasing bifurcation on equations which model the free carrier semiconductor laser. This analysis produces an amplitude equation which resembles the Swift-Hohenberg equation derived for the simpler two level laser, but with extra terms arising from the more complicated semiconductor system. New results are also presented in the analysis of phase equations for patterns, showing that defects are weak solutions of the phase diffusion equation, and that the Gaussian curvature of the phase surface condenses onto point and line defects. This latter fact allows for considerable simplification of the phase diffusion equation, and this analysis is presented as well. Finally, and most importantly, an algorithm is presented, based on the continuous wavelet transform, for the extraction of local phase and amplitude information from roll patterns. This algorithm allows a precise detection of phase grain boundaries and point defects, as well as the computation of soft modes like the mean flow. Several tests are conducted on numerically generated signals to demonstrate the applicability and precision of the algorithm. The algorithm is then applied to actual experimental convection patterns, and conclusions about the nature of the wave director field in such patterns are presented.
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Yu, Lu. "Wavelets on hierarchical trees." Diss., University of Iowa, 2016. https://ir.uiowa.edu/etd/2302.
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Signals on hierarchical trees can be viewed as a generalization of discrete signals of length 2^N. In this work, we extend the classic discrete Haar wavelets to a Haar-like wavelet basis that works for signals on hierarchical trees. We first construct a specific wavelet basis and give its inverse and normalized transform matrices.
As analogue to the classic case, operators and wavelet generating functions are constructed for the tree structure. This leads to the definition of multiresolution analysis on a hierarchical tree. We prove the previously selected wavelet basis is an orthogonal multiresolution. Classification of all possible wavelet basis that generate an orthogonal multiresolution is then given. In attempt to find more efficient encoding and decoding algorithms, we construct a second wavelet basis and show that it is also an orthogonal multiresolution. The encoding and decoding algorithms are given and their time complexity are analyzed.
In order to link change of tree structure and encoded signal, we define weighted hierarchical tree, tree cut and extension. It is then shown that a simply relation can be established without the need for global change of the transform matrix. Finally, we apply thresholding to the transform and give an upper bound of error.
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Varanis, Marcus Vinicius Monteiro. "Análise de vibrações em sistemas discretos de massas concentradas e com dois graus de liberdade através da transformada wavelet /." Rio Claro : [s.n.], 2008. http://hdl.handle.net/11449/91946.
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Orientador: José Roberto CampanhaBanca: Roberto Eugenio Lagos Mônaco
Banca: Robson Pederiva
Resumo: O estudo de vibrações diz respeito aos movimentos oscilatórios de corpos e às forças que lhes são associadas. Todos os corpos dotados de massa e elasticidade são capazes de vibrar. Deste modo, a maior parte das máquinas e estruturas estão sujeitas a certos graus de vibração A maioria das atividades humanas envolve alguma forma de vibração. O estudo do comportamento dinâmico dessas oscilações mecânicas é o objetivo deste trabalho e para isto propomos um sistema de massas concentradas e com dois graus de liberdade. O sistema será excitado por forças externas, entre elas ondas de terremoto. Com simulações numéricas estudamos o sistema, usando a transformada rápida de Fourier, transformada wavelet.
Abstract: The study of vibration concerns oscillatory movement of bodies and the forces they are associated. All bodies that have mass and elasticity are able to vibrate. Thus, most of the machines and structures are subject to certain degrees of vibration most human activities involve some form of vibration. The study of the dynamic behavior of these mechanical oscillations is the objective of this work and to propose that a system of weights and concentrated with two degrees of freedom. The system will be excited by external forces, including waves of earthquake. With numerical simulations studied the system, using the fast Fourier transform, wavelet transform.
Mestre
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Navarro, Jaime. "The Continuous Wavelet Transform and the Wave Front Set." Thesis, University of North Texas, 1993. https://digital.library.unt.edu/ark:/67531/metadc277762/.
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In this paper I formulate an explicit wavelet transform that, applied to any distribution in S^1(R^2), yields a function on phase space whose high-frequency singularities coincide precisely with the wave front set of the distribution. This characterizes the wave front set of a distribution in terms of the singularities of its wavelet transform with respect to a suitably chosen basic wavelet.
