Relevant bibliographies by topics / Wavelets

Academic literature on the topic 'Wavelets'

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Published: 4 June 2021
Last updated: 8 June 2024

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Journal articles on the topic "Wavelets"

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Battle, Guy. "Osiris wavelets and Set wavelets." Journal of Applied Mathematics 2004, no. 6 (2004): 495–528. http://dx.doi.org/10.1155/s1110757x04404070.

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An alternative to Osiris wavelet systems is introduced in two dimensions. The basic building blocks are continuous piecewise linear functions supported on equilateral triangles instead of on squares. We refer to wavelets generated in this way as Set wavelets. We introduce a Set wavelet system whose homogeneous mode density is2/5. The system is not orthonormal, but we derive a positive lower bound on the overlap matrix.
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SHUKLA, NIRAJ K. "NON-MSF A-WAVELETS FROM A-WAVELET SETS." International Journal of Wavelets, Multiresolution and Information Processing 11, no. 01 (January 2013): 1350002. http://dx.doi.org/10.1142/s0219691313500021.

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Generalizing the result of Bownik and Speegle [Approximation Theory X: Wavelets, Splines and Applications, Vanderbilt University Press, pp. 63–85, 2002], we provide plenty of non-MSF A-wavelets with the help of a given A-wavelet set. Further, by showing that the dimension function of the non-MSF A-wavelet constructed through an A-wavelet set W coincides with the dimension function of W, we conclude that the non-MSF A-wavelet and the A-wavelet set through which it is constructed possess the same nature as far as the multiresolution analysis is concerned. Some examples of non-MSF d-wavelets and non-MSF A-wavelets are also provided. As an illustration we exhibit a pathwise connected class of non-MSF non-MRA wavelets sharing the same wavelet dimension function.
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KING, EMILY J. "SMOOTH PARSEVAL FRAMES FOR L2(ℝ) AND GENERALIZATIONS TO L2(ℝd)." International Journal of Wavelets, Multiresolution and Information Processing 11, no. 06 (November 2013): 1350047. http://dx.doi.org/10.1142/s0219691313500471.

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Wavelet set wavelets were the first examples of wavelets that may not have associated multiresolution analyses. Furthermore, they provided examples of complete orthonormal wavelet systems in L2(ℝd) which only require a single generating wavelet. Although work had been done to smooth these wavelets, which are by definition discontinuous on the frequency domain, nothing had been explicitly done over ℝd, d > 1. This paper, along with another one cowritten by the author, finally addresses this issue. Smoothing does not work as expected in higher dimensions. For example, Bin Han's proof of existence of Schwartz class functions which are Parseval frame wavelets and approximate Parseval frame wavelet set wavelets does not easily generalize to higher dimensions. However, a construction of wavelet sets in [Formula: see text] which may be smoothed is presented. Finally, it is shown that a commonly used class of functions cannot be the result of convolutional smoothing of a wavelet set wavelet.
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Lal, Shyam, and Harish Yadav. "Approximation of functions belonging to Hölder’s class and solution of Lane-Emden differential equation using Gegenbauer wavelets." Filomat 37, no. 12 (2023): 4029–45. http://dx.doi.org/10.2298/fil2312029l.

