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Journal articles on the topic 'Wavelets'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

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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2

SHUKLA, NIRAJ K. "NON-MSF A-WAVELETS FROM A-WAVELET SETS." International Journal of Wavelets, Multiresolution and Information Processing 11, no. 01 (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

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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, № 06 (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 exist

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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 Gegenb

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5

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 (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 pro

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6

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 (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 co

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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 (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 t

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8

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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9

Knapp, Ralph W. "Energy distribution in wavelets and implications on resolving power." GEOPHYSICS 58, no. 1 (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

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10

E, Sasikala Reddy, and V. V. Satyanarayana Tallapragada. "Design and Implementation of New Biorthogonal Wavelets and its Application to Image Processing." International Journal of Emerging Research in Engineering, Science, and Management 1, no. 1 (2022): 05–10. https://doi.org/10.58482/ijeresm.v1i1.2.

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Wavelet transformation has been an interesting field since its exposure with wavelet-based compression standard embedded zerotree wavelet. Though, the origin of wavelets back to many decades, the presence of research at the very beginning of wavelet bases is also being carried out in the research community. This is because of the wide presence of its applicability as well as its structure of adapting to the type of problem at hand. In this paper, an approach of designing biorthogonal wavelets is presented. This approach may be extended to design variety of wavelets. This paper mainly focus on

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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 (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

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Zhang, Xi, and Noriaki Fukuda. "Lossy to lossless image coding based on wavelets using a complex allpass filter." International Journal of Wavelets, Multiresolution and Information Processing 12, no. 04 (2014): 1460002. http://dx.doi.org/10.1142/s0219691314600029.

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Wavelet-based image coding has been adopted in the international standard JPEG 2000 for its efficiency. It is well-known that the orthogonality and symmetry of wavelets are two important properties for many applications of signal processing and image processing. Both can be simultaneously realized by the wavelet filter banks composed of a complex allpass filter, thus, it is expected to get a better coding performance than the conventional biorthogonal wavelets. This paper proposes an effective implementation of orthonormal symmetric wavelet filter banks composed of a complex allpass filter for

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Gao, Li, Tao Zhao, and Yun Peng Liu. "Suppressing PD’s Narrow Band Noise in the PD Monitoring Frequency Band Using Complex Wavelet Packet Transform." Applied Mechanics and Materials 521 (February 2014): 352–57. http://dx.doi.org/10.4028/www.scientific.net/amm.521.352.

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By combining the method of construct wavelet packet and complex wavelets, complex wavelets packet is constructed with the same amplitude-frequency characteristics of corresponding real wavelet packet and the same phase spectrum of corresponding complex wavelets, and then give the specific method of constructing complex wavelets packet, evaluate the effect of original PD simulative signals direct reconstruction after decomposition by using Normalized Correlation Coefficient (NCC) and Variational Trend Parameter (VTP) also and the relative error of the amplitude, verify the capability of restore

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14

Sahu, PK, and S. Saha Ray. "Comparison on wavelets techniques for solving fractional optimal control problems." Journal of Vibration and Control 24, no. 6 (2016): 1185–201. http://dx.doi.org/10.1177/1077546316659611.

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This paper presents efficient numerical techniques for solving fractional optimal control problems (FOCP) based on orthonormal wavelets. These wavelets are like Legendre wavelets, Chebyshev wavelets, Laguerre wavelets and Cosine And Sine (CAS) wavelets. The formulation of FOCP and properties of these wavelets are presented. The fractional derivative considered in this problem is in the Caputo sense. The performance index of FOCP has been considered as function of both state and control variables and the dynamic constraints are expressed by fractional differential equation. These wavelet method

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15

Low, Yin Fen, and Rosli Besar. "Optimal Wavelet Filters for Medical Image Compression." International Journal of Wavelets, Multiresolution and Information Processing 01, no. 02 (2003): 179–97. http://dx.doi.org/10.1142/s0219691303000128.

