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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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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.
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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Olphert, Sean, and Stephen C. Power. "Higher Rank Wavelets." Canadian Journal of Mathematics 63, no. 3 (June 1, 2011): 689–720. http://dx.doi.org/10.4153/cjm-2011-012-1.
Abstract A theory of higher rank multiresolution analysis is given in the setting of abelian multiscalings. This theory enables the construction, from a higher rank MRA, of finite wavelet sets whose multidilations have translates forming an orthonormal basis in L2(ℝd). While tensor products of uniscaled MRAs provide simple examples we construct many nonseparable higher rank wavelets. In particular we construct Latin square wavelets as rank 2 variants of Haar wavelets. Also we construct nonseparable scaling functions for rank 2 variants of Meyer wavelet scaling functions, and we construct the associated nonseparable wavelets with compactly supported Fourier transforms. On the other hand we show that compactly supported scaling functions for biscaled MRAs are necessarily separable.
Shannon wavelets are studied together with their differential properties (known as connection coefficients). It is shown that the Shannon sampling theorem can be considered in a more general approach suitable for analyzing functions ranging in multifrequency bands. This generalization coincides with the Shannon wavelet reconstruction ofL2(ℝ)functions. The differential properties of Shannon wavelets are also studied through the connection coefficients. It is shown that Shannon wavelets areC∞-functions and their any order derivatives can be analytically defined by some kind of a finite hypergeometric series. These coefficients make it possible to define the wavelet reconstruction of the derivatives of theCℓ-functions.
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HOU, YU. "A COMPACTLY SUPPORTED, SYMMETRICAL AND QUASI-ORTHOGONAL WAVELET." International Journal of Wavelets, Multiresolution and Information Processing 08, no. 06 (November 2010): 931–40. http://dx.doi.org/10.1142/s0219691310003900.
Based on the wavelet theory and optimization method, a class of single wavelets with compact support, symmetry and quasi-orthogonality are designed and constructed. Some mathematical properties of the wavelets, such as orthogonality, linear phase property and vanishing moments and so on, are studied. A speech compression experiment is implemented in order to investigate the performance of signal reconstruction and speech compression for the proposed wavelets. Comparison with some conventional wavelets shows that the proposed wavelets have a very good performance of signal reconstruction and speech compression.
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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.
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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Benedetto, John J., Michael W. Frazier, and Bruno Torrésani. "Wavelets: Mathematics and Applications." Physics Today 47, no. 11 (November 1994): 90–91. http://dx.doi.org/10.1063/1.2808703.
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.
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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Jiang, Zhuhan, and Xiling Guo. "A note on the extension of a family of biorthogonal Coifman wavelet systems." ANZIAM Journal 46, no. 1 (July 2004): 111–20. http://dx.doi.org/10.1017/s1446181100013717.
AbstractWavelet systems with a maximum number of balanced vanishing moments are known to be extremely useful in a variety of applications such as image and video compression. Tian and Wells recently created a family of such wavelet systems, called the biorthogonal Coifman wavelets, which have proved valuable in both mathematics and applications. The purpose of this work is to establish along with direct proofs a very neat extension of Tian and Wells' family of biorthogonal Coifman wavelets by recovering other “missing” members of the biorthogonal Coifman wavelet systems.
The first part of this thesis is concerned with Bakers Conjecture (1984) which says that two permutable transcendental entire functions have the same Julia set. To this end, we shall exhibit that two permutable transcendental entire functions of a certain type have the same Julia set. So far, this is the best result to the conjecture. The second part relates to Newton's method to find zeros of functions. We shall look for the locations of the limits of the iterating sequence of the relaxed Newton function on its wandering domains. A relaxed Newton function with corresponding properties is constructed. The third part relates to the dynamics of ordinary differential equations and inverse problems. Given a target solution, we shall construct second-order differential equations with Legendre polynomial basis to approximate the target solution. An algorithm and numerical solutions are provided. Examples show that the approximations we have found are much better than the known results obtained by means of first-order differential equations. We shall also discuss approximation using a wavelet basis. MATLAB is used to compute the numerical results. In the fourth part, we deal with variational problems in signal and image processing. For a given signal or image represented by a function, we shall provide a good approximation to the function, which minimizes a given functional.
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Karoui, Abderrazek. "Multidimensional wavelets and applications." Thesis, University of Ottawa (Canada), 1995. http://hdl.handle.net/10393/9492.
