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1
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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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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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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Gorini, Lorenzo. "Trasformate wavelet." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2014. http://amslaurea.unibo.it/7679/.
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La presente tesi vuole dare una descrizione delle Trasformate Wavelet indirizzata alla codifica dell’immagine in formato JPEG2000. Dopo aver quindi descritto le prime fasi della codifica di un’immagine, procederemo allo studio dei difetti derivanti dall’analisi tramite la Trasformata Discreta del Coseno (utilizzata nel formato predecessore JPEG). Dopo aver quindi descritto l’analisi multirisoluzione e le caratteristiche che la differenziano da quest’ultima, analizzeremo la Trasformata Wavelet dandone solo pochi accenni teorici e cercando di dedurla, in una maniera più indirizzata all’applicazione. Concluderemo la tesi descrivendo la codifica dei coefficienti calcolati, e portando esempi delle innumerevoli applicazioni dell’analisi multirisoluzione nei diversi campi scientifici e di trasmissione dei segnali.
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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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Bopardikar, Ajit S. "Speech Encryption Using Wavelet Packets." Thesis, Indian Institute of Science, 1995. https://etd.iisc.ac.in/handle/2005/153.
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The aim of speech scrambling algorithms is to transform clear speech into an unintelligible signal so that it is difficult to decrypt it in the absence of the key.
Most of the existing speech scrambling algorithms tend to retain considerable residual intelligibility in the scrambled speech and are easy to break. Typically, a speech scrambling algorithm involves permutation of speech segments in time, frequency or time-frequency domain or permutation of transform coefficients of each speech block. The time-frequency algorithms have given very low residual intelligibility and have attracted much attention.
We first study the uniform filter bank based time-frequency scrambling algorithm with respect to the block length and number of channels. We use objective distance measures to estimate the departure of the scrambled speech from the clear speech. Simulations indicate that the distance measures increase as we increase the block length and the number of channels. This algorithm derives its security only from the time-frequency segment permutation and it has been estimated that the effective number of permutations which give a low residual intelligibility is much less than the total number of possible permutations.
In order to increase the effective number of permutations, we propose a time-frequency scrambling algorithm based on wavelet packets. By using different wavelet packet filter banks at the analysis and synthesis end, we add an extra level of security since the eavesdropper has to choose the correct analysis filter bank, correctly rearrange the time-frequency segments, and choose the correct synthesis bank to get back the original speech signal. Simulations performed with this algorithm give distance measures comparable to those obtained for the uniform filter bank based algorithm.
Finally, we introduce the 2-channel perfect reconstruction circular convolution filter bank and give a simple method for its design. The filters designed using this method satisfy the paraunitary properties on a discrete equispaced set of points in the frequency domain.
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Bopardikar, Ajit S. "Speech Encryption Using Wavelet Packets." Thesis, Indian Institute of Science, 1995. http://hdl.handle.net/2005/153.
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The aim of speech scrambling algorithms is to transform clear speech into an unintelligible signal so that it is difficult to decrypt it in the absence of the key.
Most of the existing speech scrambling algorithms tend to retain considerable residual intelligibility in the scrambled speech and are easy to break. Typically, a speech scrambling algorithm involves permutation of speech segments in time, frequency or time-frequency domain or permutation of transform coefficients of each speech block. The time-frequency algorithms have given very low residual intelligibility and have attracted much attention.
We first study the uniform filter bank based time-frequency scrambling algorithm with respect to the block length and number of channels. We use objective distance measures to estimate the departure of the scrambled speech from the clear speech. Simulations indicate that the distance measures increase as we increase the block length and the number of channels. This algorithm derives its security only from the time-frequency segment permutation and it has been estimated that the effective number of permutations which give a low residual intelligibility is much less than the total number of possible permutations.
In order to increase the effective number of permutations, we propose a time-frequency scrambling algorithm based on wavelet packets. By using different wavelet packet filter banks at the analysis and synthesis end, we add an extra level of security since the eavesdropper has to choose the correct analysis filter bank, correctly rearrange the time-frequency segments, and choose the correct synthesis bank to get back the original speech signal. Simulations performed with this algorithm give distance measures comparable to those obtained for the uniform filter bank based algorithm.
Finally, we introduce the 2-channel perfect reconstruction circular convolution filter bank and give a simple method for its design. The filters designed using this method satisfy the paraunitary properties on a discrete equispaced set of points in the frequency domain.
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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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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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Lutz, Steven S. "Hokua – A Wavelet Method for Audio Fingerprinting." Diss., CLICK HERE for online access, 2009. http://contentdm.lib.byu.edu/ETD/image/etd3247.pdf.
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Yilmaz, Sener. "Generalized Area Tracking Using Complex Discrete Wavelet Transform: The Complex Wavelet Tracker." Phd thesis, METU, 2007. http://etd.lib.metu.edu.tr/upload/3/12608643/index.pdf.
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In this work, a new method is proposed that can be used for area tracking. This method is based on the Complex Discrete Wavelet Transform (CDWT) developed by Magarey and Kingsbury. The CDWT has its advantages over the traditional Discrete Wavelet Transform such as approximate shift invariance, improved directional selectivity, and robustness to noise and illumination changes.
The proposed method is a generalization of the CDWT based motion estimation method developed by Magarey and Kingsbury. The Complex Wavelet Tracker extends the original method to estimate the true motion of regions according to a parametric motion model. In this way, rotation, scaling, and shear type of motions can be handled in addition to pure translation.
Simulations have been performed on the proposed method including both quantitative and qualitative tests. Quantitative tests are performed on synthetically created test sequences and results have been compared to true data. The performance is compared with intensity-based methods. Qualitative tests are performed on real sequences and evaluations are presented empirically. The results are compared with intensity-based methods.