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Soares, Wendel Cleber [UNESP]. "Um método não-limiar para redução de ruído em sinais de voz no domínio wavelet." Universidade Estadual Paulista (UNESP), 2009. http://hdl.handle.net/11449/100309.
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soares_wc_dr_ilha.pdf: 2948445 bytes, checksum: cf47c579c7e9a4f2d231373d9ed5f704 (MD5)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
Neste trabalho é feito um estudo dos métodos de redução de ruído aditivo em sinais de voz baseados em wavelets e, através deste estudo, propõe-se um novo método não-limiar para redução de ruído em sinais de voz no domínio wavelet. Em geral os sinais de voz podem estar contaminados com ruídos artificiais ou reais. O problema consiste que dado um sinal limpo adiciona-se o ruído branco ou colorido, obtendo assim o sinal ruidoso, ambos no domínio do tempo. O que se propõe neste trabalho, é aplicar a transformada wavelet, obtendo assim o sinal transformado no domínio wavelet, reduzindo ou atenuando o ruído sem o uso de limiar. Os métodos mais usados no domínio wavelet são os métodos de redução por limiar, pois permitem bons resultados para sinais contaminados por ruído branco, mas não são eficientes no processamento de sinais contaminados por ruído colorido, que é o tipo de ruído mais comum em situações reais. Nesses métodos, o limiar, geralmente, é calculado nos intervalos de silêncio e aplicado em todo o sinal. Os coeficientes no domínio wavelet são comparados com este limiar e aqueles que estão abaixo deste valor são eliminados ou reduzidos, fazendo assim uma aplicação linear deste limiar. Esta eliminação, na maioria das vezes, causa descontinuidades no tempo e na frequência no sinal processado. Além disso, a forma com que o limiar é calculado pode degradar os trechos de voz do sinal processado, principalmente nos casos em que o limiar depende fortemente da última janela do último trecho de silêncio. O método proposto nesta pesquisa consiste na execução de três processamentos, agindo de acordo com as suas características nas regiões de voz e silêncio, sem o uso de limiar. A execução dos três processamentos é sintetizada numa única função, denominada de função de transferência, que atua como um filtro no processamento do sinal...
In this work a study of the methods for speech noise reduction based on wavelets is done and, through this study, a new non-thresholding method for speech noise reduction in the wavelet domain is proposed. Generally, a speech signal may be corrupted by artificial or real noise. Let a clean signal be corrupted by white or colored noise, rising a noisy signal in time domain. This work proposes the wavelet application to which gives rise to in the wavelet domain. In this domain, noise is reduced or attenuated without a threshold use. After, the signal is recomposed using the inverse discrete wavelet transform. The most used methods in the wavelet domain wavelet are the thresholding reduction methods, because they allow good results for signals corrupted by white noise, but they do not have the same efficiency when processing signals corrupted by colored noise, this is the most common noise in real situations. In those methods, the threshold is usually calculated in the silence intervals and applied to the whole signal. The coefficients in the wavelet domain are compared with this threshold and those that have absolute value below this value are eliminated or reduced, making a linear application of this threshold. This elimination causes discontinuities in time and in the frequency of the processed signal. Besides, the form with that the threshold is applied can degrade the voice segments of the processed signal, principally in cases that the threshold depends strongly on the last window of the last silence segment. The method proposed in this research consists in the execution of three processing, acting according to their characteristics in the voice and silence segments, without the threshold use. The three processing execution is synthesized in an unique function, called transfer function, acting as a filter in the signal processing. This method has as main objective the overcoming... (Complete abstract click electronic access below)
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Sablik, Mathieu. "Wavelets in Abstract Hilbert Space." Thesis, Uppsala University, Department of Mathematics, 2000. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-122553.
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Andreassen, Børge Solli. "Wavelets and irregular time series." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2012. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-19011.