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In this paper, a very new technique based on the Gegenbauer wavelet series is introduced to solve the Lane-Emden differential equation. The Gegenbauer wavelets are derived by dilation and translation of an orthogonal Gegenbauer polynomial. The orthonormality of Gegenbauer wavelets is verified by the orthogonality of classical Gegenbauer polynomials. The convergence analysis of Gegenbauer wavelet series is studied in H?lder?s class. H?lder?s class H?[0,1) and H?[0,1) of functions are considered, H?[0,1) class consides with classical H?lder?s class H?[0, 1) if ?(t) = t?, 0 < ? ? 1. The Gegenbauer wavelet approximations of solution functions of the Lane-Emden differential equation in these classes are determined by partial sums of their wavelet series. In briefly, four approximations E(1) 2k?1,0, E(1) 2k?1,M, E(2) 2k?1,0, E(2) 2k?1,M of solution functions of classes H?[0, 1), H?[0, 1) by (2k?1, 0)th and (2k?1,M)th partial sums of their Gegenbauer wavelet expansions have been estimated. The solution of the Lane-Emden differential equation obtained by the Gegenbauer wavelets is compared to its solution derived by using Legendre wavelets and Chebyshev wavelets. It is observed that the solutions obtained by Gegenbauer wavelets are better than those obtained by using Legendre wavelets and Chebyshev wavelets, and they coincide almost exactly with their exact solutions. This is an accomplishment of this research paper in wavelet analysis.
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ZENG, LI, JIQIANG GUO, and CHENCHENG HUANG. "THE BACK-PROJECTION METHOD FOR CONSTRUCTING 3D NON-TENSOR PRODUCT MOTHER WAVELETS AND THE APPLICATION IN IMAGE EDGE DETECTION." International Journal of Wavelets, Multiresolution and Information Processing 10, no. 03 (May 2012): 1250026. http://dx.doi.org/10.1142/s0219691312500269.

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In this paper, a non-tensor product method for constructing three-dimension (3D) mother wavelets by back-projecting two dimension (2D) mother wavelets is presented. We have proved that if a 2D mother wavelet satisfies certain conditions, the back-projection of the 2D mother wavelet is a 3D mother wavelet. And the construction instances of 3D Mexican-hat wavelet and 3D Meyer wavelet are given. These examples imply that we can get some new 3D mother wavelets from known 1D or 2D mother wavelets by using back-projecting method. This method inaugurates a new approach for constructing non-tensor product 3D wavelet. In addition, the non-tensor product 3D Mexican-hat wavelet is used for detecting the edge of two 3D images in our experimental section. Compared with the Mallat's maximum wavelet module approach which uses 3D directional wavelets, experimental results show it can obtain better outcome especial for the edge which the orientation is not along the coordinate axis. Furthermore, the edge is more fine, and the computational cost is much smaller. The non-tensor product mother wavelets constructed by using the method of this paper also can be widely used for compression, filtering and denoising of 3D images.
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ASHUROV, RAVSHAN. "CONVERGENCE OF THE CONTINUOUS WAVELET TRANSFORMS ON THE ENTIRE LEBESGUE SET OF Lp-FUNCTIONS." International Journal of Wavelets, Multiresolution and Information Processing 09, no. 04 (July 2011): 675–83. http://dx.doi.org/10.1142/s0219691311004262.

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The almost everywhere convergence of wavelets transforms of Lp-functions under minimal conditions on wavelets is well known. But this result does not provide any information about the exceptional set (of Lebesgue measure zero), where convergence does not hold. In this paper, under slightly stronger conditions on wavelets, we prove convergence of wavelet transforms everywhere on the entire Lebesgue set of Lp-functions. On the other hand, practically all the wavelets, including Haar and "French hat" wavelets, used frequently in applications, satisfy our conditions. We also prove that the same conditions on wavelets guarantee the Riemann localization principle in L1 for the wavelet transforms.
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ZHAN, YINWEI, and HENK J. A. M. HEIJMANS. "NON-SEPARABLE 2D BIORTHOGONAL WAVELETS WITH TWO-ROW FILTERS." International Journal of Wavelets, Multiresolution and Information Processing 03, no. 01 (March 2005): 1–18. http://dx.doi.org/10.1142/s0219691305000713.

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In the literature 2D (or bivariate) wavelets are usually constructed as a tensor product of 1D wavelets. Such wavelets are called separable. However, there are various applications, e.g. in image processing, for which non-separable 2D wavelets are prefered. In this paper, we investigate the class of compactly supported orthonormal 2D wavelets that was introduced by Belogay and Wang.2 A characteristic feature of this class of wavelets is that the support of the corresponding filter comprises only two rows. We are concerned with the biorthogonal extension of this kind of wavelets. It turns out that the 2D wavelets in this class are intimately related to some underlying 1D wavelet. We explore this relation in detail, and we explain how the 2D wavelet transforms can be realized by means of a lifting scheme, thus allowing an efficient implementation. We also describe an easy way to construct wavelets with more rows and shorter columns.
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Knapp, Ralph W. "Energy distribution in wavelets and implications on resolving power." GEOPHYSICS 58, no. 1 (January 1993): 39–46. http://dx.doi.org/10.1190/1.1443350.