It is observed that the proposed method is very accurate in handling affine deformations for long term sequences and is robust to different target signatures and illumination changes. The accuracy of the proposed method is compatible with intensity-based methods. In addition to this, it can handle a wider range of cases and is robust to illuminaton changes compared to intensity-based methods.
The method can be implemented in real-time and could be a powerful replacement of current area trackers.
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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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Harbrecht, Helmut, and Reinhold Schneider. "Adaptive Wavelet Galerkin BEM." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200600559.
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The wavelet Galerkin scheme for the fast solution of boundary integral equations produces approximate solutions within discretization error accuracy offered by the underlying Galerkin method at a computational expense that stays proportional to the number of unknowns. In this paper we present an adaptive version of the scheme which preserves the super-convergence of the Galerkin method.
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Wu, Jiangfeng. "Wavelet packet division multiplexing." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0002/NQ42889.pdf.
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Lee, Chien-Hsing. "Wavelet-based transient analysis." Diss., Georgia Institute of Technology, 1998. http://hdl.handle.net/1853/14713.
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Rajpoot, Nasir Mahmood. "Adaptive wavelet image compression." Thesis, University of Warwick, 2001. http://wrap.warwick.ac.uk/67099/.
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In recent years, there has been an explosive increase in the amount of digital image data. The requirements for its storage. and communication can be reduced considerably by compressing the data while maintaining their visual quality. The work in this thesis is concerned with the compression of still images using fixed and adaptive wavelet transforms. The wavelet transform is a suitable candidate for representing an image in a compression system, due to its being an efficient representation, having an inherent multiresolution nature, and possessing a self-similar structure which lends itself to efficient quantization strategies using zerotrees. The properties of wavelet transforms are studied from a compression viewpoint. A novel augmented zerotree wavelet image coding algorithm is presented whose compression performance is comparable to the best wavelet coding results published to date. It is demonstrated that a wavelet image coder performs much better on images consisting of smooth regions than on relatively complex images. The need thus arises to explore the wavelet bases whose time-frequency tiling is adapted to a given signal, in such a way that the resulting waveforms resemble closely those present in the signal and consequently result in a sparse representation, suitable for compression purposes. Various issues related to a generalized wavelet basis adapted to the signal or image contents, the so-called best wavelet packet basis, and its selection are addressed. A new method for wavelet packet basis selection is presented, which aims to unite the basis selection process with quantization strategy to achieve better compression performance. A general zerotree structure for any arbitrary wavelet packet basis, termed the compatible zerotree structure, is presented. The new basis selection method is applied to compatible zerotree quantization to obtain a progressive wavelet packet coder, which shows significant coding gains over its wavelet counterpart on test images of diverse nature.
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梁鴻鈞 and Hung-kwan Leung. "Multi-rank wavelet filters." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2001. http://hub.hku.hk/bib/B31224714.
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May, Heather. "Wavelet-based Image Processing." University of Cincinnati / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1448037498.
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Anton, Wirén. "The Discrete Wavelet Transform." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-55063.
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In this thesis we will explore the theory behind wavelets. The main focus is on the discrete wavelet transform, although to reach this goal we will also introduce the discrete Fourier transform as it allow us to derive important properties related to wavelet theory, such as the multiresolution analysis. Based on the multiresolution it will be shown how the discrete wavelet transform can be formulated and show how it can be expressed in terms of a matrix. In later chapters we will see how the discrete wavelet transform can be generalized into two dimensions, and discover how it can be used in image processing.
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Leung, Hung-kwan. "Multi-rank wavelet filters." Hong Kong : University of Hong Kong, 2001. http://sunzi.lib.hku.hk/hkuto/record.jsp?B23242395.
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Parker, Kristen Michelle. "Watermarking with wavelet transforms." Master's thesis, Mississippi State : Mississippi State University, 2007. http://library.msstate.edu/etd/show.asp?etd=etd-11062007-153859.
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Pinnamaneni, Pujita. "Wavelet-based volume rendering." Master's thesis, Mississippi State : Mississippi State University, 2003. http://library.msstate.edu/etd/show.asp?etd=etd-04032003-160411.
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Manglani, Manish. "Wavelet Modulation in Gaussian and Rayleigh Fading Channels." Thesis, Virginia Tech, 2001. http://hdl.handle.net/10919/34396.
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Wavelet Modulation (WM)---also referred to as fractal modulation---simultaneously sends data at multiple rates through an unknown channel. This novel multirate diversity strategy offers improved message recovery over conventional modulation techniques: if the message is not received at one rate due to the channel disturbances, it can be received at another rate where the channel is clear. Previous research has demonstrated the performance of wavelet modulation in Gaussian channels.
This paper extends the investigation to the performance of wavelet modulation in time varying channels. We show that bit error rate (BER) wavelet demodulation performance in the additive, white, Gaussian noise (AWGN) channel is comparable to theoretical binary phase shift keying. Our results depict the improvement in performance that can be realized for time varying channels by utilizing the various rates of wavelet modulation; BER versus SNR curves for each fading channel show how the message at one rate can be more accurately recovered than at another rate. Furthermore, we also present results indicating the dramatic improvement in wavelet demodulation performance when multiple rates are available and utilized for demodulation. This improvement in performance is highly visible in BER performance for the AWGN and flat fading channels.
Finally, a comparison of binary phase shift keying (BPSK) and WM in a frequency selective channel is performed. The BER improvement of WM is shown when demodulation is done at rates which are least corrupted by ISI. We illustrate our new algorithm that: identifies the channel characteristics; determines which rates are maximally corrupted by ISI; and, utilizes only those uncorrupted copies in demodulation.Master of Science
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Alexander, Simon. "Two- and Three-Dimensional Coding Schemes for Wavelet and Fractal-Wavelet Image Compression." Thesis, University of Waterloo, 2001. http://hdl.handle.net/10012/1180.
