Journal articles: 'Wavelet transform'

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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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Romanchak, V. M. "Local transformations with a singular wavelet." Informatics 17, no. 1 (March 29, 2020): 39–46. http://dx.doi.org/10.37661/1816-0301-2020-17-1-39-46.

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The paper considers a local wavelet transform with a singular basis wavelet. The problem of nonparametric approximation of a function is solved by the use of the sequence of local wavelet transforms. Traditionally believed that the wavelet should have an average equal to zero. Earlier, the author considered singular wavelets when the average value is not equal to zero. As an example, the delta-shaped functions, participated in the estimates of Parzen – Rosenblatt and Nadara – Watson, were used as a wavelet. Previously, a sequence of wavelet transforms for the entire numerical axis and finite interval was constructed for singular wavelets. The paper proposes a sequence of local wavelet transforms, a local wavelet transform is defined, the theorems that formulate the properties of a local wavelet transform are proved. To confirm the effectiveness of the algorithm an example of approximating the function by use of the sum of discrete local wavelet transforms is given.

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Zeelan Basha, CMAK, K. M. Sricharan, Ch Krishna Dheeraj, and R. Ramya Sri. "A Study on Wavelet Transform Using Image Analysis." International Journal of Engineering & Technology 7, no. 2.32 (May 31, 2018): 94. http://dx.doi.org/10.14419/ijet.v7i2.32.13535.

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The wavelet transforms have been in use for variety of applications. It is widely being used in signal analysis and image analysis. There have been lot of wavelet transforms for compression, decomposition and reconstruction of images. Out of many transforms Haar wavelet transform is the most computationally feasible wavelet transform to implement. The wave analysis technique has an understandable impact on the removal of noise within the signal. The paper outlines the principles and performance of wavelets in image analysis. Compression performance and decomposition of images into different layers have been discussed in this paper. We used Haar distinct wavelet remodel (HDWT) to compress the image. Simulation of wavelet transform was done in MATLAB. Simulation results are conferred for the compression with Haar rippling with totally different level of decomposition. Energy retention and PSNR values are calculated for the wavelets. Result conjointly reveals that the extent of decomposition will increase beholding of the photographs goes on decreasing however the extent of compression is incredibly high. Experimental results demonstrate the effectiveness of the Haar wavelet transform in energy retention in comparison to other wavelet transforms.

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Willmore, Ben, Ryan J. Prenger, Michael C. K. Wu, and Jack L. Gallant. "The Berkeley Wavelet Transform: A Biologically Inspired Orthogonal Wavelet Transform." Neural Computation 20, no. 6 (June 2008): 1537–64. http://dx.doi.org/10.1162/neco.2007.05-07-513.

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We describe the Berkeley wavelet transform (BWT), a two-dimensional triadic wavelet transform. The BWT comprises four pairs of mother wavelets at four orientations. Within each pair, one wavelet has odd symmetry, and the other has even symmetry. By translation and scaling of the whole set (plus a single constant term), the wavelets form a complete, orthonormal basis in two dimensions. The BWT shares many characteristics with the receptive fields of neurons in mammalian primary visual cortex (V1). Like these receptive fields, BWT wavelets are localized in space, tuned in spatial frequency and orientation, and form a set that is approximately scale invariant. The wavelets also have spatial frequency and orientation bandwidths that are comparable with biological values. Although the classical Gabor wavelet model is a more accurate description of the receptive fields of individual V1 neurons, the BWT has some interesting advantages. It is a complete, orthonormal basis and is therefore inexpensive to compute, manipulate, and invert. These properties make the BWT useful in situations where computational power or experimental data are limited, such as estimation of the spatiotemporal receptive fields of neurons.

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Abdullah, Shahrum, S. N. Sahadan, Mohd Zaki Nuawi, and Zulkifli Mohd Nopiah. "Fatigue Data Analysis Using Continuous Wavelet Transform and Discrete Wavelet Transform." Key Engineering Materials 462-463 (January 2011): 461–66. http://dx.doi.org/10.4028/www.scientific.net/kem.462-463.461.

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The wavelet transform is well known for its ability in vibration analysis in fault detection. This paper presents the ability of wavelet transform in fatigue data analysis starts from high amplitude events detection and it is then followed by fatigue data extraction based on wavelet coefficients. Since the wavelet transform has two main categories, i.e. the continuous wavelet transforms (CWT) and the discrete wavelet transform (DWT), the comparison study were carried out in order to investigate performance of both wavelet for fatigue data analysis. CWT represents by the Morlet wavelet while DWT with the form of the 4th Order Daubechies wavelet (Db4) was also used for the analysis. An analysis begins with coefficients plot using the time-scale representation that associated to energy coefficients plot for the input value in fatigue data extraction. Ten extraction levels were used and all levels gave the damage difference, (%∆D) less than 10% with respect to original signal. From the study, both wavelet transforms gave almost similar ability in editing fatigue data but the Morlet wavelet provided faster analysis time compared to the Db4 wavelet. In comparison to have the value of different at 5%, the Morlet wavelet achieved at L= 5 while the Db4 wavelet at L=7. Even though it gave slower analysis time, both wavelets can be used in fatigue data editing but at different time consuming.

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Guido, Rodrigo Capobianco, Fernando Pedroso, André Furlan, Rodrigo Colnago Contreras, Luiz Gustavo Caobianco, and Jogi Suda Neto. "CWT × DWT × DTWT × SDTWT: Clarifying terminologies and roles of different types of wavelet transforms." International Journal of Wavelets, Multiresolution and Information Processing 18, no. 06 (August 28, 2020): 2030001. http://dx.doi.org/10.1142/s0219691320300017.