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In this thesis we study time series containing pressure measurements from a three phase flow pipeline at the Ekofisk oil field. The pipeline transports a mixture of oil, water and gas from $15$ wells for approximately 2.5km to a production facility. Our aim is to develop techniques that allow the selection and (to some extent) prediction of "non-standard" behavior in the system (sharp pressure changes and other type of instabilities). To advice this aim we perform a scalewise decomposition of the input signal/time series and investigate the behavior of each scale separately. We introduce the Sliding Window Wavelet Transform (SWWT) method. The method evaluate the variability on different scales within the time interval of a characteristic length (a window) and then trace these characteristics as the window slides in time.We use the discrete wavelet transform (DWT) in order to obtain the scalewise decomposition within the window. Using orthonormal discrete wavelets, we show that the variability of such sequences can be decomposed into their corresponding scales. Based on this, a thresholding algorithm is applied, characterizing the state of the system any given time. The results we find are promising and we show that different parameters in the thresholding algorithm extracts different types of special events. We also show that in some cases, this approach allows to predict special events before they really occur.While we investigate one particular system in this thesis, the procedures developed can be applied to other complicated systems where instability in system parameters is important.
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Loo, Patrick. "Digital watermarking using complex wavelets." Thesis, University of Cambridge, 2002. https://www.repository.cam.ac.uk/handle/1810/251833.
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Pelletier, Emile. "Instrument de-synthesis using wavelets." Thesis, University of Ottawa (Canada), 2005. http://hdl.handle.net/10393/27008.
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Our point of departure is the concept of 'additive synthesis', which is the traditional explanation for the individual of 'timbre' or 'colour' of the sound of the various musical instruments.
When an instrument sounds a note, one hears the note as if by itself, but this is not what is physically happening. What is in fact occurring is a complex waveform featuring a collection of harmonic frequencies, referred to as the spectrum.
A synthesizer attempts to imitate the sound of a particular instrument by replicating the amplitudes of its harmonics.
We use the term 'de-synthesis' to refer to the inverse procedure, computerized instrument identification.
We describe an experiment that we designed and executed with M ATLAB to explore the hypothesis that a computer will be able to recognize an instrument by its characteristic timbre.
The idea of applying wavelets to analyze music comes naturally since music consists of sound waves, and wavelets are wave shaped functions.
We propose a mathematical model that can take certain musical instrument's attack and decay features into account that utilizes Malvar wavelets: Super Malvar wavelets. Super wavelets are superpositions of ordinary wavelets in some linear combination that can be treated as a wavelet in itself. (Abstract shortened by UMI.)
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Liu, Mingyu. "Wavelets and Nyquist filter design." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape8/PQDD_0004/NQ38314.pdf.
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sun, weifeng. "WAVELETS IN REAL-TIME RENDERING." Doctoral diss., University of Central Florida, 2006. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/4026.
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Interactively simulating visual appearance of natural objects under natural illumination is a fundamental problem in computer graphics. 3D computer games, geometry modeling, training and simulation, electronic commerce, visualization, lighting design, digital libraries, geographical information systems, economic and medical image processing are typical candidate applications. Recent advances in graphics hardware have enabled real-time rasterization of complex scenes under artificial lighting environment. Meanwhile, pre-computation based soft shadow algorithms are proven effective under low-frequency lighting environment. Under the most practical yet popular all-frequency natural lighting environment, however, real-time rendering of dynamic scenes still remains a challenging problem. In this dissertation, we propose a systematic approach to render dynamic glossy objects under the general all-frequency lighting environment. In our framework, lighting integration is reduced to two rather basic mathematical operations, efficiently computing multi-function product and product integral. The main contribution of our work is a novel mathematical representation and analysis of multi-function product and product integral in the wavelet domain. We show that, multi-function product integral in the primal is equivalent to summation of the product of basis coefficients and integral coefficients. In the dissertation, we give a novel Generalized Haar Integral Coefficient Theorem. We also present a set of efficient algorithms to compute multi-function product and product integral. In the dissertation, we demonstrate practical applications of these algorithms in the interactive rendering of dynamic glossy objects under distant time-variant all-frequency environment lighting with arbitrary view conditions. At each vertex, the shading integral is formulated as the product integral of multiple operand functions. By approximating operand functions in the wavelet domain, we demonstrate rendering dynamic glossy scenes interactively, which is orders of magnitude faster than previous work. As an important enhancement to the popular Pre-computation Based Radiance Transfer (PRT) approach, we present a novel Just-in-time Radiance Transfer (JRT) technique, and demonstrate its application in real-time realistic rendering of dynamic all-frequency shadows under general lighting environment. Our work is a significant step towards real-time rendering of arbitrary scenes under general lighting environment. It is also of great importance to general numerical analysis and signal processing.Ph.D.