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The suite of a wavelet is defined as being all wavelets that share a common amplitude spectrum and total energy but differ in phase spectra. Within a suite there are also classes of wavelets. A wavelet class has a common amplitude envelope and energy distribution. As such, it includes all wavelets that differ by only a constant‐angle phase shift. Of all wavelets within suite, the zero‐phase wavelet has the minimum energy envelope width; its energy is confined to minimum time dispersion. Therefore, the zero‐phase wavelet has maximum resolving power within the suite. Because a zero‐phase wavelet shares its amplitude envelope with a class of wavelets that differ by only a constant phase shift, all wavelets of the class also have maximum resolving power within the suite. The most familiar of these is the quadrature‐phase wavelet (90‐degree phase shift). Use of the complex trace results in an evaluation of the total energy, both potential and kinetic, of the wavelet signal. Assuming the wavelet signal is the output of a velocity geophone, partial energy represents only kinetic energy. Total energy better represents wavelet energy propagating through the earth. Use of partial energy (real signal only) applies a bias that favors the zero‐phase wavelets with respect to others of its class despite identical energy distribution. This bias is corrected when the wavelet envelope is used in the evaluation rather than wavelet trace amplitude. On a wiggle‐trace seismic section (amplitude display) a zero‐phase wavelet maintains a detectability advantage in the presence of noise because of a slightly greater amplitude; however, the advantage is lost in complex trace sections (energy displays) because both reflection strength and instantaneous frequency are independent of a constant phase shift in the wavelet. These sections are identical whether the wavelet is zero‐phase, quadrature‐phase or any other constant phase value, i.e., a wavelet within the zero‐phase class. (This does not imply that reflection strength sections should replace wiggle trace ones, only that they have advantages in the solution of some problems.)
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Kathuria, Leena, Shashank Goel, and Nikhil Khanna. "Fourier–Boas-Like Wavelets and Their Vanishing Moments." Journal of Mathematics 2021 (March 6, 2021): 1–7. http://dx.doi.org/10.1155/2021/6619551.

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In this paper, we propose Fourier–Boas-Like wavelets and obtain sufficient conditions for their higher vanishing moments. A sufficient condition is given to obtain moment formula for such wavelets. Some properties of Fourier–Boas-Like wavelets associated with Riesz projectors are also given. Finally, we formulate a variation diminishing wavelet associated with a Fourier–Boas-Like wavelet.
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OTHMANI, MOHAMED, WAJDI BELLIL, CHOKRI BEN AMAR, and ADEL M. ALIMI. "A NEW STRUCTURE AND TRAINING PROCEDURE FOR MULTI-MOTHER WAVELET NETWORKS." International Journal of Wavelets, Multiresolution and Information Processing 08, no. 01 (January 2010): 149–75. http://dx.doi.org/10.1142/s0219691310003353.

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This paper deals with the features of a new wavelet network structure founded on several mother wavelets families. This new structure is similar to the classic wavelets network but it admits some differences eventually. The wavelet network basically uses the dilations and translations versions of only one mother wavelet to construct the network, but the new one uses several mother wavelets and the objective is to maximize the probability of selection of the best wavelets. Two methods are presented to assist the training procedure of this new structure. On one hand, we have an optimal selection technique that is based on an improved version of the Orthogonal Least Squares method; on the other, the Generalized Cross-Validation method to determine the number of wavelets to be selected for every mother wavelet. Some simulation results are reported to demonstrate the performance and the effectiveness of the new structure and the training procedure for function approximation in one and two dimensions.
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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 Bonatti
Dissertação (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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Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro de Ciencias Fisicas e Matematicas
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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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Books on the topic "Wavelets"

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Benedetto, John J., and Michael W. Frazier. Wavelets. Boca Raton: CRC Press, 2021. http://dx.doi.org/10.1201/9781003210450.

