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Journal articles on the topic 'Wave Transform'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

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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Prasad, Akhilesh, Praveen Kumar, and Tanuj Kumar. "Product of continuous fractional wave packet transforms." International Journal of Wavelets, Multiresolution and Information Processing 17, no. 04 (2019): 1950021. http://dx.doi.org/10.1142/s0219691319500218.

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In this paper, we investigated the fractional Fourier transform (FrFT) of the continuous fractional wave packet transform and studied some properties of continuous fractional wave packet transform. The product of continuous fractional wave packet transforms (CFrWPTs) is defined. Parseval’s relation and an inversion formula for product of CFrWPT are obtained. An example is also given.

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Tiscareno, Matthew S., and Matthew M. Hedman. "A review of Morlet wavelet analysis of radial profiles of Saturn's rings." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2126 (2018): 20180046. http://dx.doi.org/10.1098/rsta.2018.0046.

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Spiral waves propagating in Saturn's rings have wavelengths that vary with radial position within the disc. The best-quality observations of these waves have the form of radial profiles centred on a particular azimuth. In that context, the wavelength of a given spiral wave is seen to change substantially with position along the one-dimensional profile. In this paper, we review the use of Morlet wavelet analysis to understand these waves. When signal to noise is high and the cause of the wave is well understood, wavelet analysis has been used to solve for wave parameters that are diagnostic of

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Srivastava, Hari M., Firdous A. Shah та Waseem Z. Lone. "Quadratic-Phase Wave-Packet Transform in L2(ℝ)". Symmetry 14, № 10 (2022): 2018. http://dx.doi.org/10.3390/sym14102018.

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Wavelet transform is a powerful tool for analysing the problems arising in harmonic analysis, signal and image processing, sampling, filtering, and so on. However, they seem to be inadequate for representing those signals whose energy is not well concentrated in the frequency domain. In pursuit of representations of such signals, we propose a novel time-frequency transform coined as quadratic-phase wave packet transform in L2(R). The proposed transform is aimed at rectifying the conventional wavelet transform by employing a quadratic-phase Fourier transform with extra degrees of freedom. Besid

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Jian-Yu Lu and Anjun Liu. "An X wave transform." IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 47, no. 6 (2000): 1472–81. http://dx.doi.org/10.1109/58.883537.

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Hudspeth, Robert T., and Josep R. Medina. "WAVE GROUP ANALYSIS BY THE HILBERT TRANSFORM." Coastal Engineering Proceedings 1, no. 21 (1988): 66. http://dx.doi.org/10.9753/icce.v21.66.

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A methodology based on linear theory is presented for analyzing wave groups from a random sea representation in the complex plane. A wave height function [H(t)], a local frequency function, [0(t)] , and an orbital velocity function [V(t)] are defined from the Hilbert transform of the sea surface elevation. Envelopes computed by the Hilbert transform are compared with the SIWEH. A three axes representation of the mean lengths of runs of waves is employed to compare the lengths of runs computed by the discrete wave method with runs computed by the Hilbert transform method.

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Li, Xiang‐Yang, and Stuart Crampin. "Linear‐transform techniques for processing shear‐wave anisotropy in four‐component seismic data." GEOPHYSICS 58, no. 2 (1993): 240–56. http://dx.doi.org/10.1190/1.1443409.

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Most published techniques for analyzing shear‐wave splitting tend to be computing intensive, and make assumptions, such as the orthogonality of the two split shear waves, which are not necessarily correct. We present a fast linear‐transform technique for analyzing shear‐wave splitting in four‐component (two sources/ two receivers) seismic data, which is flexible and widely applicable. We transform the four‐component data by simple linear transforms so that the complicated shear‐wave motion is linearized in a wide variety of circumstances. This allows various attributes to be measured, includin

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Harada, Ken, Yoshimasa A. Ono, and Yoshio Takahashi. "Lensless Fourier transform electron holography applied to vortex beam analysis." Microscopy 69, no. 3 (2020): 176–82. http://dx.doi.org/10.1093/jmicro/dfaa008.

