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Academic literature on the topic 'Wavelet'

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Published: 4 June 2021
Last updated: 7 July 2024

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Journal articles on the topic "Wavelet"

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de Macedo, Isadora A. S., and José Jadsom S. de Figueiredo. "On the seismic wavelet estimative and reflectivity recovering based on linear inversion: Well-to-seismic tie on a real data set from Viking Graben, North Sea." GEOPHYSICS 85, no. 5 (September 1, 2020): D157—D165. http://dx.doi.org/10.1190/geo2019-0183.1.

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Tying seismic data to well data is critical in reservoir characterization. In general, the main factors controlling a successful seismic well tie are an accurate time-depth relationship and a coherent wavelet estimate. Wavelet estimation methods are divided into two major groups: statistical and deterministic. Deterministic methods are based on using the seismic trace and the well data to estimate the wavelet. Statistical methods use only the seismic trace and generally require assumptions about the wavelet’s phase or a random process reflectivity series. We have compared the estimation of the wavelet for seismic well tie purposes through least-squares minimization and zero-order quadratic regularization with the results obtained from homomorphic deconvolution. Both methods make no assumption regarding the wavelet’s phase or the reflectivity. The best-estimated wavelet is used as the input to sparse-spike deconvolution to recover the reflectivity near the well location. The results show that the wavelets estimated from both deconvolutions are similar, which builds our confidence in their accuracy. The reflectivity of the seismic section is recovered according to known stratigraphic markers (from gamma-ray logs) present in the real data set from the Viking Graben field, Norway.
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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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Abuhamdia, Tariq, Saied Taheri, and John Burns. "Laplace wavelet transform theory and applications." Journal of Vibration and Control 24, no. 9 (May 11, 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 transform are defined. Moreover, some similarities between the Laplace wavelet transform and the Laplace transform arise, where a relation between the Laplace wavelet transform and the Laplace transform is derived. This relation can be beneficial in evaluating the wavelet transform. The new wavelet transform has phase and magnitude, and can also be evaluated for most elementary signals. The Laplace wavelets inherit many properties from the SOULTI wavelets, and the Laplace wavelet transform inherits many properties from both the SOULTI wavelet transform and the Laplace transform. In addition, the investigation shows that both the LWT and the SOULTI wavelet transform give the particular solutions of specific related differential equations, and the particular solution of these linear time-invariant differential equations can in general be written in terms of a wavelet transform. Finally, the properties of the Laplace wavelet are verified by applications to frequency varying signals and to vibrations of mechanical systems for modes decoupling, and the results are compared with the generalized Morse and Morlet wavelets in addition to the short time Fourier transform’s results.
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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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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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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 (August 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-three wavelet functions are used to perform an iterative denoising and reconstruction on different noise levels that are added in sEMG signals. In addition, various possible decomposition levels and types of wavelets in the denoising procedure are tested. The results show that the best mother wavelets for tolerance of noise in denoising are the first order of Daubechies, BioSplines, and ReverseBior but the classification results are not recommended. The fifth order of Coiflet is the best wavelet in perfect reconstruction point of view. Various families can be used except the third order of BiorSplines and Discrete Meyer are not recommended to use. Suitable number of decomposition levels is four and optimal wavelets are independent of wavelet denoising algorithms.
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TODA, HIROSHI, ZHONG ZHANG, and TAKASHI IMAMURA. "PERFECT-TRANSLATION-INVARIANT CUSTOMIZABLE COMPLEX DISCRETE WAVELET TRANSFORM." International Journal of Wavelets, Multiresolution and Information Processing 11, no. 04 (July 2013): 1360003. http://dx.doi.org/10.1142/s0219691313600035.