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Combes, Jean-Michel, Alexander Grossmann, and Philippe Tchamitchian, eds. Wavelets. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-97177-8.

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Hubbard, Barbara Burke. Wavelets. Basel: Birkhäuser Basel, 1997. http://dx.doi.org/10.1007/978-3-0348-6094-9.

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Louis, Alfred Karl, Peter Maaß, and Andreas Rieder. Wavelets. Wiesbaden: Vieweg+Teubner Verlag, 1994. http://dx.doi.org/10.1007/978-3-322-92109-3.

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Louis, Alfred Karl, Peter Maaß, and Andreas Rieder. Wavelets. Wiesbaden: Vieweg+Teubner Verlag, 1998. http://dx.doi.org/10.1007/978-3-322-80136-4.

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Combes, Jean-Michel, Alexander Grossmann, and Philippe Tchamitchian, eds. Wavelets. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-75988-8.

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Gao, Robert X., and Ruqiang Yan. Wavelets. Boston, MA: Springer US, 2011. http://dx.doi.org/10.1007/978-1-4419-1545-0.

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Wavelets: A primer. Natick, Mass: A.K. Peters, 1998.

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A, Gopinath Ramesh, and Guo Haitao, eds. Introduction to wavelets and wavelet transforms: A primer. Upper Saddle River, N.J: Prentice Hall, 1998.

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Akujuobi, Cajetan M. Wavelets and Wavelet Transform Systems and Their Applications. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-87528-2.

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Book chapters on the topic "Wavelets"

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Akujuobi, Cajetan M. "Wavelets." In Wavelets and Wavelet Transform Systems and Their Applications, 13–44. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-87528-2_2.

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Vyas, Aparna, Soohwan Yu, and Joonki Paik. "Wavelets and Wavelet Transform." In Signals and Communication Technology, 45–92. Singapore: Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-7272-7_3.

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Jansen, Maarten. "Wavelets and wavelet thresholding." In Noise Reduction by Wavelet Thresholding, 9–45. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4613-0145-5_2.

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Mourad, Talbi. "Wavelets and Wavelet Transforms." In ECG Denoising Based on Total Variation Denoising and Wavelets, 1–18. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-25267-9_1.

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Gao, Robert X., and Ruqiang Yan. "Signals and Signal Processing in Manufacturing." In Wavelets, 1–15. Boston, MA: Springer US, 2010. http://dx.doi.org/10.1007/978-1-4419-1545-0_1.

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Gao, Robert X., and Ruqiang Yan. "Selection of Base Wavelet." In Wavelets, 165–87. Boston, MA: Springer US, 2010. http://dx.doi.org/10.1007/978-1-4419-1545-0_10.

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Gao, Robert X., and Ruqiang Yan. "Designing Your Own Wavelet." In Wavelets, 189–203. Boston, MA: Springer US, 2010. http://dx.doi.org/10.1007/978-1-4419-1545-0_11.

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Gao, Robert X., and Ruqiang Yan. "Beyond Wavelets." In Wavelets, 205–20. Boston, MA: Springer US, 2010. http://dx.doi.org/10.1007/978-1-4419-1545-0_12.

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Gao, Robert X., and Ruqiang Yan. "From Fourier Transform to Wavelet Transform: A Historical Perspective." In Wavelets, 17–32. Boston, MA: Springer US, 2010. http://dx.doi.org/10.1007/978-1-4419-1545-0_2.

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Gao, Robert X., and Ruqiang Yan. "Continuous Wavelet Transform." In Wavelets, 33–48. Boston, MA: Springer US, 2010. http://dx.doi.org/10.1007/978-1-4419-1545-0_3.

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Conference papers on the topic "Wavelets"

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Newland, David E. "Practical Signal Analysis: Do Wavelets Make Any Difference?" In ASME 1997 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/detc97/vib-4135.