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Wavelets have been placed at the forefront of scientific researches involving signal processing, applied mathematics, pattern recognition and related fields. Nevertheless, as we have observed, students and young researchers still make mistakes when referring to one of the most relevant tools for time–frequency signal analysis. Thus, this correspondence clarifies the terminologies and specific roles of four types of wavelet transforms: the continuous wavelet transform (CWT), the discrete wavelet transform (DWT), the discrete-time wavelet transform (DTWT) and the stationary discrete-time wavelet transform (SDTWT). We believe that, after reading this correspondence, readers will be able to correctly refer to, and identify, the most appropriate type of wavelet transform for a certain application, selecting relevant and accurate material for subsequent investigation.

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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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Hamdi, Med. "A Comparative Study in Wavelets, Curvelets and Contourlets as Denoising biomedical Images." Image Processing & Communications 16, no. 3-4 (January 1, 2011): 13–20. http://dx.doi.org/10.2478/v10248-012-0007-1.

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A Comparative Study in Wavelets, Curvelets and Contourlets as Denoising biomedical ImagesA special member of the emerging family of multi scale geometric transforms is the contourlet transform which was developed in the last few years in an attempt to overcome inherent limitations of traditional multistage representations such as curvelets and wavelets. The biomedical images were denoised using firstly wavelet than curvelets and finally contourlets transform and results are presented in this paper. It has been found that the contourlets transform outperforms the curvelets and wavelet transform in terms of signal noise ratio

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Pathak, R. S., and S. K. Singh. "The wavelet transform on spaces of type S." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 136, no. 4 (August 2006): 837–50. http://dx.doi.org/10.1017/s0308210500004753.

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The continuous wavelet transform is studied on certain Gel'fand–Shilov spaces of type S. It is shown that, for wavelets belonging to the one type of S-space defined on R, the wavelet transform is a continuous linear map of the other type of the S-space into a space of the same type (latter type) defined on R × R+. The wavelet transforms of certain ultradifferentiable functions are also investigated.

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Mandal, U. K., Sandeep Verma, and Akhilesh Prasad. "Composition of wavelet transforms and wave packet transform involving Kontorovich-Lebedev transform." Filomat 35, no. 1 (2021): 47–60. http://dx.doi.org/10.2298/fil2101047m.

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The main objective of this paper is to study the composition of continuous Kontorovich-Lebedev wavelet transform (KL-wavelet transform) and wave packet transform (WPT) based on the Kontorovich-Lebedev transform (KL-transform). Estimates for KL-wavelet and KL-wavelet transform are obtained, and Plancherel?s relation for composition of KL-wavelet transform and WPT-transform are derived. Reconstruction formula for WPT associated to KL-transform is also deduced and at the end Calderon?s formula related to KL-transform using its convolution property is obtained.

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Toda, Hiroshi, Zhong Zhang, and Takashi Imamura. "Practical design of perfect-translation-invariant real-valued discrete wavelet transform." International Journal of Wavelets, Multiresolution and Information Processing 12, no. 04 (July 2014): 1460005. http://dx.doi.org/10.1142/s0219691314600054.

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The real-valued tight wavelet frame having perfect translation invariance (PTI) has already proposed. However, due to the irrational-number distances between wavelets, its calculation amount is very large. In this paper, based on the real-valued tight wavelet frame, a practical design of a real-valued discrete wavelet transform (DWT) having PTI is proposed. In this transform, all the distances between wavelets are multiples of 1/4, and its transform and inverse transform are calculated fast by decomposition and reconstruction algorithms at the sacrifice of a tight wavelet frame. However, the real-valued DWT achieves an approximate tight wavelet frame.

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Kekre, H. B., Tanuja Sarode, and Shachi Natu. "Performance Comparison of Wavelets Generated from Four Different Orthogonal Transforms for Watermarking With Various Attacks." INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY 9, no. 3 (July 15, 2013): 1139–52. http://dx.doi.org/10.24297/ijct.v9i3.3340.

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This paper proposes a watermarking technique using different orthogonal wavelet transforms like Hartley wavelet, Kekrewavelet, Slant wavelet and Real Fourier wavelet transform generated from corresponding orthogonal transform. Theseorthogonal wavelet transforms have been generated using different sizes of component orthogonal transform matrices.For example 256*256 size orthogonal wavelet transform can be generated using 128*128 and 2*2 size componentorthogonal transform. It can also be generated using 64*64 and 4*4, 32*32 and 8*8, 16*16 and 16*16 size componentorthogonal transform matrices. In this paper the focus is to compare the performance of above mentioned transformsgenerated using 128*128 and 2*2 size component orthogonal transform and 64*64 and 4*4 size component orthogonaltransform in digital image watermarking. The other two combinations are not considered as their performance iscomparatively not as good. Comparison shows that wavelet transforms generated using (128,2) combination of orthogonalÂ transform give better performances than wavelet transforms generated using (64,4) combination of orthogonaltransformfor contrast stretching, cropping, Gaussian noise, histogram equalization and resizing attacks. Real Fourierwavelet and Slant wavelet prove to be better for histogram equalization and resizing attack respectively than DCT waveletand Walsh wavelet based watermarking presented in previous work.

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Nigam, Vaibhav, Smriti Bhatnagar, and Sajal Luthra. "Image Denoising Using Wavelet Transform and Wavelet Transform with Enhanced Diversity." Advanced Materials Research 403-408 (November 2011): 866–70. http://dx.doi.org/10.4028/www.scientific.net/amr.403-408.866.

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This paper is a comparative study of image denoising using previously known wavelet transform and new type of wavelet transform, namely, Diversity enhanced discrete wavelet transform. The Discrete Wavelet Transform (DWT) has two parameters: the mother wavelet and the number of iterations. For every noisy image, there is a best pair of parameters for which we get maximum output Peak Signal to Noise Ratio, PSNR. As the denoising algorithms are sensitive to the parameters of the wavelet transform used, in this paper comparison of DEDWT to DWT has been presented. The diversity is enhanced by computing wavelet transforms with different parameters. After the filtering of each detail coefficient, the corresponding wavelet transforms are inverted and the estimated image, having a higher PSNR, is extracted. To benchmark against the best possible denoising method three thresholding techniques have been compared. In this paper we have presented a more practical, implementation oriented work.