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The theorems, giving the condition of perfect translation invariance for discrete wavelet transforms, have already been proven. Based on these theorems, the dual-tree complex discrete wavelet transform, the 2-dimensional discrete wavelet transform, the complex wavelet packet transform, the variable-density complex discrete wavelet transform and the real-valued discrete wavelet transform, having perfect translation invariance, were proposed. However, their customizability of wavelets in the frequency domain is limited. In this paper, also based on these theorems, a new type of complex discrete wavelet transform is proposed, which achieves perfect translation invariance with high degree of customizability of wavelets in the frequency domain.
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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. Complex-functioned continuous functions of real arguments (Daubechies wavelets, Gaussian wavelets, MHat-wavelets), complex-valued functions of real arguments (Morlet and Paul wavelets), as well as real discrete functions (HААRT- and FHat-wavelets) are used as wavelet functions. The wavelet analysis method of vibration signals is disclosed at acoustic diagnostics of machines and mechanisms. Digital implementation of discrete indications of wavelets with the subsequent visualization of results in the form of scalotons is the mathematical basis of the algorithm for procession of vibration signals. It has been suggested that engineering analysis and reconstruction of signals should be implemented by means of directed and reverse continuous wavelet conversions, which are discrete by arguments. The structural and functional scheme of the multichannel system of the intelligent wavelet analysis of vibration signals in machines has been considered. The intelligent system for study of vibration signals makes it possible to form the totality of photographic parameters, when scalotons are calculated by wavelet functions. An example of experimental implementation of the wavelet conversion method of vibration signals parameters is shown. Results of scalotons calculation are shown, when MHat-wavelet and DOG-wavelet are used.
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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 canonical dual wavelet frame cannot be generated by the translations and dilations of a single function. Traits of tight wavelet frames are presented.
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Dissertations / Theses on the topic "Wavelet"

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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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Varanis, Marcus Vinicius Monteiro [UNESP]. "Análise de vibrações em sistemas discretos de massas concentradas e com dois graus de liberdade através da transformada wavelet." Universidade Estadual Paulista (UNESP), 2008. http://hdl.handle.net/11449/91946.

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Made available in DSpace on 2014-06-11T19:25:32Z (GMT). No. of bitstreams: 0 Previous issue date: 2008-07-10Bitstream added on 2014-06-13T19:53:23Z : No. of bitstreams: 1 varanis_mvm_me_rcla.pdf: 4826016 bytes, checksum: ab2c8b052e0a038577280ce930b14260 (MD5)
O estudo de vibrações diz respeito aos movimentos oscilatórios de corpos e às forças que lhes são associadas. Todos os corpos dotados de massa e elasticidade são capazes de vibrar. Deste modo, a maior parte das máquinas e estruturas estão sujeitas a certos graus de vibração A maioria das atividades humanas envolve alguma forma de vibração. O estudo do comportamento dinâmico dessas oscilações mecânicas é o objetivo deste trabalho e para isto propomos um sistema de massas concentradas e com dois graus de liberdade. O sistema será excitado por forças externas, entre elas ondas de terremoto. Com simulações numéricas estudamos o sistema, usando a transformada rápida de Fourier, transformada wavelet.
The study of vibration concerns oscillatory movement of bodies and the forces they are associated. All bodies that have mass and elasticity are able to vibrate. Thus, most of the machines and structures are subject to certain degrees of vibration most human activities involve some form of vibration. The study of the dynamic behavior of these mechanical oscillations is the objective of this work and to propose that a system of weights and concentrated with two degrees of freedom. The system will be excited by external forces, including waves of earthquake. With numerical simulations studied the system, using the fast Fourier transform, wavelet transform.
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Shi, Fangmin. "Wavelet transforms for stereo imaging." Thesis, University of South Wales, 2002. https://pure.southwales.ac.uk/en/studentthesis/wavelet-transforms-for-stereo-imaging(65abb68f-e30b-4367-a3a8-b7b3df85f566).html.