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Abstract Lensless Fourier transform holography has been developed. By treating Bragg diffraction waves as object waves and a transmitted spherical wave as a reference wave, these two waves are interfered and recorded as holograms away from the reciprocal plane. In this method, reconstruction of holograms requires only one Fourier transform. Application of this method to analyze vortex beams worked well and their amplitude and phase distributions were obtained on the reciprocal plane. By combining the conventional holography with the developed lensless Fourier transform holography, we can recon

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Lu, Jian Qi, Shan You Li та Wei Li. "Surface Wave Dispersion Imaging Using Improved τ-p Transform Approach". Applied Mechanics and Materials 353-356 (серпень 2013): 1196–202. http://dx.doi.org/10.4028/www.scientific.net/amm.353-356.1196.

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Surface wave dispersion imaging approach is crucial for multi-channel analysis of surface wave (MASW). Because the resolution of inversed S-wave velocity and thickness of a layer are directly subjected to the resolution of imaged dispersion curve. The τ-p transform approach is an efficient and commonly used approach for Rayleigh wave dispersion curve imaging. However, the conventional τ-p transform approach was severely affected by waves amplitude. So, the energy peaks of f-v spectrum were mainly gathered in a narrow frequency range. In order to remedy this shortage, an improved τ-p transform

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10

He, Chenxi. "The Use of Fourier Transform in Heat Equation and Wave Equation." Highlights in Science, Engineering and Technology 38 (March 16, 2023): 558–67. http://dx.doi.org/10.54097/hset.v38i.5881.

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In the solve for the equation for heat transfer and wave movement, using Fourier Transform to simplify the differential equation and solve it. With the periodic property of the wave including standing wave and vibrating string and heat equation and its stable solution, it can provide many new properties of the equation. Then using the same method to solve the heat equation in space, it gives a similar equation like the plane heat transfer equation. The passage mainly discussed about using Fourier transform to solve standing waves equation heat equation in steady state and in the time dependent

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Li, Peilu, Chunguang Xu, Qinxue Pan, Yuren Lu, and Shuangyi Li. "Denoising of LCR Wave Signal of Residual Stress for Rail Surface Based on Lifting Scheme Wavelet Packet Transform." Coatings 11, no. 5 (2021): 496. http://dx.doi.org/10.3390/coatings11050496.

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According to the acousto elastic effect, the residual stress on the surface of the rail can be evaluated by measuring the change in the propagation velocity of ultrasonic waves, such as longitudinal critically refracted (LCR) waves on the surface of the rail. The LCR wave signal is often polluted by a variety of noise sources, coupled with the influence of the poor surface condition of the inspected component, which greatly reduces the detectability and online measurement ability of the LCR wave signal. This paper proposes the application of the lifting scheme wavelet packet transform (LSWPT)

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Adnan K. Al-Salihi and F. Yahya. "Exact Solution of One–Dimension Damping Wave Equation Using Laplace Transforms." Albaydha University Journal 1, no. 1 (2019): 97–104. http://dx.doi.org/10.56807/buj.v1i1.10.

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In this work, the exact solution of vibrating problem described by one dimensional damped wave equation using Laplace Transform is presented. The motion of an elastic fixed ends string which are subjected to a drag force has been investigated. In addition, the role of the initial displacement has been discussed and the exact solution obtained is illustrated and graphically presented. Keywords: Laplace transforms - damping waves.

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Er., Balwinder Singh* Er. Surekha Rani. "PUNJABI CHARACTER RECOGNITION USING WAVELET AND CURVLET TECHNIQUES WITH SIFT ALGORITHM." INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY 5, no. 6 (2016): 833–37. https://doi.org/10.5281/zenodo.56025.