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Recently, the wavelet transform has emerged as a cutting edge technology, within the field of image compression research. The basis functions of the wavelet transform are known as wavelets. There are a variety of different wavelet functions to suit the needs of different applications. Among the most popular wavelets are Haar, Daubechies, Coiflet and Biorthogonal, etc. The best wavelets (functions) for medical image compression are widely unknown. The purpose of this paper is to examine and compare the difference in impact and quality of a set of wavelet functions (wavelets) to image quality fo

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Hadas-Dyduch, Monika. "Efficiency of Authored Mixed Prediction Model with Application to the Labor Market." Engineering Management Research 7, no. 1 (2018): 46. http://dx.doi.org/10.5539/emr.v7n1p46.

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The aim of this article is to evaluate the prediction of time series using a model containing wavelets. The research hypothesis is: “Models that take into account wavelets are an effective tool for predicting employment”. To verify the hypothesis, an original model was devised. The model is based on wavelet analysis with Daubechies wavelets and an exponential alignment model. The exponential alignment model been appropriately modified by the introduction of wavelet functions. The results obtained show that a model that partially includes wavelets is an effective tool in the prediction and anal

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Bayjja, M., G. Alsharahi, M. Aghoutane, and N. A. Touhami. "Comparison of Wavelet Packet and Wavelet in Solving Arbitrary Array of Parallel Wires Integral Equations in Electromagnetics." Advanced Electromagnetics 9, no. 3 (2020): 8–14. http://dx.doi.org/10.7716/aem.v9i3.1487.

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In this paper, wavelets transformation (WT) and wavelet packet transformation (WPT) are used in solving, by the method of moments, a semicircular array of parallel wires electric field integral equation. First, the integral equation is solved by applying the direct method of moments via point-matching procedure, results in a linear system with a dense matrix. Therefore, wavelet transformation and wavelet packet transformation are used to sparsify the impedance matrix, using two categories of wavelets functions, Biorthogonal (bior2.2) and Orthogonal (db4) wavelets. The far-field scattering patt

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Zhang, Fanchang, and Nanying Lan. "Seismic-gather wavelet-stretching correction based on multiwavelet decomposition algorithm." GEOPHYSICS 85, no. 5 (2020): V377—V384. http://dx.doi.org/10.1190/geo2018-0835.1.

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Normal moveout correction is crucial in seismic data processing, but it generates a wavelet-stretching effect, especially on the larger offset or incident-angle seismic data. Wavelet stretching reduces the dominant frequency of seismic data. The greater the incident angle or offset, the lower dominant the frequency becomes. This is an unfavorable effect to amplitude variation with offset analysis. Therefore, we have introduced a wavelet stretching correction method based on the multiwavelet decomposition (MWD) algorithm. First, it decomposes the near-offset pilot trace and all the far-offset s

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19

Song, Yu Yang, Rong Li, Ming Yan Li, and Wen Hui Zhang. "Relationship between Scale and Period and its Ecological Applications in Wavelet Analysis." Advanced Materials Research 726-731 (August 2013): 4252–57. http://dx.doi.org/10.4028/www.scientific.net/amr.726-731.4252.

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The relations between the scales and periods of Mexican Hat (Mexh) and Morlet (Morl) wavelets have been deduced. Based on these relations, variances, coefficients, and power spectra of these two wavelets’ original and eco-used wavelets are compared and analyzed theoretically and experimentally for the distribution pattern of Haloxylon ammodendron Bunge population in Gurban Tonggut desert, China. The research shows that: (1) Mexh and Morl eco-used wavelets can be simultaneously used to describe the distribution period of Haloxylon population and to study the same phenomenon by combining these t

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Olphert, Sean, and Stephen C. Power. "Higher Rank Wavelets." Canadian Journal of Mathematics 63, no. 3 (2011): 689–720. http://dx.doi.org/10.4153/cjm-2011-012-1.

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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 a

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Iwaszkiewicz, J., and A. Muc. "Five-phase Inverter Control Based on the Haar Wavelet Transform." Renewable Energies, Environment and Power Quality Journal 2 (July 2024): 193–201. http://dx.doi.org/10.24084/reepqj24.380.