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Kuznetsov, Nikolay A. "METHOD FOR CONSTRUCTING NONLINEAR WAVELET CODE TO ENSURE DATA INTEGRITY IN COMMUNICATION CHANNELS." T-Comm 15, no. 2 (2021): 26–32. http://dx.doi.org/10.36724/2072-8735-2021-15-2-26-32.

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A method for constructing a nonlinear wavelet code (NVC) to ensure data integrity in communication channels, taking into account current threats to information security in a modern dynamic stochastic environment, is proposed. A special place among the methods of combating threats to the integrity of information is occupied by noise-resistant encoding. The article presents a computationally effective method for ensuring data integrity in communication channels by using nonlinear transformations and wavelets. The approximation of the wavelet transform refers to the division of the signal into approximating and detailing components. Continuous and discrete wavelet transforms are widely used [2] for signal analysis in modern communication channels. The set of functions defining the wavelet transform belongs to the space of square-integrable functions on a straight line and provides a necessary condition for constructing constructions of nonlinear codes based on the theory of wavelet decomposition. As is known, in the process of wavelet analysis, the signal is decomposed along the orthogonal basis formed by shifts of the wavelet function. A distinctive feature of this approach is that convolution of the signal with wavelets allows us to identify the characteristic features of the signal in the area of localization of these wavelets. To perform computational calculations, you need a set of scaling function coefficients and a wavelet. The wavelet transform matrix depends on the coefficients of the scaling function. The results presented in the article describe a new approach to ensuring data integrity in communication channels using nvcs. A computational example is presented.

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Li, Yaoguo, and Douglas W. Oldenburg. "Rapid construction of equivalent sources using wavelets." GEOPHYSICS 75, no. 3 (May 2010): L51—L59. http://dx.doi.org/10.1190/1.3378764.

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We have developed a fast algorithm for generating an equivalent source by using fast wavelet transforms based on orthonormal, compactly supported wavelets. We apply a 2D wavelet transform to each row and column of the coefficient matrix and subsequently threshold the transformed matrix to generate a sparse representation in the wavelet domain. The algorithm then uses this sparse matrix to construct the the equivalent source directly in the wavelet domain. Performing an inverse wavelet transform then yields the equivalent source in the space domain. Using upward continuation of total-field magnetic data between uneven surfaces as examples, we have compared this approach with the direct solution using the dense matrix in the space domain. We have shown that the wavelet approach can reduce the CPU time by as many as two orders of magnitude.

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Qin, Jun, and Pengfei Sun. "Applications and Comparison of Continuous Wavelet Transforms on Analysis of A-wave Impulse Noise." Archives of Acoustics 40, no. 4 (December 1, 2015): 503–12. http://dx.doi.org/10.1515/aoa-2015-0050.

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Abstract Noise induced hearing loss (NIHL) is a serious occupational related health problem worldwide. The A-wave impulse noise could cause severe hearing loss, and characteristics of such kind of impulse noise in the joint time-frequency (T-F) domain are critical for evaluation of auditory hazard level. This study focuses on the analysis of A-wave impulse noise in the T-F domain using continual wavelet transforms. Three different wavelets, referring to Morlet, Mexican hat, and Meyer wavelets, were investigated and compared based on theoretical analysis and applications to experimental generated A-wave impulse noise signals. The underlying theory of continuous wavelet transform was given and the temporal and spectral resolutions were theoretically analyzed. The main results showed that the Mexican hat wavelet demonstrated significant advantages over the Morlet and Meyer wavelets for the characterization and analysis of the A-wave impulse noise. The results of this study provide useful information for applying wavelet transform on signal processing of the A-wave impulse noise.

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Imanbekova, T. D., A. Zhaksylyk, and I. A. Kozlov. "Applying Wavelet transform to information compression." Bulletin of Kazakh Leading Academy of Architecture and Construction 79, no. 1 (March 30, 2021): 325–31. http://dx.doi.org/10.51488/1680-080x/2021.1-42.

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This paper discusses the application of wavelet transform for information compression, analysis of discrete wavelet transform tools using the software. Algorithms for audio signal compression and image compression using wavelets are considered.

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Pathak, R. S., and Ashish Pathak. "Asymptotic Expansions of the Wavelet Transform for Large and Small Values ofb." International Journal of Mathematics and Mathematical Sciences 2009 (2009): 1–13. http://dx.doi.org/10.1155/2009/270492.

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Asymptotic expansions of the wavelet transform for large and small values of the translation parameterbare obtained using asymptotic expansions of the Fourier transforms of the function and the wavelet. Asymptotic expansions of Mexican hat wavelet transform, Morlet wavelet transform, and Haar wavelet transform are obtained as special cases. Asymptotic expansion of the wavelet transform has also been obtained for small values ofbwhen asymptotic expansions of the function and the wavelet near origin are given.

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Mustafa, Ziyad Tariq, Alaa Al-Hammami, and Jasim Al-Samarai. "Evaluation of Wavelet Transform Audio Hiding." Iraqi Journal for Computers and Informatics 40, no. 1 (December 31, 2002): 32–44. http://dx.doi.org/10.25195/ijci.v40i1.224.