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There are many techniques used to recognise the characters and out of these one is named as curve let technique and other is wavelet technique. The Punjabi characters has different type of patterns as compared to English characters. Curve let is a non- adaptive technique for multi scale object representation and curved singularities can be well approximated with very few coefficients and remain coherent waveforms under the action of the wave equation in a smooth medium. Standard wave let transforms for two dimensional functions have only very crude capabilities to resolve directional features.

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Kamashev, A. M., A. A. Duchkov, and G. S. Chernyshov. "Development of an algorithm for the suppression of multiple based on the decomposition of seismic data into wave packets." Russian Journal of Geophysical Technologies, no. 3 (January 28, 2022): 28–40. http://dx.doi.org/10.18303/10.18303/2619-1563-2021-3-28.

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This paper presents a multiple suppression algorithm based on the decomposition of seismic data into wave packets. The algorithm is based on high-resolution Radon transform and Gaussian wave packets transform. High-resolution Radon transform allows you to separate single and multiple reflected waves due to the increased resolution of the transformation in comparison with the standard approach. Having selected multiples in the Radon region, the task is set to correctly subtract them from the original seismic record. Decomposition into Gaussian wave packets allows adaptive subtraction of multipl

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Kamashev, A. M., A. A. Duchkov, and G. S. Chernyshov. "Development of an algorithm for the suppression of multiple based on the decomposition of seismic data into wave packets." Russian Journal of Geophysical Technologies, no. 3 (January 28, 2022): 28–40. http://dx.doi.org/10.18303/2619-1563-2021-3-28.

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This paper presents a multiple suppression algorithm based on the decomposition of seismic data into wave packets. The algorithm is based on high-resolution Radon transform and Gaussian wave packets transform. High-resolution Radon transform allows you to separate single and multiple reflected waves due to the increased resolution of the transformation in comparison with the standard approach. Having selected multiples in the Radon region, the task is set to correctly subtract them from the original seismic record. Decomposition into Gaussian wave packets allows adaptive subtraction of multipl

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Kamashev, A. M., A. A. Duchkov, and G. S. Chernyshov. "Development of an algorithm for the suppression of multiple based on the decomposition of seismic data into wave packets." Russian Journal of Geophysical Technologies, no. 3 (January 28, 2022): 28–40. http://dx.doi.org/10.18303//2619-1563-2021-3-28.

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This paper presents a multiple suppression algorithm based on the decomposition of seismic data into wave packets. The algorithm is based on high-resolution Radon transform and Gaussian wave packets transform. High-resolution Radon transform allows you to separate single and multiple reflected waves due to the increased resolution of the transformation in comparison with the standard approach. Having selected multiples in the Radon region, the task is set to correctly subtract them from the original seismic record. Decomposition into Gaussian wave packets allows adaptive subtraction of multipl

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Baranski, Andrzej, and Agata Szulborska. "Fourier transform square-wave voltammetry." Journal of Electroanalytical Chemistry 373, no. 1-2 (1994): 157–65. http://dx.doi.org/10.1016/0022-0728(94)03319-6.

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Lu, Jian Xu, and Cheng Jia Ma. "Research on Electrical Engineering with a New Fault Location Method of Double Terminal Based on HHT." Advanced Materials Research 1003 (July 2014): 124–29. http://dx.doi.org/10.4028/www.scientific.net/amr.1003.124.

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Among the available fault location methods based on traveling waves, calibrations of wave velocity and wave arrival time are the two main problems. This paper proposes a new fault location method which combines the two problems mentioned above. In this method, the first wave and second wave obtained at one side and the first wave obtained at the other side is used to locate the fault point. And the Hilbert-Huang transform is used in the calibration of wave arrival time, making the method more accurate than using wavelet transform. This method has the following two advantages: At first, it dism

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Sedeeg, Abdelilah Kamal H. "Some Properties and Applications of a New General Triple Integral Transform “Gamar Transform’’." Complexity 2023 (April 29, 2023): 1–21. http://dx.doi.org/10.1155/2023/5527095.