Other
Engineering and Computer Science
Computer Science
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Wu, Jiun-Yan 1972. "Extracting damping ratios using wavelets." Thesis, Massachusetts Institute of Technology, 2001. http://hdl.handle.net/1721.1/8618.
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Thesis (M.Eng.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2001.Includes bibliographical references (leaves 87-88).
The focus of this work is to evaluate the accuracy of methods for extracting damping ratios with respect to: three extraction methods, different damping ratios, added noisy data, separated modes and close modes. To achieve this goal, a simulated analytical signal is analyzed by estimating the modal parameters. The simulated analytic signal is useful because the exact values are known and the characteristic of the FRF can be varied in order to observe how the accuracy of damping ratios is affected. Results show that the Continuous Wavelet Transform method gives the most accurate estimations even for data corrupted by the noise. The Complex Exponential method presents better results in the cases with higher modes and higher damping ratios without the noise. Wavelet Packet method and Continuous Wavelet Transform method are more suitable in the cases for extracting lower damping ratios than those for higher damping ratios even for data corrupted by the noise. And in general, the estimation results are more accurate in the cases with separated modes than those with close modes.
by Jiun-Yan Wu.
M.Eng.
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Shen, Jianhong 1971. "Asymptotics of wavelets and filters." Thesis, Massachusetts Institute of Technology, 1998. http://hdl.handle.net/1721.1/47469.
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Rua, António Miguel Pinto de Oliveira Gomes. "Essays on Wavelets in Economics." Doctoral thesis, Instituto Superior de Economia e Gestão, 2011. http://hdl.handle.net/10400.5/3472.
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Doutoramento em EconomiaThe aim of this work is to highlight the usefulness of wavelet analysis in Economics. Wavelet analysis is a very promising tool as it represents a refinement of Fourier analysis. In particular, it allows one to take into account both the time and frequency domains within a unified framework, that is, one can assess simultaneously how variables are related at different frequencies and how such relationship has evolved over time. Despite the potential value of wavelet analysis, it is still a relatively unexplored tool in the study of economic phenomena. The work herein presented intends to contribute to such strand of literature. In particular, wavelet analysis is used to assess the link between money growth and inflation in the euro area, as the European Central Bank at¬tributes a key role to money within the monetary policy strategy. Addi¬tionally, a wavelet-based measure of comovement is proposed and used to study the growth comovement among the major euro area countries. Based on this measure, a measure of cohesion is developed and used to investi¬gate the cohesion among euro area countries and the cohesion within US at both the regional and state levels. Within the financial economics literature, the relationship among international stock market returns is assessed and a wavelet-based approach for measuring market risk is proposed. Finally, one also investigates the usefulness of wavelets for forecasting purposes while bridging such approach with factor-augmented models.
O objectivo deste trabalho é realçar a utilidade da análise de onduletas em Economia. A análise de onduletas é uma ferramenta muito promissora, pois representa um refinamento da análise de Fourier. Em particular, permite ter em consideração quer o domínio do tempo quer o domínio da frequência de forma unificada, ou seja, é possível avaliar simultaneamente como é que as variáveis estão relacionadas em diferentes frequências e como é que essa relação tem evoluído ao longo do tempo. Apesar do potencial interesse, a análise de onduletas constitui ainda uma ferramenta relativamente pouco utilizada no estudo de fenómenos económicos. O trabalho aqui apresentado pretende contribuir para essa vertente da literatura. Em particular, a análise de onduletas é usada para avaliar a relação entre o crescimento monetário e a inflação na área do euro, dado que o Banco Central Europeu atribui um papel fundamental para a moeda no contexto da sua estratégia de política monetária. Adicionalmente, é proposta uma medida de co-movimento baseada em onduletas sendo utilizada para estudar o co-movimento, em termos de crescimento, entre as maiores economias da área do euro. Com base nesta medida, também é proposta uma medida de coesão que é usada por sua vez para aferir a coesão entre os países da área do euro e nos Estados Unidos, quer a nível regional quer estadual. No contexto da literatura de economia financeira, a relação entre retornos de acções no mercado internacional é avaliada e é proposta uma abordagem baseada em onduletas para a medição de risco de mercado. Finalmente, a utilidade das onduletas para efeitos de previsão é investigada e a sua interacção com os modelos de factores é explorada.