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This thesis presents two novel coding schemes and applications to both two- and three-dimensional image compression. Image compression can be viewed as methods of functional approximation under a constraint on the amount of information allowable in specifying the approximation. Two methods of approximating functions are discussed: Iterated function systems (IFS) and wavelet-based approximations. IFS methods approximate a function by the fixed point of an iterated operator, using consequences of the Banach contraction mapping principle. Natural images under a wavelet basis have characteristic coefficient magnitude decays which may be used to aid approximation. The relationship between quantization, modelling, and encoding in a compression scheme is examined. Context based adaptive arithmetic coding is described. This encoding method is used in the coding schemes developed. A coder with explicit separation of the modelling and encoding roles is presented: an embedded wavelet bitplane coder based on hierarchical context in the wavelet coefficient trees. Fractal (spatial IFSM) and fractal-wavelet (coefficient tree), or IFSW, coders are discussed. A second coder is proposed, merging the IFSW approaches with the embedded bitplane coder. Performance of the coders, and applications to two- and three-dimensional images are discussed. Applications include two-dimensional still images in greyscale and colour, and three-dimensional streams (video).
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Duarte, Marco Aparecido Queiroz [UNESP]. "Redução de ruído em sinais de voz no domínio wavelet." Universidade Estadual Paulista (UNESP), 2005. http://hdl.handle.net/11449/100369.
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duarte_maq_dr_ilha.pdf: 2208096 bytes, checksum: 7daf91683010b0f39c715c9cc1ded5d8 (MD5)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
Neste trabalho é feito um estudo sobre os métodos de redução de ruído aditivo em sinais de voz baseados em wavelets e, através deste estudo, propõe-se um novo método de redução de ruído em sinais de voz no domínio wavelet. O princípio básico da maioria dos métodos de redução de ruído baseados em wavelets é a determinação e aplicação de um limiar, que permite 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, fazendo assim uma aplicação linear deste limiar. Esta eliminação acaba causando descontinuidades no tempo e na freqüência 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 neste trabalho também é baseado em corte por limiar, mas em vez de uma aplicação linear do limiar, ele faz uma aplicação não-linear, o que evita as descontinuidades causadas por outros algoritmos. O limiar é calculado nos trechos de silêncio e não depende apenas da última janela do último trecho de silêncio, mas sim de todas as janelas, já que este limiar é uma média de todos os limiares calculados neste trecho. Isto faz com que a redução do ruído seja mais uniforme e introduza menos distorções no sinal processado. Além disso, nos trechos de voz ainda é calculado um novo limiar que também será usado, em conjunto com o limiar calculado no silêncio. Isto faz com que a energia da janela que... .
In this work a study of additive noise reduction in speech based on wavelets is presented and, based on this study a new noise reduction method in speech in the wavelet domain is proposed. The basic idea of most methods of noise reduction based on wavelets is the determination and application of a threshold, that produces good results for signals contaminated by white noise, but they are not very efficient in processing signals contaminated by colored noise, which is more common in real situations. In those methods, the threshold, generally, is 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 are below this value are eliminated, making a linear application of this threshold. This elimination causes discontinuities in time and frequency of the processed signal. Besides, the way that the threshold is computed can degrade the voice segments of the processed signal, principally when the threshold depends strongly on the last window of the last silence segment. The proposed method in this work is also based in thresholding, but, instead of a linear application of the threshold, it makes a non-linear application, which avoids the discontinuities caused by other algorithms. The threshold is calculated in the silence segments and is not dependent only on the last window of the last silence segment, but of all the windows, since this threshold is an average of all thresholds calculated in this segment. It makes noise reduction more uniform and introduces less distortion in the processed signal. Besides, in the voice segments a new threshold is calculated that will be also used with the threshold calculated in the silence. It makes that the energy of the window that is being processed is also considered. This way, it is... (Complete abstract, click electronic address below).
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He, Chao. "Advanced wavelet application for video compression and video object tracking." Connect to resource, 2005. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1125659908.
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Thesis (Ph. D.)--Ohio State University, 2005.Title from first page of PDF file. Document formatted into pages; contains xvii, 158 p.; also includes graphics (some col.). Includes bibliographical references (p. 150-158). Available online via OhioLINK's ETD Center
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Durmaz, Murat. "One-dimensional Real-time Signal Denoising Using Wavelet-based Kalman Filtering." Master's thesis, METU, 2007. http://etd.lib.metu.edu.tr/upload/12608336/index.pdf.
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Denoising signals is an important task of digital signal processing. Many linear
and non-linear methods for signal denoising have been developed. Wavelet based
denoising is the most famous nonlinear denoising method lately. In the linear case,
Kalman filter is famous for its easy implementation and real-time nature. Wavelet-
Kalman filter developed lately is an important improvement over Kalman filter, in
which the Kalman filter operates in the wavelet domain, filtering the wavelet coeffi-
cients, and resulting in the filtered wavelet transform of the signal in real-time. The
real-time filtering and multiresolution representation is a powerful feature for many
real world applications.
This study explains in detail the derivation and implementation of Real-Time
Wavelet-Kalman Filter method to remove noise from signals in real-time. The filter
is enhanced to use different wavelet types than the Haar wavelet, and also it is
improved to operate on higer block sizes than two. Wavelet shrinkage is integrated
to the filter and it is shown that by utilizing this integration more noise suppression
is obtainable. A user friendly application is developed to import, filter and export
signals in Java programming language. And finally, the applicability of the proposed
method to suppress noise from seismic waves coming from eartquakes and to enhance
spontaneous potentials measured from groundwater wells is also shown.