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The paper presents a novel five-phase cascade inverter control method based on the Haar wavelets transform. The inverter is built from two or three two level inverters in every phase. The instantaneous value of the output voltage of the cascaded inverter is composed as a synthesis of the selected Haar wavelets. An analytical system of determining the best possible set of Haar orthogonal wavelets is presented. On the basis of the applied Haar wavelets, the control signals of the inverter switches are calculated. The cascaded five-phase inverter with a star connected resistive-inductive load was

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Zhang, Ming, Zhuo Ma, and Min Xuan Zhang. "FPGA Implementation of Rational Symmetric Biorthogonal 11-9 Wavelet Transform." Applied Mechanics and Materials 182-183 (June 2012): 1791–95. http://dx.doi.org/10.4028/www.scientific.net/amm.182-183.1791.

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Coefficients of most existing wavelets are irrational, and it costs much hardware resources when implementing on FPGA, which is inefficient especially in embedded system. Some rational wavelets can overcome this deficiency by elaborate design. Motivated by previous works on rational wavelets, we establish a hardware structure for rational 1-D symmetric biorthogonal 11-9 wavelet and implement it on Xilinx FPGA XC3S500E. The experiment reveals that the area in slices of rational 1-D 11-9 wavelet is less than 1/2 of the pipelined 9-7 wavelet when implementing on FPGA.

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Ye, Jun-Fu, Jaan-Rong Tsay, and Dieter Fritsch. "Wavelets for Self-Calibration of Aerial Metric Camera Systems." Photogrammetric Engineering & Remote Sensing 90, no. 9 (2024): 575–87. http://dx.doi.org/10.14358/pers.24-00002r2.

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In this paper, wavelets are applied to develop new models for the self-calibration of aerial metric camera systems. It is well known and mathematically proven that additional parameters (APs) can compensate image distortions and remaining error sources by a rigorous photogrammetric bundle-block adjustment. Thus, kernel functions based on orthogonal wavelets (e. g., asymmetric Daubechies wave- lets, least asymmetric Daubechies wavelets, Battle-Lemarié wavelets, Meyer wavelets) are used to build the wavelets-based family of APs for self-calibrating digital frame cameras. These new APs are called

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Naik, Ameya K., and Raghunath S. Holambe. "A unified framework for the design of low-complexity wavelet filters." International Journal of Wavelets, Multiresolution and Information Processing 15, no. 06 (2017): 1750054. http://dx.doi.org/10.1142/s0219691317500540.

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An outline is presented for construction of wavelet filters with compact support. Our approach does not require any extensive simulations for obtaining the values of design variables like other methods. A unified framework is proposed for designing halfband polynomials with varying vanishing moments. Optimum filter pairs can then be generated by factorization of the halfband polynomial. Although these optimum wavelets have characteristics close to that of CDF 9/7 (Cohen-Daubechies-Feauveau), a compact support may not be guaranteed. Subsequently, we show that by proper choice of design paramete

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Gulai, A. V., and V. M. Zaitsev. "INTELLIGENT TECHNOLOGY OF WAVELET ANALYSIS OF VIBRATION SIGNALS." Doklady BGUIR, no. 7-8 (December 29, 2019): 101–8. http://dx.doi.org/10.35596/1729-7648-2019-126-8-101-108.

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During solution of engineering problems of machinery dynamics a need of revealing the harmonic components often arises in the narrow timing gate. This requires the use of wavelet-transformation oscillation methods and introduction of intelligent systems to hardware and software used in the experiment. The wavelet is considered as a short in time signal functional window, which has its internal structure in the form of a fading wavelike burst, and it is characterized by a scale of display of certain events in the field of the signal frequency spectrum, as well as and by time axis shifts. Comple

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Cattani, Carlo. "Shannon Wavelets Theory." Mathematical Problems in Engineering 2008 (2008): 1–24. http://dx.doi.org/10.1155/2008/164808.

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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 hypergeom

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VYAS, APARNA, and RAJESHWARI DUBEY. "NON-MSF WAVELETS FROM SIX INTERVAL MSF WAVELETS." International Journal of Wavelets, Multiresolution and Information Processing 09, no. 03 (2011): 375–85. http://dx.doi.org/10.1142/s021969131100416x.

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In this article, we obtain two classes of non-MSF wavelets by considering two different classes of six-interval wavelet sets provided by Arcozzi, Behera and Madan (J. Geom. Anal.13 (2003) 557–579). Out of these classes one is countable, the non-MSF wavelets of which are non-MRA and the other one is uncountable, the non-MSF wavelets of which are MRA. The set of all non-MSF MRA wavelets of the latter class is shown to be pathconnected.