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Audio hiding is method for embedding information into an audio signal. It seeks to do so in a robust Fashion, while not perceivably degrading the host signal (coves audio). Hiding data in audio signals presents & varicty of challenges: due in part to the wider dynamic and differential range of the Human Auditory System (HAS) as compared to other senses. Transform are usually used for robust audio hiding (audio watcrmarking). But, the audio hiding process is affected by the type of transform used. Therefore, this paper presents an evaluation of wavelet transform hiding in comprison with sclccted types of transforms (Walsh transform and cosine transform) hiding. In order to generate the audio stegecover, the research concludce (Wavelet, Walsh, or Cosine) transform of the audio cover, replacing some transformed cover cocfficients with secret audio message coefficients, and inverse (Wavelet, Walsit, or Carsine Irannom for audio cover with replaced coefficients. While, the extracting method concludes (Wavelel, Walsh, or Cosine runsform of the stego ove18 and extracting the secrecy extracted Audio message.

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Brassarote, Gabriela De Oliveira Nascimento, Eniuce Menezes de Souza, and João Francisco Galera Monico. "Multiscale Analysis of GPS Time Series from Non-decimated Wavelet to Investigate the Effects of Ionospheric Scintillation." TEMA (São Carlos) 16, no. 2 (September 7, 2015): 119. http://dx.doi.org/10.5540/tema.2015.016.02.0119.

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Due to the numerous application possibilities, the theory of wavelets has been applied in several areas of research. The Discrete Wavelet Transform is the most known version. However, the downsampling required for its calculation makes it sensitive to the origin, what is not ideal for some applications,mainly in time series. On the other hand, the Non-Decimated Discrete Wavelet Transform (or Maximum Overlap Discrete Wavelet Transform, Stationary Wavelet Transform, Shift-invariant Discrete Wavelet Transform, Redundant Discrete Wavelet Transform) is shift invariant, because it considers all the elements of the sample, by eliminating the downsampling and, consequently, represents a time series with the same number of coefficients at each scale. In the present paper, the objective is to present the theorical aspects of the a multiscale/multiresolution analysis of non-stationary time series from non-decimated wavelets in terms of its implementation using the same pyramidal algorithm of the decimated wavelet transform. An application with real time series of the effect of the ionospheric scintillation on artificial satellite signals is investigated. With this analysis some information and hidden patterns which can not be detected in the time domain, may therefore be explained in the space-frequency domain.

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Kozłowski, Bartosz. "Time series denoising with wavelet transform." Journal of Telecommunications and Information Technology, no. 3 (September 30, 2005): 91–95. http://dx.doi.org/10.26636/jtit.2005.3.320.

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This paper concerns the possibilities of applying wavelet analysis to discovering and reducing distortions occurring in time series.Wavelet analysis basics are briefly reviewed. WaveShrink method including three most common shrinking variants (hard, soft, and non-negative garrote shrinkage functions) is described. Another wavelet-based filtering method, with parameters depending on the length of wavelets, is introduced. Sample results of filtering follow the descriptions of both methods. Additionally the results of the use of both filtering methods are compared. Examples in this paper deal only with the simplest “mother” wavelet function – Haar basic wavelet function.

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Vafaie, Sepideh, and Eysa Salajegheh. "Comparisons of wavelets and contourlets for vibration-based damage identification in the plate structures." Advances in Structural Engineering 22, no. 7 (January 20, 2019): 1672–84. http://dx.doi.org/10.1177/1369433218824903.

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The objective of the present study is to compare a new approach based on contourlet transform and a traditional method based on wavelet transform to demonstrate curve damages in plate structures. The contourlet transform approach, as a novel two-dimensional development of wavelet transform, was extended to deal with inherent restrictions of wavelets. According to previous studies, wavelets have indicated poor performance to detect curve damages due to its basic elements. Therefore, this study utilized contourlet transform as a new method having an efficient performance to display this kind of discontinuities. In this research, contourlet transform and wavelet transform have been applied to a plate using four fixed boundary conditions including circle damages with arbitrary specifications and location in order to demonstrate their performance in damage identification. Comparing damage shape attained from contourlet transform and wavelet transform, it was revealed that contourlet transform could be utilized as an accessible and useful technique to detect damage with curvature.

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Natu, Prachi, H. B. Kekre, and Tanuja Sarode. "Performance Comparison of Hartley Transform with Hartley Wavelet and Hybrid Hartley Wavelet Transforms for Image Data Compression." INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY 12, no. 6 (February 18, 2014): 3634–41. http://dx.doi.org/10.24297/ijct.v12i6.3137.

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This paper proposes image compression using Hybrid Hartley wavelet transform. The paper compares the results of Hybrid Hartley wavelet transform with that of orthogonal Hartley transform and Hartley Wavelet Transform. Hartley wavelet is generated from Hartley transform and Hybrid Hartley wavelet is generated from Hartley transform combined with other orthogonal transform which contributes to local features of an image. RMSE values are calculated by varying local component transform in hybrid Hartley wavelet transform and changing the size of it. Sizes of local component transform is varied as N=8, 16, 32, 64. Experiments are performed on twenty sample color images of size 256x256x3. Performance of Hartley Transform, Hartley Wavelet transform and Hybrid Hartley wavelet Transform is compared in terms of compression ratio and bit rate. Performance of Hartley wavelet is 35 to 37% better than that of Hartley transform whereas performance of hybrid Hartley wavelet is still improved than Hartley wavelet transform by 15 to 20%. Hartley-DCT pair gives best results among all Hybrid Hartley Transforms. Using hybrid wavelet maximum compression ratio up to 32 is obtained with acceptable quality of reconstructed image.

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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 function on phase space whose high-frequency singularities are precisely the elements in the analytic wavefront set off.

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Fang, Lanting, Lenan Wu, and Yudong Zhang. "A Novel Demodulation System Based on Continuous Wavelet Transform." Mathematical Problems in Engineering 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/513849.