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Neumann, Julia. "Adaptive conjoint wavelet-support vector classifiers." [S.l. : s.n.], 2004. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB11675448.
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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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Niedermeier, Andreas Georg. "Wavelet-Methoden in der SAR-Bildverarbeitung ein Wavelet-basiertes Wasserstandslinienverfahren zur Topographiebestimmung im Wattenmeer /." [S.l.] : [s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=964720728.
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Niemöller, Andreas. "Die Wavelet-Analyse als chemometrisches Werkzeug - The wavelet transform as a tool in chemometrics." Gerhard-Mercator-Universitaet Duisburg, 2002. http://www.ub.uni-duisburg.de/ETD-db/theses/available/duett-06122002-115451/.
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In most cases chemometric methods (PCA, PCR, PLS) are used for data modelling when NIR-spectrometry is applied for analytical purposes. This work is about the application of the wavelet-transform as a tool in chemometrics for analysing NIR-spectra. Beside aspects of data pretreatment, like smoothing of NIR-spectra, and data compression the focus was set on NIR-analysis using wavelet-transformed NIR-spectra. A new method for building multivariate calibration models based on wavelet-coefficients selected by a genetic algorithm is introduced. In addition the results obtained by calibrating wavelet-coefficients using PCR and PLS are descriped. Furthermore the identification of post consumer plastic waste by wavelet-transformed NIR-spectra and an artificial neural network is demonstrated. Two new special types of wavelets which allow analysing finitely extended signals (like spectra) without introducing artifacts near the boundaries were applied
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Colldeforns, Papiol Gemma. "Wavelet approach in computational finance." Doctoral thesis, Universitat Autònoma de Barcelona, 2018. http://hdl.handle.net/10803/462118.
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En el món de les finances computacionals, tant els preus de derivats com la gestió de riscos han atret molt d'interès entre els professionals i l'acadèmia. Aquesta tesi pretén proporcionar tècniques basades en ondetes a fi de millorar algunes de les metodologies utilitzades en aquestes àrees. Les ondetes són famílies de funcions que es poden traslladar i dilatar arbitràriament generant bases ortogonals de L2(). En relació amb elles, ha sorgit una col·lecció de mètodes d'inversió de Fourier que es basen en l'aproximació de funcions a partir de la projecció en la base d’ondetes, de tal manera que els coeficients de l'expansió s'expressen mitjançant la transformada de Fourier de la funció a aproximar.
El mètode SWIFT (Shannon wavelet inverse Fourier technique) per valorar opcions d'estil europeu en un subjacent s'ha publicat i presentat recentment com una tècnica precisa, robusta i altament eficient basada en les ondetes de Shannon. Motivats per la valoració d’un tipus d'opcions exòtiques anomenades opcions arc iris, que depenen de diversos actius, un dels objectius de la tesi és l'extensió multidimensional del mètode SWIFT. Aquesta extensió hereta les propietats del mètode unidimensional i la convergència exponencial n'és una. Gràcies a la naturalesa de les ondetes de Shannon, no és necessari un truncament a priori del rang d'integració, tenim una estimació de l'error i fem ús d’algorismes de la transformada ràpida de Fourier per accelerar els càlculs. El mètode es prova a partir de diversos exemples comparant-lo amb mètodes recents en la literatura.
En l’àmbit de gestió de risc, són els reguladors els que s’encarreguen de determinar la quantitat de capital que les entitats financeres han de guardar per estar preparades per suportar pèrdues inesperades. És l’anomenat comitè de Basilea el que s’encarrega dels reguladors bancaris mundials. Recentment, el comitè ha revisat els estàndards establerts pel capital mínim per risc de mercat i, entre altres canvis, suggereix d'una banda moure l’estès ús de la mesura de risc VaR cap a la mesura ES, i l'altra banda, considerar la incorporació del risc derivat a causa de la no-liquiditat del mercat. És per això, que un segon objectiu de la tesi és presentar un nou mètode numèric basat en SWIFT per als càlculs del VaR (Value-at-Risk) i l’ES (Expected Shortfall) tenint en compte un horitzó de temps estocàstic per tenir en compte els problemes de liquiditat del mercat. Es consideren dos enfocaments diferents: l’aproximació delta-gamma que aproxima quadràticament el valor de la cartera en el canvi de valor dels factors de risc, i també l’aproximació del valor logarítmic de la cartera a partir de processos estocàstics coneguts com ara el Merton o el Kou.