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Gao, Jing Li, and Shi Hui Cheng. "The Traits of Canonical Banach Frames Generated by Multiple Scaling Functions and Applications in Applied Materials." Advanced Materials Research 684 (April 2013): 663–66. http://dx.doi.org/10.4028/www.scientific.net/amr.684.663.

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Frame theory has become a popular subject in scientific research during the past twenty years. In our study we use generalized multiresolution analyses in with dilation factor 4. We describe, in terms of the underlying multiresolution structure, all generalized multiresolution analyses Parseval frame wavelets all semi-orthogonal Parseval frame wavelets in . We show that there exist wavelet frame generated by two functions which have good dual wavelet frames, but for which the canonical dual wavelet frame does not consist of wavelets, according to scaling functions. That is to say, the canonica

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Abuhamdia, Tariq, Saied Taheri, and John Burns. "Laplace wavelet transform theory and applications." Journal of Vibration and Control 24, no. 9 (2017): 1600–1620. http://dx.doi.org/10.1177/1077546317707103.

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This study introduces the theory of the Laplace wavelet transform (LWT). The Laplace wavelets are a generalization of the second-order under damped linear time-invariant (SOULTI) wavelets to the complex domain. This generalization produces the mother wavelet function that has been used as the Laplace pseudo wavelet or the Laplace wavelet dictionary. The study shows that the Laplace wavelet can be used to transform signals to the time-scale or time-frequency domain and can be retrieved back. The properties of the new generalization are outlined, and the characteristics of the companion wavelet

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Ahmadi, H., G. Dumont, F. Sassani, and R. Tafreshi. "Performance of Informative Wavelets for Classification and Diagnosis of Machine Faults." International Journal of Wavelets, Multiresolution and Information Processing 01, no. 03 (2003): 275–89. http://dx.doi.org/10.1142/s0219691303000189.

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This paper deals with an application of wavelets for feature extraction and classification of machine faults in a real-world machine data analysis environment. We have utilized informative wavelet algorithm to generate wavelets and subsequent coefficients that are used as feature variables for classification and diagnosis of machine faults. Informative wavelets are classes of functions generated from a given analyzing wavelet in a wavelet packet decomposition structure in which for the selection of best wavelets, concepts from information theory, i.e. mutual information and entropy are utilize

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Ahmad, Owais. "Characterization of tight wavelet frames with composite dilations in L2(Rn)." Publications de l'Institut Math?matique (Belgrade) 113, no. 127 (2023): 121–29. http://dx.doi.org/10.2298/pim2327121a.

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Tight wavelet frames are different from the orthonormal wavelets because of redundancy. By sacrificing orthonormality and allowing redundancy, the tight wavelet frames become much easier to construct than the orthonormal wavelets. Guo, Labate, Lim, Weiss, and Wilson [Electron. Res. Announc. Am. Math. Soc. 10 (2004), 78-87] introduced the theory of wavelets with composite dilations in order to provide a framework for the construction of waveforms defined not only at various scales and locations but also at various orientations. In this paper, we provide the characterization of composite wavelet

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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 (2010): 931–40. http://dx.doi.org/10.1142/s0219691310003900.

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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 sp

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Zhang, Xinming, Jiaqi Liu, and Ke'an Liu. "A Wavelet Galerkin Finite-Element Method for the Biot Wave Equation in the Fluid-Saturated Porous Medium." Mathematical Problems in Engineering 2009 (2009): 1–18. http://dx.doi.org/10.1155/2009/142384.

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A wavelet Galerkin finite-element method is proposed by combining the wavelet analysis with traditional finite-element method to analyze wave propagation phenomena in fluid-saturated porous medium. The scaling functions of Daubechies wavelets are considered as the interpolation basis functions to replace the polynomial functions, and then the wavelet element is constructed. In order to overcome the integral difficulty for lacking of the explicit expression for the Daubechies wavelets, a kind of characteristic function is introduced. The recursive expression of calculating the function values o

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Zhao, Jian Tang, and Hong Lin Guo. "Constructive Approaches to Biorthogonal Finitely Supported Ternary Wavelets and Wavelet Wraps." Advanced Materials Research 219-220 (March 2011): 504–7. http://dx.doi.org/10.4028/www.scientific.net/amr.219-220.504.