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Abstract Signal decomposition by time-frequency and time-scale mapping is an essential element of most diagnostic signal analysis. Is the wavelet method of decomposition any better than the short-time Fourier transform and Wigner-Ville methods? This paper explores the effectiveness of wavelets for diagnostic signal analysis. The author has found that harmonic wavelets are particularly suitable because of their simple structure in the frequency domain, but it is still difficult to produce high-definition time-frequency maps. New details of the theory of harmonic wavelet analysis are described which provide the basis for computational algorithms designed to improve map definition.
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Newland, David E. "Progress in the Application of Wavelet Theory to Vibration Analysis." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0378.

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Abstract For vibration signal analysis, the objective is usually to extract frequency data from a signal and study how the signal’s frequency content changes with time. Because wavelets are local functions of time, each with a predetermined frequency content, wavelet analysis provides a good means of doing this. As a result, practical wavelet analysis is growing rapidly. There are many different wavelets to use but no accepted procedure for choosing between them. This paper discusses various alternative wavelets for practical calculations and describes two of the key numerical algorithms. Examples of recent applications using these algorithms are reviewed, including vibration monitoring and detection, transient signal analysis and denoising.
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Freeman, Mark O., Ken A. Duell, Brett Bock, and Adam S. Fedor. "Introduction to wavelets and considerations for optical implementation." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1992. http://dx.doi.org/10.1364/oam.1992.fa1.

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Wavelets have gained the attention of the signal processing community for their usefulness in analyzing nonstationary signals, for their mathematical elegance, and for their relative ease of computation. This paper is intended to introduce the audience to the basic principles of wavelet analysis and to consider where optical techniques can be applied advantageously. A signal is decomposed on a set of basis functions created by scaling and shifting a single fundamental wavelet. The space and frequency localization of the resulting wavelet transform, spanning the range from pure Nyquist sampling (no frequency localization) to Fourier transforms (no spatial localization), is determined by the choice of this fundamental wavelet. A common choice for the fundamental wavelet has compact support in the signal domain and bandpass-like behavior in the frequency domain. With this choice, rapidly varying information is well localized in the signal domain while slowly varying information is well localized in the frequency domain. We will discuss what constitutes an allowed fundamental wavelet, orthogonal and nonorthogonal wavelet bases, and the choice of sampling intervals in shift and scale. We will also discuss some of our theoretical results on filtering noise from nonstationary signals by using the wavelet transform for nonstationary spectrum estimation. In considering the use of optical techniques for wavelet computations, it is important to be aware of the digital competition. One reason for the popularity of wavelets is that O(N) algorithms exist for their digital computation. This is stiff competition for an optical system if the only advantage that can be claimed is speed. We will discuss the possible advantages of optical systems related to continuous rather than discretely sampled shift coordinates and the ease of implementing arbitrary scaling factors and nonseparable 2D wavelet functions. Finally, we will present an optical system for computing 2D wavelet transforms.
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Zheng, Youqi, Hongchun Wu, and Liangzhi Cao. "Neutron Transport Solution Using the Daubechies’ Wavelets in the Spatial Discretization." In 18th International Conference on Nuclear Engineering. ASMEDC, 2010. http://dx.doi.org/10.1115/icone18-29429.

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This paper describes a one-dimensional wavelet-based spatial discretization scheme for the first-order neutron transport equation. Two special features are introduced: i) the spatial variable is discretized using the Daubechies’ wavelets on the interval, and the neutron flux is represented in term of the wavelet series in a normalized node, the tradition SN angular discretization scheme is used in solving the equation, and ii) the wavelet Galerkin method is applied here, using the Daubechies’ scaling function as both the trialing function and weighting function, the integrations of Daubechies’ scaling function and its derivative in the Galerkin system are calculated numerically, using the difference quotient instead of the derivative. The boundary conditions and interface conditions are given in the exact form of wavelets series and added into the Galerkin system in special locations. The LU decomposition method is applied to solving the matrix in formed in the Galerkin system. The test results on several benchmark problems indicate that the wavelet-based spatial discretization scheme in this paper is capable of handling the first-order neutron transport equation, accurate in treating the boundary condition while using the wavelets expansion in spatial discretization, effective in treating the transport problems in the deep penetrating medium and in strong heterogeneous medium.
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Semenov, Vladimir, and Aleksandr Shurbin. "USING WAVELETS WITH A RECTANGULAR AMPLITUDE-FREQUENCY RESPONSE TO FILTER SIGNALS." In CAD/EDA/SIMULATION IN MODERN ELECTRONICS 2021. Bryansk State Technical University, 2021. http://dx.doi.org/10.30987/conferencearticle_61c997ef29ef52.74618218.