El risc de crèdit és el risc de pèrdues per part del deutor en cas que no compleixi els acords i en general és la principal font de risc en un banc comercial. En aquesta tesi, investiguem el problema de calcular les mesures de risc de crèdit de les carteres sota els models multifactorials Gaussians i de t-còpula. És ben sabut que els mètodes de Montecarlo, que són els que generalment s’empren, són molt exigents des del punt de vista computacional en aquestes situacions. Per millorar aquests problemes, a la tesi presentem tècniques numèriques eficients i robustes basades en les ondetes de Haar per recuperar la funció de distribució acumulada de la variable de pèrdues a partir de la seva funció característica. L'anàlisi de l'error i els resultats obtinguts en l'apartat d'experiments numèrics mostren una maquinària fiable i útil per al mesurament de capital de risc de crèdit d'acord amb el Pilar II dels Acords de Basilea.In the computational finance world both derivatives pricing and risk management have attracted lots of interest amongst practitioners and academia. This thesis aims to provide wavelets based techniques to enhance some of the methodologies used in the mentioned areas. Wavelets are families of functions that can be arbitrarily translated and dilated in order to generate orthogonal basis of L2(). In relation to them, a collection of Fourier inversion methods has emerged; they are based on the approximation of functions by projecting on the wavelets basis such that the coefficients of the expansion are expressed by means of the Fourier transform of the function to approximate. The SWIFT (Shannon wavelet inverse Fourier technique) method for pricing European-style options on one underlying asset was recently published and presented as an accurate, robust and highly efficient technique based on Shannon wavelets. One of the achievements of the thesis is the extension of the method to higher dimensions by pricing exotic option contracts, called rainbow options, whose payoff depends on multiple assets. The multidimensional extension inherits the properties of the one-dimensional method, being the exponential convergence one of them. Thanks to the nature of local Shannon wavelets basis, we do not need to rely on a-priori truncation of the integration range, we have an error bound estimate and we use fast Fourier transform (FFT) algorithms to speed up computations. We test the method for several examples comparing it with state-of-the-art methods found in the literature. When managing the risk, regulators measure the risk exposure of a financial institution to determine the amount of capital that the institution must hold as a buffer against unexpected losses. The Basel Committee on Banking Supervision (BCBS) is the committee of the world's bank regulators. BCBS has recently set out the revised standards for minimum capital requirements for market risk, it has focused, among other things, on the two key areas of moving risk measures from Value-at-Risk (VaR) to Expected Shortfall (ES) and considering a comprehensive incorporation of the risk of market illiquidity. Another goal of this thesis is the presentation of a novel numerical method based on SWIFT to compute the VaR and ES of a given portfolio within the stochastic holding period framework to take into account liquidity issues. Two approaches are considered: the delta-gamma approximation, for modelling the change in value of the portfolio as a quadratic approximation of the change in value of the risk factors, and some of the state-of-the-art stochastic processes for driving the dynamics of the log-value change of the portfolio like the Merton jump-diffusion model and the Kou model. Credit risk is the risk of losses from the obligor's failure to honour the contractual agreements and it is usually the main source of risk in a commercial bank. In this thesis, we also investigate the challenging problem of estimating credit risk measures of portfolios with exposure concentration under the multi-factor Gaussian and multi-factor t-copula models. It is well-known that Monte Carlo (MC) methods are highly demanding from the computational point of view in these situations. To overcome this issue, we present efficient and robust numerical techniques based on the Haar wavelets theory for recovering the cumulative distribution function of the loss variable from its characteristic function. The analysis of the approximation error and the results obtained in the numerical experiments section show a reliable and useful machinery for credit risk capital measurement purposes in line with Pillar II of the Basel Accords.
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Rivera, Vega Nestor. "Reservoir characterization using wavelet transforms." Texas A&M University, 2003. http://hdl.handle.net/1969.1/482.
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Automated detection of geological boundaries and determination of cyclic events controlling deposition can facilitate stratigraphic analysis and reservoir characterization. This study applies the wavelet transformation, a recent advance in signal analysis techniques, to interpret cyclicity, determine its controlling factors, and detect zone boundaries. We tested the cyclostratigraphic assessments using well log and core data from a well in a fluvio-eolian sequence in the Ormskirk Sandstone, Irish Sea. The boundary detection technique was tested using log data from 10 wells in the Apiay field, Colombia.
We processed the wavelet coefficients for each zone of the Ormskirk Formation and determined the wavelengths of the strongest cyclicities. Comparing these periodicities with Milankovitch cycles, we found a strong correspondence of the two. This suggests that climate exercised an important control on depositional cyclicity, as had been concluded in previous studies of the Ormskirk Sandstone.
The wavelet coefficients from the log data in the Apiay field were combined to form features. These vectors were used in conjunction with pattern recognition techniques to perform detection in 7 boundaries. For the upper two units, the boundary was detected within 10 feet of their actual depth, in 90% of the wells. The mean detection performance in the Apiay field is 50%.
We compared our method with other traditional techniques which do not focus on selecting optimal features for boundary identification. Those methods resulted in detection performances of 40% for the uppermost boundary, which lag behind the 90% performance of our method.
Automated determination of geologic boundaries will expedite studies, and knowledge of the controlling deposition factors will enhance stratigraphic and reservoir characterization models. We expect that automated boundary detection and cyclicity analysis will prove to be valuable and time-saving methods for establishing correlations and their uncertainties in many types of oil and gas reservoirs, thus facilitating reservoir exploration and management.
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Harbrecht, Helmut, Michael Konik, and Reinhold Schneider. "Fully Discrete Wavelet Galerkin Schemes." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200600441.
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The present paper is intended to give a survey of the developments of the wavelet Galerkin boundary element method. Using appropriate wavelet bases for the discretization of boundary integral operators yields numerically sparse system matrices. These system matrices can be compressed to O(N_j) nonzero matrix entries without loss of accuracy of the underlying Galerkin scheme. Herein, O(N_j) denotes the number of unknowns. As we show in the present paper, the assembly of the compressed system matrix can be performed within optimal complexity. By numerical experiments we provide examples which corroborate the theory.
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Huang, Wensheng. "Wavelet Transform Adaptive Signal Detection." NCSU, 1999. http://www.lib.ncsu.edu/theses/available/etd-19991104-151423.