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Stereo vision is a means of obtaining three-dimensional information by considering the same scene from two different positions. Stereo correspondence has long been and will continue to be the active research topic in computer vision. The requirement of dense disparity map output is great demand motivated by modern applications of stereo such as three-dimensional high-resolution object reconstruction and view synthesis, which require disparity estimates in all image regions. Stereo correspondence algorithms usually require significant computation. The challenges are computational economy, accuracy and robustness. While a large number of algorithms for stereo matching have been developed, there still leaves the space for improvement especially when a new mathematical tool such as wavelet analysis becomes mature. The aim of the thesis is to investigate the stereo matching approach using wavelet transform with a view to producing efficient and dense disparity map outputs. After the shift invariance property of various wavelet transforms is identified, the main contributions of the thesis are made in developing and evaluating two wavelet approaches (the dyadic wavelet transform and complex wavelet transform) for solving the standard correspondence problem. This comprises an analysis of the applicability of dyadic wavelet transform to disparity map computation, the definition of a waveletbased similarity measure for matching, the combination of matching results from different scales based on the detectable minimum disparity at each scale and the application of complex wavelet transform to stereo matching. The matching method using the dyadic wavelet transform is through SSD correlation comparison and is in particular detailed. A new measure using wavelet coefficients is defined for similarity comparison. The approach applying a dual tree of complex wavelet transform to stereo matching is formulated through phase information. A multiscale matching scheme is applied for both the matching methods. Imaging testing has been made with various synthesised and real image pairs. Experimental results with a variety of stereo image pairs exhibit a good agreement with ground truth data, where available, and are qualitatively similar to published results for other stereo matching approaches. Comparative results show that the dyadic wavelet transform-based matching method is superior in most cases to the other approaches considered.
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Gorini, Lorenzo. "Trasformate wavelet." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2014. http://amslaurea.unibo.it/7679/.

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La presente tesi vuole dare una descrizione delle Trasformate Wavelet indirizzata alla codifica dell’immagine in formato JPEG2000. Dopo aver quindi descritto le prime fasi della codifica di un’immagine, procederemo allo studio dei difetti derivanti dall’analisi tramite la Trasformata Discreta del Coseno (utilizzata nel formato predecessore JPEG). Dopo aver quindi descritto l’analisi multirisoluzione e le caratteristiche che la differenziano da quest’ultima, analizzeremo la Trasformata Wavelet dandone solo pochi accenni teorici e cercando di dedurla, in una maniera più indirizzata all’applicazione. Concluderemo la tesi descrivendo la codifica dei coefficienti calcolati, e portando esempi delle innumerevoli applicazioni dell’analisi multirisoluzione nei diversi campi scientifici e di trasmissione dei segnali.
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Navarro, Jaime. "The Continuous Wavelet Transform and the Wave Front Set." Thesis, University of North Texas, 1993. https://digital.library.unt.edu/ark:/67531/metadc277762/.

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In this paper I formulate an explicit wavelet transform that, applied to any distribution in S^1(R^2), yields a function on phase space whose high-frequency singularities coincide precisely with the wave front set of the distribution. This characterizes the wave front set of a distribution in terms of the singularities of its wavelet transform with respect to a suitably chosen basic wavelet.
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Bopardikar, Ajit S. "Speech Encryption Using Wavelet Packets." Thesis, Indian Institute of Science, 1995. https://etd.iisc.ac.in/handle/2005/153.

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The aim of speech scrambling algorithms is to transform clear speech into an unintelligible signal so that it is difficult to decrypt it in the absence of the key. Most of the existing speech scrambling algorithms tend to retain considerable residual intelligibility in the scrambled speech and are easy to break. Typically, a speech scrambling algorithm involves permutation of speech segments in time, frequency or time-frequency domain or permutation of transform coefficients of each speech block. The time-frequency algorithms have given very low residual intelligibility and have attracted much attention. We first study the uniform filter bank based time-frequency scrambling algorithm with respect to the block length and number of channels. We use objective distance measures to estimate the departure of the scrambled speech from the clear speech. Simulations indicate that the distance measures increase as we increase the block length and the number of chan­nels. This algorithm derives its security only from the time-frequency segment permutation and it has been estimated that the effective number of permutations which give a low residual intelligibility is much less than the total number of possible permutations. In order to increase the effective number of permutations, we propose a time-frequency scrambling algorithm based on wavelet packets. By using different wavelet packet filter banks at the analysis and synthesis end, we add an extra level of security since the eavesdropper has to choose the correct analysis filter bank, correctly rearrange the time-frequency segments, and choose the correct synthesis bank to get back the original speech signal. Simulations performed with this algorithm give distance measures comparable to those obtained for the uniform filter bank based algorithm. Finally, we introduce the 2-channel perfect reconstruction circular convolution filter bank and give a simple method for its design. The filters designed using this method satisfy the paraunitary properties on a discrete equispaced set of points in the frequency domain.
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Bopardikar, Ajit S. "Speech Encryption Using Wavelet Packets." Thesis, Indian Institute of Science, 1995. http://hdl.handle.net/2005/153.