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Considering the problem of EBPSK signal demodulation, a new approach based on the wavelet scalogram using continuous wavelet transform is proposed. Our system is twofold: an adaptive wavelet construction method that replaces manual selection existing wavelets method and, on the other hand, a nonlinear demodulation system based on image processing and pattern classification is proposed. To evaluate the performance of the adaptive wavelet and compare the performance of the proposed system with the existing systems, a series of comprehensive simulation experiments is conducted under the environment of uniform white noise, colored noise, and additive white Gaussian noise channel, respectively. Simulation results of different wavelets show that the system using adaptive wavelet has lower bit error rate (BER). Moreover, simulation results of several systems show that the BER of the proposed system is the lowest among all systems, such as amplitude detection, integral detection, and some continuous wavelet transform systems (specific scales and times and maximum lines). In a word, the adaptive wavelet construction proposed in this paper yields superior performances compared with the manual selection, and the proposed system has better performances than the existing systems. Index terms are signal demodulation, adaptive wavelet, continuous wavelet transform, and BER.

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Dibal, P. Y., E. N. Onwuka, J. Agajo, and C. O. Alenoghena. "Enhanced discrete wavelet packet sub-band frequency edge detection using Hilbert transform." International Journal of Wavelets, Multiresolution and Information Processing 16, no. 01 (January 2018): 1850009. http://dx.doi.org/10.1142/s0219691318500091.

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The wavelet packet transform as a mathematical tool has found recent application in spectrum sensing. The result of this application has produced very promising results. Primarily, wavelets were designed for edge detection in images. Recently, cognitive radio literature have reported on wavelet application to detect sub-band frequency edges in wide band spectrum. In this paper, we present the combination of the Hilbert transform and the wavelet packet transform with the aim of enhancing the detection of the sub-band frequency edges of a wavelet-packet-decomposed signal. The simulation results show the effectiveness of this approach. The new scheme detected sub-band frequency edges of the wavelet-packet-decomposed signal much better than the wavelet packet transform without combination with the Hilbert transform.

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ZHU, XIU-GE, BAO-BIN LI, and DENG-FENG LI. "ORTHOGONAL WAVELET TRANSFORM OF SIGNAL BASED ON COMPLEX B-SPLINE BASES." International Journal of Wavelets, Multiresolution and Information Processing 10, no. 06 (November 2012): 1250054. http://dx.doi.org/10.1142/s0219691312500543.

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In this paper, an orthogonal wavelet transform of signal based on complex B-spline bases is given. The new wavelet transform realizes accurate computation of coefficients of complex B-spline base functions. It integrates good properties of orthogonality, symmetry and continuity, and offers better approximations to continuous signal than do the Haar wavelet and Daubechies wavelets. All algorithms of the new orthogonal wavelet transform are based on explicit formulas and easy to be implemented.

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Nanavati, Sachin P., and Prasanta K. Panigrahi. "Wavelet transform." Resonance 9, no. 3 (March 2004): 50–64. http://dx.doi.org/10.1007/bf02834988.

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LEWALLE, JACQUES. "FIELD RECONSTRUCTION FROM SINGLE SCALE CONTINUOUS WAVELET COEFFICIENTS." International Journal of Wavelets, Multiresolution and Information Processing 07, no. 01 (January 2009): 131–42. http://dx.doi.org/10.1142/s0219691309002738.

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The redundancy of continuous wavelet transforms implies that the wavelet coefficients are not independent of each other. This interdependence allows the reconstruction or approximation of the wavelet transform, and of the original field, from a subset of the wavelet coefficients. Contrasting with lines of modulus maxima, known to provide useful partition functions and some data compaction, the reconstruction from single-scale coefficients is derived for the Hermitian family of wavelets. The formula is exact in the continuum for d-dimensional fields, and its limitations under discretization are illustrated.

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Toda, Hiroshi, Zhong Zhang, and Takashi Imamura. "Perfect-translation-invariant variable-density complex discrete wavelet transform." International Journal of Wavelets, Multiresolution and Information Processing 12, no. 04 (July 2014): 1460001. http://dx.doi.org/10.1142/s0219691314600017.

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The theorems giving the conditions for discrete wavelet transforms (DWTs) to achieve perfect translation invariance (PTI) have already been proven, and based on these theorems, the dual-tree complex DWT and the complex wavelet packet transform, achieving PTI, have already been proposed. However, there is not so much flexibility in their wavelet density. In the frequency domain, the wavelet density is fixed by octave filter banks, and in the time domain, each wavelet is arrayed on a fixed coordinate, and the wavelet packet density in the frequency domain can be only designed by dividing an octave frequency band equally in linear scale, and its density in the time domain is constrained by the division number of an octave frequency band. In this paper, a novel complex DWT is proposed to create variable wavelet density in the frequency and time domains, that is, an octave frequency band can be divided into N filter banks in logarithmic scale, where N is an integer larger than or equal to 3, and in the time domain, a distance between wavelets can be varied in each level, and its transform achieves PTI.

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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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ČASTOVÁ, NINA, DAVID HORÁK, and ZDENĚK KALÁB. "DESCRIPTION OF SEISMIC EVENTS USING WAVELET TRANSFORM." International Journal of Wavelets, Multiresolution and Information Processing 04, no. 03 (September 2006): 405–14. http://dx.doi.org/10.1142/s0219691306001336.

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This paper deals with engineering application of wavelet transform for processing of real seismological signals. Methodology for processing of these slight signals using wavelet transform is presented in this paper. Briefly, three basic aims are connected with this procedure:. 1. Selection of optimal wavelet and optimal wavelet basis B opt for selected data set based on minimal entropy: B opt = arg min B E(X,B). The best results were reached by symmetric complex wavelets with scaling coefficients SCD-6. 2. Wavelet packet decomposition and filtration of data using universal criterion of thresholding of the form [Formula: see text], where σ is minimal variance of the sum of packet decomposition of chosen level. 3. Cluster analysis of decomposed data. All programs were elaborated using program MATLAB 5.