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Wavelet Transform Adaptive Signal Detection is a signal detection method that uses the Wavelet Transform Adaptive Filter (WTAF). The WTAF is the application of adaptive filtering on the subband signals obtained by wavelet decomposition and reconstruction. The WTAF is an adaptive filtering technique that leads to good convergence and low computational complexity. It can effectively adapt to non-stationary signals, and thus could find practical use for transient signals. Different architectures for implementing the WTAF were proposed and studied in this dissertation. In terms of the type of the wavelet transform being used, we presented the DWT based WTAF and the wavelet tree based WTAF. In terms of the position of the adaptive filter in the signal paths of the system, we presented the Before-Reconstruction WTAF, in which the adaptive filter is placed before the reconstruction filter; and the After-Reconstruction WTAF, in which the adaptive filter is placed after the reconstruction filter. This could also be considered as implementing the adaptive filtering in different domains, with the Before-Reconstruction structure corresponding to adaptive filtering in the scale-domain, and the After-Reconstruction structure corresponding to adaptive filtering in the time-domain. In terms of the type of the error signal used in the WTAF, we presented the output error based WTAF and the subband error based WTAF. In the output error based WTAF, the output error signal is used as input to the LMS algorithm. In the subband error based WTAF, the error signal in each subband is used as input to the LMS algorithm. The algorithms for the WTAF were also generalized in this work. In order to speed up the calculation, we developed the block LMS based WTAF, which modifies the weights of the adaptive filter block-by-block instead of sample-by-sample. Experimental studies were performed to study the performance of different implementation schemes for the WTAF. Simulations were performed on different WTAF algorithms with a sinusoidal input and with a pulse input. The speed and stability properties of each structure were studied experimentally and theoretically. It was found that different WTAF structures had different tradeoffs in terms of stability, performance, computational complexity, and convergence speed. The WTAF algorithms were applied to an online measurement system for fabric compressional behavior and they showed encouraging results. A 3-stage DWT based WTAF and a block WTAF based on a 3-stage DWT was employed to process the noisy force-displacement signal acquired from the online measurement system. The signal-to-noise ratio was greatly increased by applying these WTAFs, which makes a lower sampling rate a possibility. The reduction of the required time for data sampling and processing greatly improves the system speed to meet faster testing requirements. The WTAF algorithm could also be used in other applications requiring fast processing, such as in the real-time applications in communications, measurement, and control.
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Rangaswamy, Vidya. "Phoneme Recognition Using Wavelet Packets." Digital Archive @ GSU, 2006. http://digitalarchive.gsu.edu/cs_theses/16.
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Life would be much easier if there were no typing involved in preparing a document, typing an email, paying online bills, entering credit card details, booking flights, hotels or car rentals online. Imagine a system that would recognize speech and convert it into another form to do these functions automatically. The fact that most people can speak faster than they can type gives a good reason to have a speech recognizer. This thesis concentrates on developing a speaker independent, speech recognizer using Wavelet Packet Transform. Speech corpus in the form of phonemes is collected from an American male and an Indian Female. The subjects chosen for phoneme recognition vary in a number of factors like the accent, gender, age, microphone used to record speech, environment in which phonemes are recorded, etc. These factors increase the complexity of speech recognition. We also assume that the emotions of the speakers are the same and the speakers are stationary while recording phonemes.
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Remenyi, Norbert. "Contributions to Bayesian wavelet shrinkage." Diss., Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/45898.
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This thesis provides contributions to research in Bayesian modeling and shrinkage in the wavelet domain. Wavelets are a powerful tool to describe phenomena rapidly changing in time, and wavelet-based modeling has become a standard technique in many areas of statistics, and more broadly, in sciences and engineering. Bayesian modeling and estimation in the wavelet domain have found useful applications in nonparametric regression, image denoising, and many other areas. In this thesis, we build on the existing
techniques and propose new methods for applications in nonparametric regression, image denoising, and partially linear models.
The thesis consists of an overview chapter and four main topics. In Chapter 1, we provide an overview of recent developments and the current status of Bayesian wavelet shrinkage research. The chapter contains an extensive literature review consisting of almost 100 references. The main focus of the overview chapter is on nonparametric regression, where the observations come from an unknown function contaminated with Gaussian noise. We present many methods which employ model-based and adaptive shrinkage of the wavelet coefficients through Bayes rules. These includes new developments such as dependence models, complex wavelets, and Markov chain Monte Carlo (MCMC) strategies. Some applications of Bayesian wavelet shrinkage, such as curve classification, are discussed.
In Chapter 2, we propose the Gibbs Sampling Wavelet Smoother (GSWS), an adaptive wavelet denoising methodology. We use the traditional mixture prior on the wavelet coefficients, but also formulate a fully Bayesian hierarchical model in the wavelet domain accounting for the uncertainty of the prior parameters by placing hyperpriors on them. Since a closed-form solution to the Bayes estimator does not exist, the procedure is computational, in which the posterior mean is computed via MCMC simulations. We show how to efficiently develop a Gibbs sampling algorithm for the proposed model. The developed procedure is fully Bayesian, is adaptive to the underlying signal, and provides good denoising performance compared to state-of-the-art methods. Application of the method is illustrated on a real data set arising from the analysis of metabolic pathways, where an iterative shrinkage procedure is developed to preserve the mass balance of the metabolites in the system. We also show how the methodology can be extended to complex wavelet bases.
In Chapter 3, we propose a wavelet-based denoising methodology based on a Bayesian hierarchical model using a double Weibull prior. The interesting feature is that in contrast to the mixture priors traditionally used by some state-of-the-art methods, the wavelet coefficients are modeled by a single density. Two estimators are developed, one based on the posterior mean and the other based on the larger posterior mode; and we show how to calculate these estimators efficiently. The methodology provides good denoising performance, comparable even to state-of-the-art methods that use a mixture prior and an empirical Bayes setting of hyperparameters; this is demonstrated by simulations on standard test functions. An application to a real-word data set is also considered.