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Magarey, Julian. "Motion estimation using complex wavelets." Thesis, University of Cambridge, 1997. https://www.repository.cam.ac.uk/handle/1810/273016.
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Cao, Siyang. "Radar Sensing Based on Wavelets." The Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1416996784.
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Cao, Jiansheng. "Construction of piecewise linear wavelets." [Johnson City, Tenn. : East Tennessee State University], 2002. http://etd-submit.etsu.edu/etd/theses/available/etd-0715102-142035/unrestricted/CaoJ071802a.pdf.
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Dérian, Pierre. "Wavelets and Fluid Motion Estimation." Rennes 1, 2012. https://ecm.univ-rennes1.fr/nuxeo/site/esupversions/5cdcde8f-715b-4725-a6d4-4eea6474aead.
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Ces travaux se situent dans la problématique d'élaboration d'outils de mesure adaptés aux caractéristiques des écoulements fluides. Le développement de l'imagerie digitale, associée à l'utilisation de techniques de visualisation d'écoulements en mécanique des fluides, permet d'envisager l'extraction, à l'aide de méthodes de vision par ordinateur, du mouvement d'écoulements perçu dans des séquences d'images. L'objectif consiste ici à proposer une nouvelle approche de type « flux optique » pour l'estimation multiéchelle de mouvements de fluides, en s'appuyant sur une représentation en ondelettes du mouvement recherché. Cette formulation en ondelettes introduit un formalisme multiéchelle, intéressant tant du point de vue de l'estimation du flux optique que de la représentation de champs de vitesse turbulents. Elle permet en outre la construction de bases à divergence nulle, respectant ainsi une contrainte issue de la physique des fluides. Plusieurs types de régularisation sont présentés; la plus simple procède par troncature de la base aux petites échelles, la plus complexe utilise les coefficients de connexion de la base d'ondelette pour construire des schémas d'ordre élevé. Les approches proposées sont évaluées sur des images synthétiques dans un premier temps, puis sur des images expérimentales d'écoulements caractéristiques. Les résultats obtenus sont comparés à ceux fournis par la méthode usuelle des « corrélations croisées », mettant en avant les intérêts et les limites de l'estimateurThis work falls within the general problematic of designing measurement tools adapted to the specificities of fluid flows. The development of digital imaging, combined with visualization techniques commonly employed in experimental fluid dynamics, enables to extract the apparent flow motion from image sequences, thanks to computer vision methods. The objective is to propose a novel “optical flow” algorithm dedicated to the multiscale motion estimation of fluid flows, using a wavelet representation of the unknown motion field. This wavelet formulation introduces a multiscale framework, conveniently adapted both to the optical flow estimation and to the representation of turbulent motion fields. It enables as well to design divergence-free bases, thereby respecting a constraint given by fluid dynamics. Several regularization schemes are proposed; the simplest consists in truncating the basis at fine scales, while the most complex builds high-order schemes from the connection coefficients of the wavelet basis. Proposed methods are evaluated on synthetic images in the first place, then on actual experimental images of characteristic fluid flows. Results are compared to those given by the usual “cross-correlations”, highlighting the advantages and limits of the wavelet-based estimator
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Shi, Fangmin. "Wavelet transforms for stereo imaging." Thesis, University of South Wales, 2002. https://pure.southwales.ac.uk/en/studentthesis/wavelet-transforms-for-stereo-imaging(65abb68f-e30b-4367-a3a8-b7b3df85f566).html.