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The aim of speech scrambling algorithms is to transform clear speech into an unintelligible signal so that it is difficult to decrypt it in the absence of the key. Most of the existing speech scrambling algorithms tend to retain considerable residual intelligibility in the scrambled speech and are easy to break. Typically, a speech scrambling algorithm involves permutation of speech segments in time, frequency or time-frequency domain or permutation of transform coefficients of each speech block. The time-frequency algorithms have given very low residual intelligibility and have attracted much attention. We first study the uniform filter bank based time-frequency scrambling algorithm with respect to the block length and number of channels. We use objective distance measures to estimate the departure of the scrambled speech from the clear speech. Simulations indicate that the distance measures increase as we increase the block length and the number of chan­nels. This algorithm derives its security only from the time-frequency segment permutation and it has been estimated that the effective number of permutations which give a low residual intelligibility is much less than the total number of possible permutations. In order to increase the effective number of permutations, we propose a time-frequency scrambling algorithm based on wavelet packets. By using different wavelet packet filter banks at the analysis and synthesis end, we add an extra level of security since the eavesdropper has to choose the correct analysis filter bank, correctly rearrange the time-frequency segments, and choose the correct synthesis bank to get back the original speech signal. Simulations performed with this algorithm give distance measures comparable to those obtained for the uniform filter bank based algorithm. Finally, we introduce the 2-channel perfect reconstruction circular convolution filter bank and give a simple method for its design. The filters designed using this method satisfy the paraunitary properties on a discrete equispaced set of points in the frequency domain.
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Tieng, Quang Minh. "Wavelet transform based techniques for the recognition of objects in images." Thesis, Queensland University of Technology, 1996.

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Despite its short history, the wavelet transform has found application in a remarkable diversity of disciplines: Mathematics, Physics, Numerical Analysis,Signal Processing and others. In this thesis, we explore applications of this transform in image analysis and devise several algorithms for recognising objects in an image of a scene. Five different algorithms, consisting of representations and matching techniques, have been proposed for handling different kinds of objects in different situations.
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Varanis, Marcus Vinicius Monteiro. "Análise de vibrações em sistemas discretos de massas concentradas e com dois graus de liberdade através da transformada wavelet /." Rio Claro : [s.n.], 2008. http://hdl.handle.net/11449/91946.

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Orientador: José Roberto Campanha
Banca: Roberto Eugenio Lagos Mônaco
Banca: Robson Pederiva
Resumo: O estudo de vibrações diz respeito aos movimentos oscilatórios de corpos e às forças que lhes são associadas. Todos os corpos dotados de massa e elasticidade são capazes de vibrar. Deste modo, a maior parte das máquinas e estruturas estão sujeitas a certos graus de vibração A maioria das atividades humanas envolve alguma forma de vibração. O estudo do comportamento dinâmico dessas oscilações mecânicas é o objetivo deste trabalho e para isto propomos um sistema de massas concentradas e com dois graus de liberdade. O sistema será excitado por forças externas, entre elas ondas de terremoto. Com simulações numéricas estudamos o sistema, usando a transformada rápida de Fourier, transformada wavelet.
Abstract: The study of vibration concerns oscillatory movement of bodies and the forces they are associated. All bodies that have mass and elasticity are able to vibrate. Thus, most of the machines and structures are subject to certain degrees of vibration most human activities involve some form of vibration. The study of the dynamic behavior of these mechanical oscillations is the objective of this work and to propose that a system of weights and concentrated with two degrees of freedom. The system will be excited by external forces, including waves of earthquake. With numerical simulations studied the system, using the fast Fourier transform, wavelet transform.
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Books on the topic "Wavelet"

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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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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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Numerical analysis of wavelet methods. Amsterdam: Elsevier, 2003.

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Resnikoff, Howard L., and Raymond O. Wells. Wavelet Analysis. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-0593-7.

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Ruch, David K., and Patrick J. Van Fleet. Wavelet Theory. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2009. http://dx.doi.org/10.1002/9781118165652.

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Chan, Y. T. Wavelet Basics. Boston, MA: Springer US, 1995. http://dx.doi.org/10.1007/978-1-4615-2213-3.