In Chapter 4, we propose a wavelet shrinkage method based on a neighborhood of wavelet coefficients, which includes two neighboring coefficients and a parental coefficient. The methodology is called Lambda-neighborhood wavelet
shrinkage, motivated by the shape of the considered neighborhood. We propose a Bayesian hierarchical model using a contaminated exponential prior on the total mean energy in the Lambda-neighborhood. The hyperparameters in the model are estimated by the empirical Bayes method, and the posterior mean, median, and Bayes factor are obtained and used in the estimation of the total mean energy. Shrinkage of the neighboring coefficients is based on the ratio of the estimated and observed energy. The proposed methodology is comparable and often superior to several established wavelet denoising methods that utilize neighboring information, which is demonstrated by extensive simulations. An application to a real-world data set from inductance plethysmography is considered, and an extension to image denoising is discussed.
In Chapter 5, we propose a wavelet-based methodology for estimation and variable selection in partially linear models. The inference is conducted in the wavelet domain, which provides a sparse and localized decomposition appropriate for nonparametric components with various degrees of smoothness. A hierarchical Bayes model is formulated on the parameters of this representation, where the estimation and variable selection is performed by a Gibbs sampling procedure. For both the parametric and nonparametric part of the model we are using point-mass-at-zero contamination priors with a double exponential spread distribution. In this sense we extend the model of Chapter 2 to partially linear models. Only a few papers in the area of partially linear wavelet models exist, and we show that the proposed methodology is often superior to the existing methods with respect to the task of estimating model parameters. Moreover, the method is able to perform Bayesian variable selection by a stochastic search for the parametric part of the model.
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Donovan, George C. "Fractal functions, splines, and wavelet." Diss., Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/30411.
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Wang, Judith. "Wavelet-based traffic matrix modeling." Thesis, McGill University, 2011. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=96944.
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The traffic matrix is essential for many network management tasks because it provides the amount of traffic that flows between every origin-destination (OD) pair in a network. We focus on two traffic matrix problems: compression and estimation. Traffic matrices contain substantial amounts of data because they are collected at short timescales over long periods. We investigate techniques to compress traffic matrices using wavelet transforms, which allows us to isolate common underlying patterns present within traffic matrix datasets. In addition, it is expensive for network operators to measure traffic matrices directly. We demonstrate a new traffic matrix estimation method that is based on using our compressing transforms and methods for sparse estimation. Our estimation method also relies on inexpensive link-level measurements. We assess the performance of our wavelet-based traffic matrix model by testing it on two traffic matrix datasets.La matrice de trafic est essentielle pour de nombreuses tâches de gestion de réseau parce qu'elle fourni le volume de trafic qui circule entre chaque paire d'origine et destination (OD) dans un réseau. Nous concentrons sur deux problèmes avec la matrice de trafic: la compression et l'estimation. Les matrices de trafic contiennent de grandes quantités de données parce qu'elles sont recueillies à des délais courts pendant de longues périodes. Nous examinons des techniques pour compresser les matrices de trafic en utilisant les transformées en ondelettes, qui nous permet d'isoler les tendances communes dans les matrices de trafic. En plus, il est coûteux pour les opérateurs de réseau de measurer les matrices de traficdirectement. Nous développons une nouvelle méthode pour estimer la matrice de trafic qui est basée sur les transformées en ondelettes et les méthodes d'estimation rares. Notre méthode d'estimation s'appuie également sur le volume de trafic traversant chaque lien dans un réseau, ce qui est peu coûteux de recueillir. Nous évaluons la performance de notre modèle pour la matrice de trafic en le testant sur deux ensembles de données.
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Tsakiroglou, Evangelia. "Wavelet-based parametric spectrum estimation." Thesis, Imperial College London, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.342234.
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Ghafoori, Elyar. "Wavelet transform and neural network." Thesis, California State University, Long Beach, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=1527935.
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Automatic and accurate detection of Atrial Fibrillation (AF) from the noninvasive ECG signal is imperative in Electrocardiography. AF is mainly reflected in the ECG signal with the absence of P wave and/or irregular RR intervals. Signal processing tools can assess such detailed changes in the ECG, leading to an accurate diagnosis of AF. The proposed method relies on proper noise filtering, Stationary Wavelet Transform, and signal Power Spectrum Estimation. A feature extraction technique and a Neural Network classifier have been employed to determine the presence and absence of the AF episodes. Implementation of the proposed method with 5-fold cross validation on more than 230 hours of ECG data from MIT-BIH arterial fibrillation annotated database demonstrated an accuracy of 93% in classification of the AF and normal ECG signals.
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Long, Christopher J. "Wavelet methods in speech recognition." Thesis, Loughborough University, 1999. https://dspace.lboro.ac.uk/2134/14108.
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In this thesis, novel wavelet techniques are developed to improve parametrization of speech signals prior to classification. It is shown that non-linear operations carried out in the wavelet domain improve the performance of a speech classifier and consistently outperform classical Fourier methods. This is because of the localised nature of the wavelet, which captures correspondingly well-localised time-frequency features within the speech signal. Furthermore, by taking advantage of the approximation ability of wavelets, efficient representation of the non-stationarity inherent in speech can be achieved in a relatively small number of expansion coefficients. This is an attractive option when faced with the so-called 'Curse of Dimensionality' problem of multivariate classifiers such as Linear Discriminant Analysis (LDA) or Artificial Neural Networks (ANNs). Conventional time-frequency analysis methods such as the Discrete Fourier Transform either miss irregular signal structures and transients due to spectral smearing or require a large number of coefficients to represent such characteristics efficiently. Wavelet theory offers an alternative insight in the representation of these types of signals. As an extension to the standard wavelet transform, adaptive libraries of wavelet and cosine packets are introduced which increase the flexibility of the transform. This approach is observed to be yet more suitable for the highly variable nature of speech signals in that it results in a time-frequency sampled grid that is well adapted to irregularities and transients. They result in a corresponding reduction in the misclassification rate of the recognition system. However, this is necessarily at the expense of added computing time. Finally, a framework based on adaptive time-frequency libraries is developed which invokes the final classifier to choose the nature of the resolution for a given classification problem. The classifier then performs dimensionaIity reduction on the transformed signal by choosing the top few features based on their discriminant power. This approach is compared and contrasted to an existing discriminant wavelet feature extractor. The overall conclusions of the thesis are that wavelets and their relatives are capable of extracting useful features for speech classification problems. The use of adaptive wavelet transforms provides the flexibility within which powerful feature extractors can be designed for these types of application.