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In this paper, the notion of biorthogonal two-directional shortly supported wavelets with poly-scale is developed. A new method for designing two-directional biorthogonal wavelets is proposed. The existence of shortly supported biorthogonal vector-valued wavelets associated with a pair of biorthogonal compactly supported vector-valued scaling functions is investigated. A novel constructive method for designing a sort of biorthogonal vector-valued wavelet wraps is presented and their biorthogonality traits are characerized. Two biorthogonality formulas regarding these wavelet wraps are establis

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Apolonio, Felipe A., Daniel H. T. Franco, and Fábio N. Fagundes. "A Note on Directional Wavelet Transform: Distributional Boundary Values and Analytic Wavefront Sets." International Journal of Mathematics and Mathematical Sciences 2012 (2012): 1–11. http://dx.doi.org/10.1155/2012/758694.

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By using a particular class of directional wavelets (namely, the conical wavelets, which are wavelets strictly supported in a proper convex cone in thek-space of frequencies), in this paper, it is shown that a tempered distribution is obtained as a finite sum of boundary values of analytic functions arising from the complexification of the translational parameter of the wavelet transform. Moreover, we show that for a given distributionf∈𝒮′(ℝn), the continuous wavelet transform offwith respect to a conical wavelet is defined in such a way that the directional wavelet transform offyields a funct

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Cattani, Carlo, and Aleksey Kudreyko. "Application of Periodized Harmonic Wavelets towards Solution of Eigenvalue Problems for Integral Equations." Mathematical Problems in Engineering 2010 (2010): 1–8. http://dx.doi.org/10.1155/2010/570136.

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This article deals with the application of the periodized harmonic wavelets for solution of integral equations and eigenvalue problems. The solution is searched as a series of products of wavelet coefficients and wavelets. The absolute error for a general case of the wavelet approximation was analytically estimated.

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K, Subramanyam, and Ramasri T. "Design of Biorthogonal Wavelets based on Spline and Spline-like Functions for Image Compression." International Journal of Emerging Research in Engineering, Science, and Management 1, no. 1 (2022): 11–17. https://doi.org/10.58482/ijeresm.v1i1.3.

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Wavelet theory inspired from Fourier analysis is based on the basis function and its properties. Different wavelets use different basis functions which may better suit to some applications. The properties of basis functions along with their shape and magnification effects the performance of an application. The standard biorthogonal wavelets utilize spline functions for their construction. In this paper first the design procedure of biorthogonal wavelets is presented. Then a modified spline function is proposed. Based on the proposed spline function, three biorthogonal wavelets are designed wit

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Jurado, F., and S. Lopez. "A wavelet neural control scheme for a quadrotor unmanned aerial vehicle." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2126 (2018): 20170248. http://dx.doi.org/10.1098/rsta.2017.0248.

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Wavelets are designed to have compact support in both time and frequency, giving them the ability to represent a signal in the two-dimensional time–frequency plane. The Gaussian, the Mexican hat and the Morlet wavelets are crude wavelets that can be used only in continuous decomposition. The Morlet wavelet is complex-valued and suitable for feature extraction using the continuous wavelet transform. Continuous wavelets are favoured when high temporal and spectral resolution is required at all scales. In this paper, considering the properties from the Morlet wavelet and based on the structure of

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T.N., Vasanthakumari. "REVIEW PAPER ON WAVELET TRANSFORMATIONS." Shanlax International Journal of Arts, Science and Humanities 6, S2 (2019): 62–69. https://doi.org/10.5281/zenodo.2573681.

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<em>Wavelets are mathematical tool that modify the data into different frequency components, and then study each component with a resolution matched to its scale. They have major advantages over traditional Fourier methods in analysing physical situations where the signal contains discontinuities and sharp spikes like Noises. Wavelets were developed independently in the fields of mathematics, quantum physics, electrical engineering, and seismic geology. Interchanges between these fields during the last decades have led to many new wavelet applications such as image compression, turbulence, hum

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Fu, Shengyu, B. Muralikrishnan, and J. Raja. "Engineering Surface Analysis With Different Wavelet Bases." Journal of Manufacturing Science and Engineering 125, no. 4 (2003): 844–52. http://dx.doi.org/10.1115/1.1616947.