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Chan, Y. T. Wavelet Basics. Boston, MA: Springer US, 1995.

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Wavelet theory. Providence, R.I: American Mathematical Society, 2011.

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Chan, Y. T. Wavelet basics. Boston: Kluwer Academic Publishers, 1995.

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Pathak, Ram Shankar. The Wavelet Transform. Paris: Atlantis Press, 2009. http://dx.doi.org/10.2991/978-94-91216-24-4.

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Book chapters on the topic "Wavelet"

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Farouk, Mohamed Hesham. "Wavelets, Wavelet Filters, and Wavelet Transforms." In SpringerBriefs in Electrical and Computer Engineering, 11–19. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-02732-6_3.

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Farouk, Mohamed Hesham. "Wavelets, Wavelet Filters, and Wavelet Transforms." In SpringerBriefs in Electrical and Computer Engineering, 11–21. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-69002-5_3.

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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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Akujuobi, Cajetan M. "Wavelet Transforms." In Wavelets and Wavelet Transform Systems and Their Applications, 61–79. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-87528-2_4.

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Goebbels, Steffen, and Stefan Ritter. "Wavelets und schnelle Wavelet-Transformation ∗." In Mathematik verstehen und anwenden: Differenzialgleichungen, Fourier- und Vektoranalysis, Laplace-Transformation und Stochastik, 441–53. Berlin, Heidelberg: Springer Berlin Heidelberg, 2023. http://dx.doi.org/10.1007/978-3-662-68369-9_15.

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Resnikoff, Howard L., and Raymond O. Wells. "Wavelet Approximation." In Wavelet Analysis, 202–35. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-0593-7_9.

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Lin, E. B. "Wavelet Transforms and Wavelet Approximations." In Approximation, Probability, and Related Fields, 357–65. Boston, MA: Springer US, 1994. http://dx.doi.org/10.1007/978-1-4615-2494-6_27.

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Averbuch, Amir Z., Pekka Neittaanmaki, and Valery A. Zheludev. "Periodic Spline Wavelets and Wavelet Packets." In Spline and Spline Wavelet Methods with Applications to Signal and Image Processing, 133–82. Dordrecht: Springer Netherlands, 2014. http://dx.doi.org/10.1007/978-94-017-8926-4_8.

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Conference papers on the topic "Wavelet"

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Sheng, Yunglong, Danny Roberge, Taiwei Lu, and Harold Szu. "Optical wavelet matched filters." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1992. http://dx.doi.org/10.1364/oam.1992.fn1.

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The wavelet transform decomposes a signal onto a set of basis wavelet functions that are dilated and shifted from the mother functions h(t), satisfying an admissible condition. This transform is compact in both time and frequency domains and is therefore efficient for time-dependent frequency analysis of the signal. We consider the wavelet transform as the correlations between the signal and a bank of wavelet filters, each having a fixed scale.1 Thus, the wavelet transform of a 1D signal is implemented in an optical correlator with multiple strip wavelet filters, and the wavelet transform of a 2D signal is implemented in a multichannel optical correlator. We make the matched filters recording the 4D wavelet transforms of a 2D input image for optical pattern recognition. With the isotropic Mexican-hat wavelets, the wavelet transform becomes the well known Laplacian-Gaussian operator for zero-crossing edge detection. However, we synthesize the filters by combining the wavelet transform filters and the conventional matched filters in the same Fourier plane for pattern recognition. The experimental results will be shown.
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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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Staszewski, Wiesław J. "Wavelet Novelty Measure for Machinery Diagnostics." In ASME 1997 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/detc97/vib-4140.

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Abstract The paper is concerned with wavelet analysis for fault detection in machinery diagnostics. A new approach based on novelty detection is presented. The method involves a wavelet compression algorithm to vibration data in order to extract a set of features which are related to the fault. The compression algorithm uses orthogonal Daubechies’ wavelets and a simple thresholding procedure. The wavelet based novelty measure is established as a statistical distance between decoded data representing different fault advancements.
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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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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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De A. Coelho, Rodrigo, Hugerles S. Silva, and Núbia S. D. Brito. "Análise da Distribuição de Energia na Decomposição de Sinais no Domínio Wavelet." In Congresso Brasileiro de Automática - 2020. sbabra, 2020. http://dx.doi.org/10.48011/asba.v2i1.1472.