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Indrusiak, M. L. S., A. J. Kozakevicius, and S. V. Möller. "WAVELET ANALYSIS CONSIDERATIONS FOR EXPERIMENTAL NONSTATIONARY FLOW PHENOMENA." Revista de Engenharia Térmica 15, no. 1 (June 30, 2016): 67. http://dx.doi.org/10.5380/reterm.v15i1.62149.

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In this work, wavelet transforms are the analysis tools for studying transient and discontinuous phenomena associated to turbulent flows. The application in quest results from velocity measurements with hot wire anemometry in the transient wake considering a circular cylinder in an aerodynamic channel. Continuous and discrete wavelet transforms are applied and compared with the corresponding results given by the Fourier transform. For the continuous wavelet transform, the Morlet function was adopted as transform basis, and for the discrete case, the Daubechies orthonormal wavelet with 20 null moments. Results using the discrete wavelet packet transform are also presented and compared. A wake past a cylinder was analytically simulated and compared with the actual one, both in transient flow. The ability of the wavelet transforms in the analysis of unsteady phenomena and the potential of the wavelet approach as a complementary tool to the Fourier spectrum for the analysis of stationary phenomena is presented and discussed.

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BAHRI, MAWARDI, and ECKHARD S. M. HITZER. "CLIFFORD ALGEBRA Cl3,0-VALUED WAVELET TRANSFORMATION, CLIFFORD WAVELET UNCERTAINTY INEQUALITY AND CLIFFORD GABOR WAVELETS." International Journal of Wavelets, Multiresolution and Information Processing 05, no. 06 (November 2007): 997–1019. http://dx.doi.org/10.1142/s0219691307002166.

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In this paper, it is shown how continuous Clifford Cl3,0-valued admissible wavelets can be constructed using the similitude group SIM(3), a subgroup of the affine group of ℝ3. We express the admissibility condition in terms of a Cl3,0 Clifford Fourier transform and then derive a set of important properties such as dilation, translation and rotation covariance, a reproducing kernel, and show how to invert the Clifford wavelet transform of multivector functions. We invent a generalized Clifford wavelet uncertainty principle. For scalar admissibility constant, it sets bounds of accuracy in multivector wavelet signal and image processing. As concrete example, we introduce multivector Clifford Gabor wavelets, and describe important properties such as the Clifford Gabor transform isometry, a reconstruction formula, and an uncertainty principle for Clifford Gabor wavelets.

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Chen, Zhi Xin, Xue Dao Shu, Cheng Lin Wang, and Shi Kun Xie. "The Matching Pursuit Method for Extracting Feature Based on DT-CWT and its Application." Applied Mechanics and Materials 37-38 (November 2010): 1497–502. http://dx.doi.org/10.4028/www.scientific.net/amm.37-38.1497.

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A matching pursuit method based on Dual-Tree Complex Wavelet Transform (DT-CWT) is proposed for extracting feature. Many new orthogonal wavelet bases formed Hilbert transform pairs is constructed by the method which is based on the sufficient and necessary condition on constructing wavelet, via the flat delay filter, and translated the problem into resolving algebraic equations. And taking these wavelets as choice object, a matching pursuit method based on DT-CWT is used for extracting feature. The matching pursuit method is based on series expansion of the signal by a set of elementary functions of orthogonal wavelets formed Hilbert transform pairs to match feature more effectively. Simulation testing and field experiments confirm that the proposed method is effective especially in extracting impulsive feature on high intensity noise, which matching pursuit method based on Discrete Wavelet Transform and other wavelet de-noising methods based on threshold and frequency-band, etc cannot do it completely.

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Prosser, R., and R. S. Cant. "The theoretical development of wavelets in reacting flows." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 214, no. 11 (November 1, 2000): 1363–73. http://dx.doi.org/10.1243/0954406001523335.

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This paper focuses on the simulation of turbulent reacting flows via recent developments in wavelet-based analyses. The unique data compression properties of wavelet methods render them especially attractive for such simulations, in which the length and time-scales of interest originate from both physical and chemical processes and may span several orders of magnitude. The particular difficulties encountered when representing reacting flow problems on non-periodic domains, and how these difficulties have led to the adoption of a biorthogonal wavelet framework, are discussed. This leads to consideration of interpolating wavelet transforms based on second-generation wavelets, for which a fast transform algorithm is presented. Issues raised by the application of wavelet transform methods to the reacting Navier-Stokes equations, including the calculation of differential operators, the extension to two and three dimensions and the evaluation of non-linear terms, are examined. The implications of the wavelet approach for the representation of the turbulent energy cascade are explored briefly. Finally, some future directions for research into the extension of wavelet analysis as an underpinning technology for computational fluid dynamics are indicated.

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Ashory, Mohammad-Reza, Ahmad Ghasemi-Ghalebahman, and Mohammad-Javad Kokabi. "Damage detection in laminated composite plates via an optimal wavelet selection criterion." Journal of Reinforced Plastics and Composites 35, no. 24 (September 30, 2016): 1761–75. http://dx.doi.org/10.1177/0731684416667563.

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Delamination is a potential risk of failure considered as one of the failure modes and frequently occurs in composites due to its relatively low inter-laminar fracture toughness. In recent years, the majority of activities in this field have been focused on raising the level of sensitivity of these devising methods for detecting tiny damages. In this article, damage detection method via wavelet transform has been examined, and an appropriate procedure has been proposed to increase sensitivity of this transform for damage detection. Among the inherent impediments of classical wavelet transforms, the generality of these transforms and ignoring the studied signal can be mentioned. Consequently, various wavelet selection algorithms leading to provide appropriate wavelet functions with respect to the characteristics of the signal have been examined. As a novelty in the field, the correlation between wavelet and strain energy signal is considered as a criterion for optimal wavelet selection. In wavelet transforms, in addition to original wavelet functions, the signals used for damage detection are also of high importance. To achieve this goal, the frequency-weighted strain energy ratio signals resulting from intact and damaged forms have been exploited. Also, the edges’ effects were removed through stringing of plane mode shape signals. Moreover, by summing wavelet coefficients in all scale factors plus natural frequencies, the focus can bring to the detection of one or more damages in a laminated composite plate with symmetric layup. Finally, a quantitative measure to compare different wavelets has been presented.