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Stereo vision is a means of obtaining three-dimensional information by considering the same scene from two different positions. Stereo correspondence has long been and will continue to be the active research topic in computer vision. The requirement of dense disparity map output is great demand motivated by modern applications of stereo such as three-dimensional high-resolution object reconstruction and view synthesis, which require disparity estimates in all image regions. Stereo correspondence algorithms usually require significant computation. The challenges are computational economy, accuracy and robustness. While a large number of algorithms for stereo matching have been developed, there still leaves the space for improvement especially when a new mathematical tool such as wavelet analysis becomes mature. The aim of the thesis is to investigate the stereo matching approach using wavelet transform with a view to producing efficient and dense disparity map outputs. After the shift invariance property of various wavelet transforms is identified, the main contributions of the thesis are made in developing and evaluating two wavelet approaches (the dyadic wavelet transform and complex wavelet transform) for solving the standard correspondence problem. This comprises an analysis of the applicability of dyadic wavelet transform to disparity map computation, the definition of a waveletbased similarity measure for matching, the combination of matching results from different scales based on the detectable minimum disparity at each scale and the application of complex wavelet transform to stereo matching. The matching method using the dyadic wavelet transform is through SSD correlation comparison and is in particular detailed. A new measure using wavelet coefficients is defined for similarity comparison. The approach applying a dual tree of complex wavelet transform to stereo matching is formulated through phase information. A multiscale matching scheme is applied for both the matching methods. Imaging testing has been made with various synthesised and real image pairs. Experimental results with a variety of stereo image pairs exhibit a good agreement with ground truth data, where available, and are qualitatively similar to published results for other stereo matching approaches. Comparative results show that the dyadic wavelet transform-based matching method is superior in most cases to the other approaches considered.
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Tieng, Quang Minh. "Wavelet transform based techniques for the recognition of objects in images." Thesis, Queensland University of Technology, 1996.
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Despite its short history, the wavelet transform has found application in a remarkable diversity of disciplines: Mathematics, Physics, Numerical Analysis,Signal Processing and others. In this thesis, we explore applications of
this transform in image analysis and devise several algorithms for recognising objects in an image of a scene. Five different algorithms, consisting of representations and matching techniques, have been proposed for handling different kinds of objects in different situations.
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Scaini, Davide. "Wavelet-based spatial audio framework : from ambisonics to wavelets: a novel approach to spatial audio." Doctoral thesis, Universitat Pompeu Fabra, 2019. http://hdl.handle.net/10803/668214.
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Ambisonics is a complete theory for spatial audio whose building blocks are the spherical harmonics.
Some of the drawbacks of low order Ambisonics, like poor source directivity and small sweet-spot, are directly related to the properties of spherical harmonics.
In this thesis we illustrate a novel spatial audio framework similar in spirit to Ambisonics that replaces the spherical harmonics by an alternative set of functions with compact support: the spherical wavelets.
We develop a complete audio chain from encoding to decoding, using discrete spherical wavelets built on a multiresolution mesh.
We show how the wavelet family and the decoding matrices to loudspeakers can be generated via numerical optimization.
In particular, we present a decoding algorithm optimizing acoustic and psychoacoustic parameters that can generate decoding matrices to irregular layouts for both Ambisonics and the new wavelet format.
This audio workflow is directly compared with Ambisonics.Ambisonics és una teoria completa d’àudio espacial construïda a partir dels harmònics esfèrics. Alguns dels inconvenients d'Ambisonics de baix ordre, com ara una localització pobra i una àrea petita d’escolta òptima, estan directament relacionats amb les propietats dels harmònics esfèrics. En aquesta tesi presentem un nou formalisme d’àudio espacial basat en Ambisonics substituint però els harmònics esfèrics per les ondetes esfèriques. Desenvolupem una cadena d’àudio completa, des de la codificació fins a la descodificació, a través de l'ús de ondetes discretes construïdes en una malla de multirresolució. Mostrem com es pot generar la família de ondetes i les matrius de descodificació a altaveus mitjançant una optimització numèrica. Presentem un algorisme de descodificació que pot generar matrius de descodificació a conjunts irregulars d'altaveus tant per a Ambisonics com per al nou format basat en ondetes. Finalment, comparem aquest nou formalisme d’àudio amb Ambisonics.
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King, Emily Jeannette. "Wavelet and frame theory frame bound gaps, generalized shearlets, Grassmannian fusion frames, and p-adic wavelets /." College Park, Md.: University of Maryland, 2009. http://hdl.handle.net/1903/9636.
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Thesis (Ph.D.) -- University of Maryland, College Park, 2009.Thesis research directed by: Dept. of Mathematics. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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He, Lianyun. "Experience with wavelets in volume rendering." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape7/PQDD_0003/MQ42069.pdf.