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Tait, Crawford. "Wavelet analysis for onset detection." Thesis, University of Glasgow, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.363156.
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Silva, Eduardo Antonio Barros da. "Wavelet transforms for image coding." Thesis, University of Essex, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.282495.
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Aljohani, Hassan Musallam S. "Wavelet methods and inverse problems." Thesis, University of Leeds, 2017. http://etheses.whiterose.ac.uk/18830/.
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Archaeological investigations are designed to acquire information without damaging the archaeological site. Magnetometry is one of the important techniques for producing a surface grid of readings, which can be used to infer underground features. The inversion of this data, to give a fitted model, is an inverse problem. This type of problem can be ill-posed or ill-conditioned, making the estimation of model parameters less stable or even impossible. More precisely, the relationship between archaeological data and parameters is expressed by a likelihood. It is not possible to use the standard regression estimate obtained through the likelihood, which means that no maximum likelihood estimate exists. Instead, various constraints can be added through a prior distribution with an estimate produced using the posterior distribution. Current approaches incorporate prior information describing smoothness, which is not always appropriate. The biggest challenge is that the reconstruction of an archaeological site as a single layer requires various physical features such as depth and extent to be assumed. By applying a smoothing prior in the analysis of stratigraphy data, however, these features are not easily estimated. Wavelet analysis has proved to be highly efficient at eliciting information from noisy data. Additionally, complicated signals can be explained by interpreting only a small number of wavelet coefficients. It is possible that a modelling approach, which attempts to describe an underlying function in terms of a multi-level wavelet representation will be an improvement on standard techniques. Further, a new method proposed uses an elastic-net based distribution as the prior. Two methods are used to solve the problem, one is based on one-stage estimation and the other is based on two stages. The one-stage considers two approaches a single prior for all wavelet resolution levels and a level-dependent prior, with separate priors at each resolution level. In a simulation study and a real data analysis, all these techniques are compared to several existing methods. It is shown that the methodology using a single prior provides good reconstruction, comparable even to several established wavelet methods that use mixture priors.
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de, Wit Tjaart Cornelis. "Wavelet analysis of geomagnetic jerks." Master's thesis, University of Cape Town, 2013. http://hdl.handle.net/11427/6620.
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Geomagnetic jerks, or secular variation impulses, are abrupt changes in the slope of the first time derivative of the Earth's magnetic field. These changes occur on time scales of the order of a year. It has been demonstrated that the jerks might be more singular than previously supposed; their """"regularity"""" is closer to 1.5 than to 2. Although discovered over 30 years ago, geomagnetic jerks remain poorly understood. Their origin probably lies in the magnetohydrodynamics that is responsible for the maintenance of the Earth's magnetic field produced within the Earth's liquid and convecting core (through a so-called geo-dynamo process). A wavelet tool was programmed in MATLAB and a wavelet analysis applied to detect and characterize singular events, or jerks, in the time series made of monthly mean values of the east component of the geomagnetic field from 45 selected worldwide observatories. The analysis was first performed on various synthetic series made up of a """"main"""" signal of smooth variation intervals separated by singular events, a white noise and an """"external"""" signal made up of the sum of a few harmonic signals. Conditions, in which the singular events could be clearly isolated and their associated """"regularities"""" recovered, are highlighted. Geomagnetic jerks were detected globally in 1969, 1978, 1991 and 1999. Furthermore, geomagnetic jerks are also thought to have also occurred in 1901, 1913 and 1925, but due to the small number of observatories with long enough records to allow for detection during this period, their extent is unclear. Two further geomagnetic jerks were found to have occurred around 1937 and 1952, but due to these events not being detected by all the observatories with records covering this period, these events might not be of the same extent or origin. The results of the geomagnetic jerks detected here and the phase jumps detected in the Chandler wobble are compared and the remarkable coincidence highlighted. The spatio-temporal behaviour of jerks, for example where jerks arrive in the northern hemisphere before the southern hemisphere, is explored. Using k-means clustering, an antipodal relationship is proposed between regional trends in the time delay in the detection of geomagnetic jerks at the surface of the Earth. It is possible that this finding may shed some new light on the origin of geomagnetic jerks. The wavelet analysis was also used to investigate whether the nature of geomagnetic jerks could be classified into one of the following three categories: geomagnetic jerks are the result of some instability starting at the time of the jerk; geomagnetic jerks are the result of some continuous oscillations; that geomagnetic jerks possibly reflect a process ending at the time of the jerk. A startling pattern emerged that suggested that the 1969 jerk corresponded to an event starting at that time, the 1978 jerk corresponding to an event ending at that time, and lastly an event again starting in 1990. This implied that the 1969 and 1978 jerks might have been the result of a common phenomenon starting in 1969 and ending almost a decade later in 1978.
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Choe, Gwangwoo. "Merged arithmetic for wavelet transforms /." Full text (PDF) from UMI/Dissertation Abstracts International, 2000. http://wwwlib.umi.com/cr/utexas/fullcit?p3004235.
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