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The wavelet transform is the transmission of a signal through a bandpass filter. The design of wavelets with a rectangular amplitude-frequency response makes it possible to obtain almost ideal digital filters. The wavelet transform is calculated in the frequency domain using the fast Fourier transform.
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Chancey, Valeta Carol, George T. Flowers, and Candice L. Howard. "A Harmonic Wavelets Approach for Extracting Transient Patterns From Measured Rotor Vibration Data." In ASME Turbo Expo 2001: Power for Land, Sea, and Air. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/2001-gt-0241.

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Vibration analysis is a powerful diagnostic tool for rotating machinery problems. Traditional approaches to vibration signature analysis have focused on the Fourier transform, which tends to average out transient effects. Recent work in the area of wavelets has allowed for the characterization of signals in frequency and in time, which, if properly interpreted, can provide substantial insight, particularly with regard to transient behaviors. There are many different wavelets, but the harmonic wavelet was developed specifically for vibration analysis. It uses an algorithm based upon the FFT, which makes it particularly attractive to many in the vibration analysis community. This paper considers the harmonic wavelet as a tool for extracting transient patterns from measured vibration data. A method for characterizing transient behaviors using the harmonic wavelet is described and illustrated using simulation and experimental results.
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Nikravesh, Seyed Majid Yadavar, Hossein Taheri, and Peter Wagstaff. "Identification of Appropriate Wavelet for Vibration Study of Mechanical Impacts." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-62348.

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The purpose of this paper is to discuss the selection of the most appropriate wavelets to analyze the vibration response of structures due to mechanical impacts. For this reason the wavelet transformation is briefly introduced, then the different types of wavelets, which are commonly used in this type of application are presented. Subsequently, the effects of selecting different types of wavelet to study the vibrations of a mechanical system are evaluated using a mathematical model. Afterwards, the wavelet transform is used to analyze the experimental response caused by the impact of a hammer on a test plate. This shows that the existence of a zone of local response due to reinforcement under the plate’s cover can be distinguished using the wavelet analysis.
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Daneshmand, Farhang, Abdolaziz Abdollahi, Mehdi Liaghat, and Yousef Bazargan Lari. "Free Vibration Analysis of Frame Structures Using BSWI Method." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-68417.

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Vibration analysis for complicated structures, or for problems requiring large numbers of modes, always requires fine meshing or using higher order polynomials as shape functions in conventional finite element analysis. Since it is hard to predict the vibration mode a priori for a complex structure, a uniform fine mesh is generally used which wastes a lot of degrees of freedom to explore some local modes. By the present wavelets element approach, the structural vibration can be analyzed by coarse mesh first and the results can be improved adaptively by multi-level refining the required parts of the model. This will provide accurate data with less degrees of freedom and computation. The scaling functions of B-spline wavelet on the interval (BSWI) as trial functions that combines the versatility of the finite element method with the accuracy of B-spline functions approximation and the multiresolution strategy of wavelets is used for frame structures vibration analysis. Instead of traditional polynomial interpolation, scaling functions at the certain scale have been adopted to form the shape functions and construct wavelet-based elements. Unlike the process of wavelets added directly in the other wavelet numerical methods, the element displacement field represented by the coefficients of wavelets expansions is transformed from wavelet space to physical space via the corresponding transformation matrix. To verify the proposed method, the vibrations of a cantilever beam and a plane structures are studied in the present paper. The analyses and results of these problems display the multi-level procedure and wavelet local improvement. The formulation process is as simple as the conventional finite element method except including transfer matrices to compute the coupled effect between different resolution levels. This advantage makes the method more competitive for adaptive finite element analysis. The results also show good agreement with those obtained from the classical finite element method and analytical solutions.
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de Moraes, Francisco José Vicente, and Hans Ingo Weber. "Deconvolution by Wavelets for Extracting Impulse Response Functions." In ASME 1997 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/detc97/vib-4136.