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Traditional surface texture analysis involves filtering surface profiles into different wavelength bands commonly referred to as roughness, waviness and form. The primary motivation in filtering surface profiles is to map each band to the manufacturing process that generated the part and the intended functional performance of the component. Current trends in manufacturing are towards tighter tolerances and higher performance standards that require close monitoring of the process. Thus, there is a need for finer bandwidths for process mapping and functional correlation. Wavelets are becoming in

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Serdenko, Taisiia, and Kateryna Liashko. "Signal coding based on wavelet analysis." Modeling and Information Systems in Economics, no. 103 (December 5, 2023): 188–96. https://doi.org/10.33111/mise.103.16.

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The article focuses on the analysis of the application of wavelet transforms in signal and image encoding. Wavelets are defined as a powerful tool in numerous technical and scientific disciplines, capable of effectively highlighting and processing signal characteristics at various levels of resolution. The article emphasizes the significance of wavelets in the encryption of images and signals, particularly regarding optimization of the encryption time and providing protection against various attacks. In today’s world, digital communication and data processing are gaining incredible importance,

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Ashurov, Ravshan. "On the almost-everywhere convergence of the continuous wavelet transforms." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 142, no. 6 (2012): 1121–29. http://dx.doi.org/10.1017/s030821051000123x.

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Almost-everywhere convergence of wavelet transforms of Lp-functions under minimal conditions on wavelets was proved by Rao et al. in 1994. However, results on convergence almost everywhere do not provide any information regarding the exceptional set (of Lebesgue measure zero), where convergence does not hold. We prove that if a wavelet ψ satisfies a single additional condition xψ(x) ∈ L1 (R), then, instead of almost-everywhere convergence, we have a more sophisticated result, i.e. convergence of wavelet transforms everywhere on the entire Lebesgue set of Lp-functions. For example, wavelets wit

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Phinyomark, Angkoon, Chusak Limsakul, and Pornchai Phukpattaranont. "Optimal Wavelet Functions in Wavelet Denoising for Multifunction Myoelectric Control." ECTI Transactions on Electrical Engineering, Electronics, and Communications 8, no. 1 (2009): 43–52. http://dx.doi.org/10.37936/ecti-eec.201081.172001.

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Wavelet analysis is one of the most important methods for analyzing the surface Electromyography (sEMG) signal. The aim of this study was to investigate the wavelet function that is optimum to identify and denoise the sEMG signal for multifunction myoelectric control. This study is motivated by the fact that there is no universal mother wavelet that is suitable for all types of signal. The right wavelet function becomes to achieve the optimal performance. In this study, the optimal wavelets are evaluated in term of mean square error of two criterions, namely denoising and reconstruction. Fifty

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Kumar, Susheel, Gaurav Kumar Mishra, Sudhir Kumar Mishra, and Shyam Lal. "PSEUDO CHEBYSHEV WAVELETS IN TWO DIMENSIONS AND THEIR APPLICATIONS IN THE THEORY OF APPROXIMATION OF FUNCTIONS BELONGING TO LIPSCHITZ CLASS." South East Asian Journal of Mathematics and Mathematical Sciences 20, no. 02 (2024): 247–68. https://doi.org/10.56827/seajmms.2024.2002.19.

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In 2022, the concept of one-dimensional pseudo Chebyshev wavelets was introduced by the authors. Building upon this research, the present article extends the study to two-dimensional pseudo Chebyshev wavelets. It defines and verifies the two-dimensional pseudo Chebyshev wavelet expansion for a functions of two variables. The paper proposes a novel algorithm utilizing the two-dimensional pseudo Chebyshev wavelet method to address computation problems in approximation theory. To demonstrate the validity and applicability of the results, the methods are illustrated through an example and compared

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Mittal, R. C., and Sapna Pandit. "Quasilinearized Scale-3 Haar wavelets-based algorithm for numerical simulation of fractional dynamical systems." Engineering Computations 35, no. 5 (2018): 1907–31. http://dx.doi.org/10.1108/ec-09-2017-0347.