In this thesis, one- as well as multi-dimensional biorthogonal wavelet filters are designed and used for the construction of compactly supported wavelet bases. In particular, an adaptation of the McClellan transformation is used to design nonseparable 2-D biorthogonal wavelet bases. Some examples of 2-D biorthogonal wavelet filters are given in the case of the quincunx sampling lattice. Some theoretical and technical results known in the one-dimensional case have been generalized to the n-dimensional case. This generalization leads to a better understanding of the theory and design of multidimensional biorthogonal wavelets. An important part of the thesis devoted to the design of fast discrete wavelet transforms. The main ingredient of the algorithms is the use of a one-point quadrature formula for approximating the nest coefficients of the signals together with a suitable design and implementation of symmetric biorthogonal filters. Special attention is given to the case where the signals have sharp transition points. In this case, a smoothing process has been used to obtain an accurate reconstruction of the signal.
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Bowman, Christopher 1969. "Pattern formation and wavelets." Diss., The University of Arizona, 1997. http://hdl.handle.net/10150/288741.
This thesis is a collection of results associated with pattern formation, and consists of several novel results. A multi-scale analysis is carried out near the lasing bifurcation on equations which model the free carrier semiconductor laser. This analysis produces an amplitude equation which resembles the Swift-Hohenberg equation derived for the simpler two level laser, but with extra terms arising from the more complicated semiconductor system. New results are also presented in the analysis of phase equations for patterns, showing that defects are weak solutions of the phase diffusion equation, and that the Gaussian curvature of the phase surface condenses onto point and line defects. This latter fact allows for considerable simplification of the phase diffusion equation, and this analysis is presented as well. Finally, and most importantly, an algorithm is presented, based on the continuous wavelet transform, for the extraction of local phase and amplitude information from roll patterns. This algorithm allows a precise detection of phase grain boundaries and point defects, as well as the computation of soft modes like the mean flow. Several tests are conducted on numerically generated signals to demonstrate the applicability and precision of the algorithm. The algorithm is then applied to actual experimental convection patterns, and conclusions about the nature of the wave director field in such patterns are presented.
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Pelletier, Emile. "Instrument de-synthesis using wavelets." Thesis, University of Ottawa (Canada), 2005. http://hdl.handle.net/10393/27008.
Our point of departure is the concept of 'additive synthesis', which is the traditional explanation for the individual of 'timbre' or 'colour' of the sound of the various musical instruments.
When an instrument sounds a note, one hears the note as if by itself, but this is not what is physically happening. What is in fact occurring is a complex waveform featuring a collection of harmonic frequencies, referred to as the spectrum.
A synthesizer attempts to imitate the sound of a particular instrument by replicating the amplitudes of its harmonics.
We use the term 'de-synthesis' to refer to the inverse procedure, computerized instrument identification.
We describe an experiment that we designed and executed with M ATLAB to explore the hypothesis that a computer will be able to recognize an instrument by its characteristic timbre.
The idea of applying wavelets to analyze music comes naturally since music consists of sound waves, and wavelets are wave shaped functions.
We propose a mathematical model that can take certain musical instrument's attack and decay features into account that utilizes Malvar wavelets: Super Malvar wavelets. Super wavelets are superpositions of ordinary wavelets in some linear combination that can be treated as a wavelet in itself. (Abstract shortened by UMI.)
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Shen, Jianhong 1971. "Asymptotics of wavelets and filters." Thesis, Massachusetts Institute of Technology, 1998. http://hdl.handle.net/1721.1/47469.
Hunter, Karin M. "Interpolatory refinable functions, subdivision and wavelets." Thesis, Stellenbosch : University of Stellenbosch, 2005. http://hdl.handle.net/10019.1/1156.
Thesis (DSc (Mathematical Sciences))--University of Stellenbosch, 2005. Subdivision is an important iterative technique for the efficient generation of curves and
surfaces in geometric modelling. The convergence of a subdivision scheme is closely connected
to the existence of a corresponding refinable function. In turn, such a refinable
function can be used in the multi-resolutional construction method for wavelets, which
are applied in many areas of signal analysis.
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Sablik, Mathieu. "Wavelets in Abstract Hilbert Space." Thesis, Uppsala University, Department of Mathematics, 2000. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-122553.
Signals on hierarchical trees can be viewed as a generalization of discrete signals of length 2^N. In this work, we extend the classic discrete Haar wavelets to a Haar-like wavelet basis that works for signals on hierarchical trees. We first construct a specific wavelet basis and give its inverse and normalized transform matrices.
As analogue to the classic case, operators and wavelet generating functions are constructed for the tree structure. This leads to the definition of multiresolution analysis on a hierarchical tree. We prove the previously selected wavelet basis is an orthogonal multiresolution. Classification of all possible wavelet basis that generate an orthogonal multiresolution is then given. In attempt to find more efficient encoding and decoding algorithms, we construct a second wavelet basis and show that it is also an orthogonal multiresolution. The encoding and decoding algorithms are given and their time complexity are analyzed.