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A Transformada Wavelet Discreta (TWD) é uma das ferramentas mais aplicadas para estudos sobre a qualidade da energia elétrica (QEE). Entretanto, dependendo do filtro utilizado, a decomposição efetuada pela TWD pode implicar em vazamento espectral. O vazamento espectral pode acarretar uma má representação de componentes de frequência, o que é prejudicial a análise da QEE. Nesta conjuntura, este trabalho apresenta uma análise da distribuição de energia e do vazamento espectral na decomposição de sinais efetuada pela Transformada Wavelet Discreta Redundante (TWDR) e pela Transformada Wavelet Packet Discreta Redundante (TWPDR). Em sinais de teste, analisou-se a energia de cada coeficiente da TWDR e da TWPDR, bem como sua concentração em sua banda passante ideal. Para tanto, foram utilizadas funções wavelet com diferentes comprimentos. Os resultados indicaram que wavelets curtas acarretam um vazamento de energia superior ao de wavelets longas.
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Di, Haibin, and Aria Abubakar. "Self-Supervised Learning for Automated Seismic Wavelet Extraction." In ADIPEC. SPE, 2022. http://dx.doi.org/10.2118/211823-ms.

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Abstract Seismic wavelet extraction is a fundamental but crucial component in seismic data analysis, which aims at estimating the source wavelet for better decoding the subsurface reflectivities from seismic signals and calibrating the measurements between logging and seismic. Due to the rock heterogeneity, however, seismic energy attenuates during its propagation, and correspondingly the seismic wavelet is considered varying from shallow to deep as well as from near to far offsets, causing the wavelet time-variant. While machine learning (ML) appears feasible for assisting the challenge, without a comprehensive understanding of the seismic propagation, representative training labels cannot be prepared, and supervised learning appears less applicable. This study proposes implementing self-supervised learning into time-variant seismic wavelet extraction. Specifically, the proposed network is in the architecture of a dual-task auto-encoder (DTAE). Starting from 1-D seismic amplitude, the DTAE first uses an encoder to extract a set of features at multiple scales, which are then split into two flows, with one through a decoder that aims at reconstructing the input 1D seismic signal and the other through a few convolutional layers that aim at matching the spectrum between seismic trace and extracted wavelet. Correspondingly, the objective function of training such DTAE consists of two parts, the mean-square-error of the amplitude reconstruction and the mean-square-error of the spectrum matching. The proposed workflow is tested on various field datasets, and compared to the statistical wavelets, the extracted wavelets are of better match with the spectrum variation of seismic from shallow to deep and from near offset to far offset.
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Adel Gabry, Mohamed, Ibrahim Eltaleb, M. Y. Soliman, S. M. Farouq-Ali, Paul J. Cook, Florian A. Soom, and Yves Guglielmi. "Validation of Continuous Wavelet Transform Closure Detection Technique Using Strain Measurements." In SPE Hydraulic Fracturing Technology Conference and Exhibition. SPE, 2023. http://dx.doi.org/10.2118/212360-ms.

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Abstract Although closure detection has a crucial role in hydraulic fracturing operations, significant debate surrounds the various methodologies to determine its value. Several competing methodologies have been presented in the literature that sometimesyield significantly different estimates of closure pressure and time. The conventional techniques rely on assumptions that may be competing or even contradictory. The continuous wavelets transform technique is a data transform technique that convolves the pressure and/or temperature data using a short wavy signal called "wavelet". The wavelet transform provides a representation of the pressure signal by letting the translation and scale parameters of the wavelets vary continuously. That enables the analyst to find the details of the pressure data by observing the wavelet energy spectrum for the monitored signal (pressure and/or temperature) signal. In this case the event of contact between two fracture faces and complete fracture closure is clearly identified. As a part of The EGS Collab project, a series of fracture injection tests have been conducted to estimate the minimum principal stress with direct observation of well bore deformation using the SIMFIP tool (Step-Rate Injection Method for Fracture In-Situ Properties). The tool monitors the deformation using strain gauges as a fracture opens and closes during multiple tests. The publicly available data provide a great opportunity to experimentally calibrate the new technique for detecting the closure event using continuous wavelet transform. The effect of fracture closure events and fracture faces contact events detected using continuous wavelet transform were compared to the experimental measured deformation. The continuous wavelet transform technique for closure detection showed an agreement with the deformation measurement. The effect of the presence of natural fractures and complex fracture closure events were recognized using the continuous wavelet transform technique. The Contineous Wavelet Transform (CWT) is a global technique that can be applied to the pressure decline data without requiring further information about the reservoir geomechanical parameters or pumping data. The technique can be easily embedded in machine learning algorithms for hydraulic fracturing diagnostics.
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Abu-Mahfouz, Issam, Amit Banerjee, and Ma’moun Abu-Ayyad. "Fatigue Damage Diagnosis Using Statistical, Spectral, and Wavelet Analysis Techniques." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-66518.