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Sampath, Hemalatha. "Automated ventricular measurements using Gabor wavelets." Morgantown, W. Va. : [West Virginia University Libraries], 2007. https://eidr.wvu.edu/etd/documentdata.eTD?documentid=5511.
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Thesis (M.S.)--West Virginia University, 2007.Title from document title page. Document formatted into pages; contains ix, 76 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 71-76).
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Hoover, Kenneth R. "Dimension functions of rationally dilated wavelets /." view abstract or download file of text, 2007. http://proquest.umi.com/pqdweb?did=1400959361&sid=1&Fmt=2&clientId=11238&RQT=309&VName=PQD.
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Thesis (Ph. D.)--University of Oregon, 2007.Typescript. Includes vita and abstract. Includes bibliographical references (leaves 80-83) and index. Also available for download via the World Wide Web; free to University of Oregon users.
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Klapper, Jennifer Helen. "Data analysis with complex Daubechies wavelets." Thesis, University of Leeds, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.634529.
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Wavelet thresholding is an increasingly popular method of nonparametric smoothing. Both real-valued and complex-valued Daubechies wavelets exist. However, to date, complex-valued wavelets have attracted little attention in the statistical literature compared to real-valued wavelets. The broad aim of this thesis is to further the application of complex-valued Daubechies wavelets within the wavelet thresholding framework. Much of the previous work that applied complex-valued wavelets focused upon their application to real-valued data. However, complex-valued data exist and arise in multiple scientific areas. This thesis firstly examines how one method of applying complex-valued wavelets performs on complex-valued data before modifying the methodology to allow for native denoising of complex-valued data. A large number of smoothing regimes exist within the wavelet framework, known as 'thresholding rules'. The majority of these thresholding rules have been designed for use in conjunction with real-valued wavelets. One such thresholding rule is known as 'block thresholding' whereby the data is considered in blocks, rather than as individual data points, to allow for correlation between neighbouring data points. A further thresholding method is known as the 'fiducial thresholding' method which attempts to circumvent perceived problems within the Bayesian approach. Within this thesis these two thresholding rules are developed to allow for the application of complex-valued wavelets; the difference in their performance when using real- and complex-valued wavelets is investigated by simulation.
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鍾鈞鎂 and Jun-mei Zhong. "Application of wavelets in image compression." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2000. http://hub.hku.hk/bib/B42575667.
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Ignácio, Ubiratã Azevedo. "Aplicação de wavelets em inpainting digital." Universidade do Vale do Rio do Sinos, 2007. http://www.repositorio.jesuita.org.br/handle/UNISINOS/2245.
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Previous issue date: 26Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Inpainting Digital é uma técnica recente que permite completar a falta de informação em imagens, seja por falha ou por remoção intencional de alguma área ou objeto. Uma das atribuições importantes do inpainting digital é de que deve ser capaz de alterar uma imagem, de forma que não seja simples perceber que esta alteração foi feita; caracteriza uma modificação indetectável. Os métodos para determinar como esta falta de informação será preenchida variam desde a criação do primeiro modelo de inpainting digital. Contudo, sempre deve ser mantida uma coerência no preenchimento, que fará com que a região preenchida automaticamente aparente como parte da imagem verdadeira. As técnicas atuais tratam este preenchimento como uma propagação da estrutura da área que está ao redor da região a ser preenchida, trabalhando diretamente no domímio das cores, utilizando abordagens como Variação Total e Equações Diferenciais Parciais. Neste trabalho, é feito o uso de transformada Wavelet para a aplicação de inpainting digita
Digital Inpainting is a recent techinique that allows the filling of missing information in images. One important attribute of a digital inpainting technique is the ability of altering an image in such a way that it is not simple for the human observer to detect the modification, characterizing an undetectable modification. The strategies for filling missing parts vary since the first inpainting model, but one thing that remains is the fact that the filled area must be coherent with the original part of the image. Current techniques handle the filling as a structure propagation problem, working directly in the image color domain, and based on concepts like Total Variation or Partial Diferential Equations. In this work, we present a digital inpainting model that works exclusively in Wavelet domain,filling the target area with a texture synthesis mechanism using the properties of the Wavelet Transform