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Abstract The extraction of Impulse Response Functions (Markov parameters) is a major feature on dynamic systems identification. The convolution integral is a most important input-output relationship for linear systems. Existing methods for calculating the IRFs from the convolution integral are carried out in time or frequency domains. The orthonormal wavelet transform consists on decomposing a given signal on mutually orthogonal local basis functions. It is possible to make use of the orthogonal properties of wavelets for calculating the convolution integral. The wavelet domain preserves the temporal nature of data and, simultaneously, different frequency bands are isolated by the multiresolution analysis, without loosing the orthogonality of the wavelet terms. Algorithm matrices are well conditioned and the method is not very sensitive to output noise. Simulated and experimental analysis are performed and results presented.
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Aretakis, N., and K. Mathioudakis. "Wavelet Analysis for Gas Turbine Fault Diagnostics." In ASME 1996 International Gas Turbine and Aeroengine Congress and Exhibition. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/96-gt-343.

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The application of wavelet analysis to diagnosing faults in Gas Turbines is examined in the present paper. Applying the Wavelet Transform to time signals obtained from sensors placed on an engine, gives information which is in correspondence to their Fourier Transform. Diagnostic techniques based on Fourier analysis of signals can therefore be transposed to the Wavelet analysis. In the paper the basic properties of wavelets, in relation to the nature of turbomachinery signals, are discussed. The possibilities for extracting diagnostic information by means of wavelets are examined, by studying the applicability to existing data from vibration, unsteady pressure and acoustic measurements. Advantages offered, with respect to existing methods based on harmonic analysis, are discussed as well as particular requirements related to practical application.
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Reports on the topic "Wavelets"

1

Schlossnagle, G., J. M. Restrepo, and G. K. Leaf. Periodized wavelets. Office of Scientific and Technical Information (OSTI), December 1993. http://dx.doi.org/10.2172/10144057.

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Restrepo, J. M., G. K. Leaf, and G. Schlossnagle. Periodized Daubechies wavelets. Office of Scientific and Technical Information (OSTI), March 1996. http://dx.doi.org/10.2172/211651.

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Welland, Grant V., and Brian DeFacio. Wavelets and Scattering. Fort Belvoir, VA: Defense Technical Information Center, July 1994. http://dx.doi.org/10.21236/ada292746.

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Topiwala, Pankaj N., and David Colella. Introduction to Wavelets. Fort Belvoir, VA: Defense Technical Information Center, July 1993. http://dx.doi.org/10.21236/ada268465.

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Kaiser, Gerald. Realizing Sources for Electromagnetic Wavelets and Implementing the Wavelet Radar Concept. Fort Belvoir, VA: Defense Technical Information Center, January 2008. http://dx.doi.org/10.21236/ada481826.

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Suter, Bruce W. Wavelets and Signal Processing. Fort Belvoir, VA: Defense Technical Information Center, August 1996. http://dx.doi.org/10.21236/ada324106.

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Del Rose, Michael. Voice Digit Recognition Using Wavelets. Fort Belvoir, VA: Defense Technical Information Center, November 2004. http://dx.doi.org/10.21236/ada634136.

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Tan, C. Y. Peak finding using biorthogonal wavelets. Office of Scientific and Technical Information (OSTI), February 2000. http://dx.doi.org/10.2172/750842.

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Crovella, Mark, and Eric Kolaczyk. Graph Wavelets for Spatial Traffic Analysis. Fort Belvoir, VA: Defense Technical Information Center, July 2002. http://dx.doi.org/10.21236/ada442573.

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Suter, Bruce W. Wavelets, Signal Processing and Matrix Computations. Fort Belvoir, VA: Defense Technical Information Center, September 1994. http://dx.doi.org/10.21236/ada283832.

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