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Purpose The main purpose of this work is to develop a novel algorithm based on Scale-3 Haar wavelets (S-3 HW) and quasilinearization for numerical simulation of dynamical system of ordinary differential equations. Design/methodology/approach The first step in the development of the algorithm is quasilinearization process to linearize the problem, and then Scale-3 Haar wavelets are used for space discretization. Finally, the obtained system is solved by Gauss elimination method. Findings Some numerical examples of fractional dynamical system are considered to check the accuracy of the algorithm

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Singh, Ashok Kumar, and Hemant Bhate. "Stochastic wavelets from minimizers of an uncertainty principle: An example." International Journal of Wavelets, Multiresolution and Information Processing 18, no. 06 (2020): 2050046. http://dx.doi.org/10.1142/s0219691320500460.

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This paper proposes a method through which a family of wavelets can be obtained. This is done by choosing each member based on a random variable. The method is preferred in situations where a single mother wavelet proves inadequate and an evolving sequence of mother wavelets is needed but a priori the next member in the sequence is uncertain. The adopted approach is distinct from the way spatiotemporal wavelets are used or even the way stochastic processes have been studied using spatiotemporal wavelets.

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HUANG, YONGDONG, and ZHENGXING CHENG. "PARAMETRIZATION OF COMPACTLY SUPPORTED TRIVARIATE ORTHOGONAL WAVELET FILTER." International Journal of Wavelets, Multiresolution and Information Processing 05, no. 04 (2007): 627–39. http://dx.doi.org/10.1142/s0219691307001938.

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Multivariate wavelets analysis is a powerful tool for multi-dimensional signal processing, but tensor product wavelets have a number of drawbacks. In this paper, we give an algorithm of parametric representation compactly supported trivariate orthogonal wavelet filter, which simplifies the study of trivariate orthogonal wavelet. Four examples are also given to demonstrate the method.

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Rakowski, Waldemar. "Application of Cubic Box Spline Wavelets in the Analysis of Signal Singularities." International Journal of Applied Mathematics and Computer Science 25, no. 4 (2015): 927–41. http://dx.doi.org/10.1515/amcs-2015-0066.

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Abstract In the subject literature, wavelets such as the Mexican hat (the second derivative of a Gaussian) or the quadratic box spline are commonly used for the task of singularity detection. The disadvantage of the Mexican hat, however, is its unlimited support; the disadvantage of the quadratic box spline is a phase shift introduced by the wavelet, making it difficult to locate singular points. The paper deals with the construction and properties of wavelets in the form of cubic box splines which have compact and short support and which do not introduce a phase shift. The digital filters ass

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GRIVET-TALOCIA, STEFANO, and ANITA TABACCO. "WAVELETS ON THE INTERVAL WITH OPTIMAL LOCALIZATION." Mathematical Models and Methods in Applied Sciences 10, no. 03 (2000): 441–62. http://dx.doi.org/10.1142/s0218202500000252.

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This paper introduces a novel construction of wavelets on the unit interval. With this construction, explicit upper bounds for the length of the modified border wavelets filters can be given. This insures a good localization of the border wavelets when a triangular biorthogonalization scheme is employed. The resulting wavelet bases are then well-suited for the adaptive solution of partial differential equations.

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ZENG, LI, RUI MA, JIANYUAN HUANG, and P. R. HUNZIKER. "THE CONSTRUCTION OF 2D ROTATIONALLY INVARIANT WAVELETS AND THEIR APPLICATION IN IMAGE EDGE DETECTION." International Journal of Wavelets, Multiresolution and Information Processing 06, no. 01 (2008): 65–82. http://dx.doi.org/10.1142/s0219691308002227.

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Construction of rotationally invariant 2D wavelets is important in image processing, but is difficult. In this paper, the discrete form of a 2D rotationally invariant wavelet is constructed by back-projection from a 1D symmetrical wavelet. Such rotationally invariant 2D wavelets allow effective edge detection in any direction. These wavelets are combined with the 2D directional wavelets for the use in non-maximum suppression edge detection. The resulting binary edges are characterized by finer contours, differential detection characteristics and noise robustness compared to other edge detector

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