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McAulay, Alastair D. "Optical wavelet transform classifier with positive real Fourier transform wavelets." Optical Engineering 32, no. 6 (1993): 1333. http://dx.doi.org/10.1117/12.135839.

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Watson, J. N., P. S. Addison, and A. Sibbald. "The De-Noising of Sonic Echo Test Data through Wavelet Transform Reconstruction." Shock and Vibration 6, no. 5-6 (1999): 267–72. http://dx.doi.org/10.1155/1999/175750.

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This paper presents the results of feasibility study into the application of the wavelet transform signal processing method to sonic based non-destructive testing techniques. Finite element generated data from cast in situ foundation piles were collated and processed using both continuous and discrete wavelet transform techniques. Results were compared with conventional Fourier based methods. The discrete Daubechies wavelets and the continuous Mexican hat wavelet were used and their relative merits investigated. It was found that both the continuous Mexican hat and discrete Daubechies D8 wavelets were significantly better at locating the pile toe compared than the Fourier filtered case. The wavelet transform method was then applied to field test data and found to be successful in facilitating the detection of the pile toe.

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Taha, Saleem, and Walid Mahmood. "New techniques for Daubechies wavelets and multiwavelets implementation using quantum computing." Facta universitatis - series: Electronics and Energetics 26, no. 2 (2013): 145–56. http://dx.doi.org/10.2298/fuee1302145t.

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In this paper, new techniques to implement the Daubechies wavelets and multiwavelets are presented using quantum computing synthesis structures. Also, a new quantum implementation of inverse Daubechies multiwavelet transform is proposed. The permutation matrices, particular unitary matrices, play a pivotal role. The particular set of permutation matrices arising in quantum wavelet and multiwavelet transforms is considered, and efficient quantum circuits that implement them are developed. This allows the design of efficient and complete quantum circuits for the quantum wavelet and multiwavelet transforms.

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Jansen, Maarten. "Non-equispaced B-spline wavelets." International Journal of Wavelets, Multiresolution and Information Processing 14, no. 06 (November 2016): 1650056. http://dx.doi.org/10.1142/s0219691316500569.

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This paper has three main contributions. The first is the construction of wavelet transforms from B-spline scaling functions defined on a grid of non-equispaced knots. The new construction extends the equispaced, biorthogonal, compactly supported Cohen–Daubechies–Feauveau wavelets. The new construction is based on the factorization of wavelet transforms into lifting steps. The second and third contributions are new insights on how to use these and other wavelets in statistical applications. The second contribution is related to the bias of a wavelet representation. It is investigated how the fine scaling coefficients should be derived from the observations. In the context of equispaced data, it is common practice to simply take the observations as fine scale coefficients. It is argued in this paper that this is not acceptable for non-interpolating wavelets on non-equidistant data. Finally, the third contribution is the study of the variance in a non-orthogonal wavelet transform in a new framework, replacing the numerical condition as a measure for non-orthogonality. By controlling the variances of the reconstruction from the wavelet coefficients, the new framework allows us to design wavelet transforms on irregular point sets with a focus on their use for smoothing or other applications in statistics.

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Prasad, Akhilesh, and U. K. Mandal. "Wavelet transforms associated with the Kontorovich–Lebedev transform." International Journal of Wavelets, Multiresolution and Information Processing 15, no. 02 (February 7, 2017): 1750011. http://dx.doi.org/10.1142/s0219691317500114.

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The main objective of this paper is to study continuous wavelet transform (CWT) using the convolution theory of Kontorovich–Lebedev transform (KL-transform) and discuss some of its basic properties. Plancherel’s as well as Parseval’s relation and Reconstruction formula for CWT are obtained and some examples are also given. The discrete version of the wavelet transform associated with KL-transform is also given and reconstruction formula is derived.

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Low, Yin Fen, and Rosli Besar. "Optimal Wavelet Filters for Medical Image Compression." International Journal of Wavelets, Multiresolution and Information Processing 01, no. 02 (June 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 for implementation in a digitized still medical image compression with different modalities. We used two approaches to the measurement of medical image quality: objectively, using peak signal to noise ratio (PSNR) and subjectively, using perceived image quality. Finally, we defined an optimal wavelet filter for each modality of medical image.

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Stepanov, Andrey. "Polynomial, Neural Network, and Spline Wavelet Models for Continuous Wavelet Transform of Signals." Sensors 21, no. 19 (September 26, 2021): 6416. http://dx.doi.org/10.3390/s21196416.

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In this paper a modified wavelet synthesis algorithm for continuous wavelet transform is proposed, allowing one to obtain a guaranteed approximation of the maternal wavelet to the sample of the analyzed signal (overlap match) and, at the same time, a formalized representation of the wavelet. What distinguishes this method from similar ones? During the procedure of wavelets’ synthesis for continuous wavelet transform it is proposed to use splines and artificial neural networks. The paper also suggests a comparative analysis of polynomial, neural network, and wavelet spline models. It also deals with feasibility of using these models in the synthesis of wavelets during such studies like fine structure of signals, as well as in analysis of large parts of signals whose shape is variable. A number of studies have shown that during the wavelets’ synthesis, the use of artificial neural networks (based on radial basis functions) and cubic splines enables the possibility of obtaining guaranteed accuracy in approaching the maternal wavelet to the signal’s sample (with no approximation error). It also allows for its formalized representation, which is especially important during software implementation of the algorithm for calculating the continuous conversions at digital signal processors and microcontrollers. This paper demonstrates the possibility of using synthesized wavelet, obtained based on polynomial, neural network, and spline models, during the performance of an inverse continuous wavelet transform.