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The objective of this work is to illustrate a comparative investigation into the signatures of crack initiation and propagation using vibration and displacement signals. Experimental tests were performed on low carbon steel specimen under fully reversed bending cycles in a cantilever support configuration. Accelerometer and displacement-sensor vibration signals were collected using a National Instrument data acquisition system. Several methods, such as statistical moments, FFT, Wavelets, and short-time-frequency analysis techniques, were used to analyze the collected signals. It was found that the wavelet analysis gave the most consistent patterns in tracking crack initiation and propagation. For the wavelet analysis, extensive comparative investigation was conducted to select the optimum combination of wavelet packets for crack detection and monitoring.
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Wirasaet, Damrongsak, and Samuel Paolucci. "Application of an Adaptive Wavelet Method to Natural-Convection Flow in a Differentially Heated Cavity." In ASME 2005 Summer Heat Transfer Conference collocated with the ASME 2005 Pacific Rim Technical Conference and Exhibition on Integration and Packaging of MEMS, NEMS, and Electronic Systems. ASMEDC, 2005. http://dx.doi.org/10.1115/ht2005-72864.

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We describe an adaptive wavelet method based on interpolating wavelets applied to the solution of a natural-convection flow. The adaptive wavelet method, owing to the approximation capabilities and spatial localization of wavelet functions, enables the solution of problems with local grid resolution consistent with the local demand of the physical problem. The adaptive method is applied to simulate the flow in a differentially heated square cavity at large Rayleigh numbers. Numerical results, whenever possible, are compared with those previously published.
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Reports on the topic "Wavelet"

1

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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Kozaitis, Samuel P. Optical Wavelet Transform. Fort Belvoir, VA: Defense Technical Information Center, October 1997. http://dx.doi.org/10.21236/ada339152.

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Waagen, D. E., J. D. Argast, and J. R. McDonnell. Evolving Wavelet Compression Strategies. Fort Belvoir, VA: Defense Technical Information Center, June 1994. http://dx.doi.org/10.21236/ada281247.

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Wilson, Gary R. Wavelet Based Cumulant Processing. Fort Belvoir, VA: Defense Technical Information Center, September 1993. http://dx.doi.org/10.21236/ada272003.

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Shensa, M. J. The Discrete Wavelet Transform. Fort Belvoir, VA: Defense Technical Information Center, June 1991. http://dx.doi.org/10.21236/ada239642.

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Li, Shaomeng, and Christopher Meyer Sewell. Wavelet Transforms using VTK-m. Office of Scientific and Technical Information (OSTI), September 2016. http://dx.doi.org/10.2172/1329546.

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Madych, Wolodymyr, and K. Grochenig. Multivariate Wavelet Representations and Approximations. Fort Belvoir, VA: Defense Technical Information Center, October 1994. http://dx.doi.org/10.21236/ada290147.

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Chul, Charles K. Wavelet Analysis and Its Applications. Fort Belvoir, VA: Defense Technical Information Center, January 1995. http://dx.doi.org/10.21236/ada291735.

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Chui, Charles K. Wavelet Analysis and Its Applications. Fort Belvoir, VA: Defense Technical Information Center, January 1995. http://dx.doi.org/10.21236/ada301762.

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Subotic, N. S., L. Collins, M. Reiley, B. Thelen, and J. Gorman. Wavelet Transform Based Target Detection. Fort Belvoir, VA: Defense Technical Information Center, May 1995. http://dx.doi.org/10.21236/ada303470.

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