In order to link change of tree structure and encoded signal, we define weighted hierarchical tree, tree cut and extension. It is then shown that a simply relation can be established without the need for global change of the transform matrix. Finally, we apply thresholding to the transform and give an upper bound of error.
Potter, Merle C., Jack L. Lessing, and Edward F. Aboufadel. "Wavelets." In Advanced Engineering Mathematics, 670–98. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-17068-4_11.
Morettin, Pedro A., Aluísio Pinheiro, and Brani Vidakovic. "Wavelets." In SpringerBriefs in Mathematics, 11–35. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-59623-5_2.
Davidson, Kenneth R., and Allan P. Donsig. "Wavelets." In Undergraduate Texts in Mathematics, 406–48. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-98098-0_15.
Bonneau, Georges-Pierre. "BLaC Wavelets and Non-Nested Wavelets." In Mathematics and Visualization, 147–63. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-662-04388-2_7.
Chui, Charles K., and Qingtang Jiang. "Compactly Supported Wavelets." In Applied Mathematics, 433–98. Paris: Atlantis Press, 2013. http://dx.doi.org/10.2991/978-94-6239-009-6_9.
Cheney, Ward, and Will Light. "Wavelets, I." In Graduate Studies in Mathematics, 272–84. Providence, Rhode Island: American Mathematical Society, 2009. http://dx.doi.org/10.1090/gsm/101/34.
Cheney, Ward, and Will Light. "Wavelets II." In Graduate Studies in Mathematics, 285–311. Providence, Rhode Island: American Mathematical Society, 2009. http://dx.doi.org/10.1090/gsm/101/35.
Jensen, Arne, and Anders la Cour-Harbo. "Wavelets in Matlab." In Ripples in Mathematics, 211–32. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-56702-5_13.
Hariharan, G. "Shifted Chebyshev Wavelets and Shifted Legendre Wavelets—Preliminaries." In Forum for Interdisciplinary Mathematics, 33–50. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-32-9960-3_3.
Gershtansky, Itai, and Shai Dekel. "Active Geometric Wavelets." In Springer Proceedings in Mathematics, 95–109. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4614-0772-0_7.
Тези доповідей конференцій з теми "Wavelets (Mathematics)":
1
Sommen, F., Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Haar Wavelets is a Clifford Algebra." In Numerical Analysis and Applied Mathematics. AIP, 2007. http://dx.doi.org/10.1063/1.2790266.
Černá, Dana, and Václav Finěk. "Optimized Construction of Biorthogonal Spline‐Wavelets." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2990873.
Traversoni, Leonardo, Yi Xu, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Velocity and Object Detection Using Quaternion Wavelets." In Numerical Analysis and Applied Mathematics. AIP, 2007. http://dx.doi.org/10.1063/1.2790268.
Bernstein, Swanhild, Svend Ebert, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Spherical Wavelets, Kernels and Symmetries." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2009: Volume 1 and Volume 2. AIP, 2009. http://dx.doi.org/10.1063/1.3241585.
Majak, Jüri, Martin Eerme, Anti Haavajõe, Ramachandran Karunanidhi, Dieter Scholz, and Anti Lepik. "Function approximation using Haar wavelets." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2019. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0026543.
Singh, Ram Chandra, and Rajeev Bhatla. "Wavelets in meteorology." In EMERGING APPLICATIONS OF WAVELET METHODS: 7th International Congress on Industrial and Applied Mathematics - Thematic Minisymposia. AIP, 2012. http://dx.doi.org/10.1063/1.4740045.
Bahri, Syamsul, Lailia Awalushaumi, and Marliadi Susanto. "The Approximation of Nonlinear Function using Daubechies and Symlets Wavelets." In International Conference on Mathematics and Islam. SCITEPRESS - Science and Technology Publications, 2018. http://dx.doi.org/10.5220/0008521103000306.
Zahra, Noor e., Hulya Kodal Sevindir, Zafer Aslan, and A. H. Siddiqi. "Wavelets in medical imaging." In EMERGING APPLICATIONS OF WAVELET METHODS: 7th International Congress on
Industrial and Applied Mathematics - Thematic Minisymposia. American Institute of Physics, 2012. http://dx.doi.org/10.1063/1.4740036.
Siddiqi, A. H. "Wavelets in oil industry." In EMERGING APPLICATIONS OF WAVELET METHODS: 7th International Congress on Industrial and Applied Mathematics - Thematic Minisymposia. AIP, 2012. http://dx.doi.org/10.1063/1.4740041.
Černá, Dana, Václav Finěk, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Construction of Orthonormal Wavelets Using Symbolic Algebraic Methods." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2009: Volume 1 and Volume 2. AIP, 2009. http://dx.doi.org/10.1063/1.3241329.