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Fajardo, Carlos, Oscar Mauricio Reyes, and Ana Ramirez. "Seismic Data Compression Using 2D Lifting-Wavelet Algorithms." Ingeniería y Ciencia 11, no. 21 (January 30, 2015): 221–38. http://dx.doi.org/10.17230/ingciencia.11.21.11.

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Different seismic data compression algorithms have been developed in or-der to make the storage more efficient, and to reduce both the transmission time and cost. In general, those algorithms have three stages: transforma-tion, quantization and coding. The Wavelet transform is highly used tocompress seismic data, due to the capabilities of the Wavelets on representing geophysical events in seismic data. We selected the lifting scheme to implement the Wavelet transform because it reduces both computational and storage resources. This work aims to determine how the transforma-tion and the coding stages affect the data compression ratio.Several 2Dlifting-based algorithms were implemented to compress three different seis-mic data sets. Experimental results obtained for different filter type, filterlength, number of decomposition levels and coding scheme, are presented in this work.

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Ghasemi-Ghalebahman, Ahmad, Mohammad-Reza Ashory, and Mohammad-Javad Kokabi. "A proper lifting scheme wavelet transform for vibration-based damage identification in composite laminates." Journal of Thermoplastic Composite Materials 31, no. 5 (July 6, 2017): 668–88. http://dx.doi.org/10.1177/0892705717718239.

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Damage detection using the wavelet transform was investigated and appropriate approaches to raising the method’s sensitivity level were proposed. In addition, the current study attempted to implement the impulse wavelet design algorithm in order to present appropriate wavelet function with respect to the characteristics of the signal. The initial wavelet function corresponding to the impulse response of composite plate was achieved using impulse wavelet algorithm in time domain. The function was optimized using lifting scheme method. To detect damages, an appropriate signal was selected through applying wavelet transform. To enhance damage identification, first, the edges’ effect of wavelet transform was removed, then a higher accuracy was observed by summing the wavelet coefficients in all scale factors for each mode shape and the wavelet coefficients for all mode shapes. The article also presents a quantitative measure to compare different wavelets.

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Bochkarev, A. V. "Resolving of Overlapping Asymmetrical Chromatographic Peaks by Using Wavelet-Transform and Gram-Charlier Peak Model." Journal of Physics: Conference Series 2096, no. 1 (November 1, 2021): 012068. http://dx.doi.org/10.1088/1742-6596/2096/1/012068.

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Abstract The paper describes a method for resolving overlapping asymmetric peaks that make up a chromatogram. The presented method uses the Gram-Charlier model in the form of the first three terms of the Gram-Charlier series as a basis. Using the wavelet transform, the parameters of this model are determined, which is used to describe a single or overlapping chromatographic peak. Hermitian wavelets of the first four orders are used in the computation of the wavelet transform. To speed up the computation of multiple wavelet transforms, the possibility of coding a signal using the Chebyshev-Hermite functions is considered in order to further restore the set of wavelet transforms simultaneously. According to the presented method, the parameters of the peaks are determined by analytical expressions without using the numerical approximation of the chromatogram by the peak model, which avoids the disadvantages of the numerical approach. The resulting method is used to resolve overlapping asymmetric peaks. The advantage of the method over others is shown by calculating the area of each of the resolved peaks.

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Pandey, J. N., N. K. Jha, and O. P. Singh. "The continuous wavelet transform in n-dimensions." International Journal of Wavelets, Multiresolution and Information Processing 14, no. 05 (August 24, 2016): 1650037. http://dx.doi.org/10.1142/s0219691316500375.

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Daubechies obtained the [Formula: see text]-dimensional inversion formula for the continuous wavelet transform of spherically symmetric wavelets in [Formula: see text] with convergence interpreted in the [Formula: see text]-norm. From the wavelet [Formula: see text], Daubechies generated a doubly indexed family of wavelets [Formula: see text] by restricting the dilation parameter [Formula: see text] to be a real number greater than zero and the translation parameter [Formula: see text] belonging to [Formula: see text]. We show that [Formula: see text] can be chosen to be in [Formula: see text] with none of the components [Formula: see text] vanishing. Further, we prove that if [Formula: see text] and [Formula: see text] are continuous in [Formula: see text], then the convergence besides being in [Formula: see text] is also pointwise in [Formula: see text]. We advance our theory further to the case when [Formula: see text] and [Formula: see text] both belong to [Formula: see text] then convergence of the wavelet inversion formula is pointwise at all points of continuity of [Formula: see text]. This result significantly enhances the applicability of the wavelet inversion formula to the image processing.

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Liu, Shu-Guang, Jun-Hua Chen, and Hong-Yi Fan. "Wavelet transform for Fresnel-transformed mother wavelets." Chinese Physics B 20, no. 12 (December 2011): 120305. http://dx.doi.org/10.1088/1674-1056/20/12/120305.

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Mabrouk, Anouar Ben, and Imen Rezgui. "On some $q$-Bessel type continuous wavelet transform." Boletim da Sociedade Paranaense de Matemática 42 (May 22, 2024): 1–19. http://dx.doi.org/10.5269/bspm.62547.

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In this paper we continue as in \cite{Rezguietal} to exploit the modified variants of Bessel function in the framework of $q$-theory to construct wavelet operators. A generalized $q$-Bessel type function has been introduced leading to an associated mother wavelet which in turns has induced a continuous wavelet transform. Finally, Plancherel/Parceval type relations have been proved. Such variants of wavelets permit in some sense to approximate solutions of ODEs and PDEs by transforming them to recurrent sequences.

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Journal articles on the topic 'Wavelet transform'

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