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The goal of this study is to suggest a new general triple integral transform known as Gamar transform. Next, we compare the current transform to a number of existing triple integral transforms such as those by Laplace, Sumudu, Elzaki, Aboodh, and Laplace–Aboodh–Sumudu. We outline its essential properties and prove some important results, including linearity property, existence theorem, triple convolution theorem, and derivatives properties. Moreover, the proposed new transform is applied to solve some partial differential equations (PDEs) such as Laplace, Mboctara, and Wave equations. The capa

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Sun, Daozhong, Yunhua Wang, Feng Luo, and Xianxian Luo. "A New Quasi-Linear Integral Transform Between Ocean Wave Spectrum and Phase Spectrum of an XTI-SAR." Remote Sensing 17, no. 10 (2025): 1790. https://doi.org/10.3390/rs17101790.

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Cross-Track Interferometric Synthetic Aperture Radar (XTI-SAR) can utilize variations in interferometric phase to measure sea surface velocity along radar radial direction and sea surface height, which can be used for ocean wave parameter inversion. However, research on the imaging mechanisms of XTI-SAR systems for ocean waves remains understudied, and there are still some problems in its perception. To further study the imaging mechanism of XTI-SAR measurement systems for ocean waves, this paper describes research based on the nonlinear integral transform model and the quasi-linear integral t

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Ziani, Said. "Contribution to Single-Channel Fetal Electrocardiogram Identification." Traitement du Signal 39, no. 6 (2022): 2055–60. http://dx.doi.org/10.18280/ts.390617.

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This paper presents the recognition of fetal ECG signals from a single-channel recording. The Continuous Wavelet Transform generates a two-dimensional representation of a single-dimension input containing fetal electrocardiogram waves, which are accurately located and isolated. By segmenting this 2D representation using Otsu's method, the continuous wavelet transform of each wave may be estimated. The temporal expression of the wave is then rebuilt by calculating the Inverse Continuous Wavelet Transform. The continuity between each sample allows us to follow the waves from one image to the nex

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Wu, Li-Chung, Beng-Chun Lee, Chia Chuen Kao, Dong-Jiing Doong, and Chih-Chiang Chang. "APPLYING THE WAVELET TRANSFORM TO STUDY THE FEATURES OF FREAK WAVES." Coastal Engineering Proceedings 1, no. 32 (2011): 69. http://dx.doi.org/10.9753/icce.v32.waves.69.

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The issues of freak waves are more and more popular since the late 1980s. This study tries to use the wavelet scalogram of freak wave records to investigate the energy characteristics during the occurrence of the freak waves. Through the analysis of the wave energy and phase, it is found that as freak waves occur, the component waves will lead to constructive superposition due to similar phases. The wavelet scalogram provides the other idea to explain the feature of freak waves.

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Serdyukov, Aleksander S. "Ground-roll extraction using the Karhunen-Loeve transform in the time-frequency domain." GEOPHYSICS 87, no. 2 (2022): A19—A24. http://dx.doi.org/10.1190/geo2021-0453.1.

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Ground-roll suppression is critical for seismic reflection data processing. Many standard methods, i.e., f-k fan filtering, fail when spatially aliased surface wave interference is present in the data. Spatial aliasing is a common problem; receiver spacing is often not dense enough to extract wavenumbers of low-velocity surface waves. It has long been known that the Karhunen-Loeve (KL) transform can be used to suppress aliased ground roll. However, the ground roll should be flattened before suppression, which is challenging due to the dispersion of surface wave velocities. I propose to solve t

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Zhou, Binzhong, та Stewart A. Greenhalgh. "Linear and parabolic τ-p transforms revisited". GEOPHYSICS 59, № 7 (1994): 1133–49. http://dx.doi.org/10.1190/1.1443669.

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New derivations for the conventional linear and parabolic τ-p transforms in the classic continuous function domain provide useful insight into the discrete τ-p transformations. For the filtering of unwanted waves such as multiples, the derivation of the τ-p transform should define the inverse transform first, and then compute the forward transform. The forward transform usually requires a p‐direction deconvolution to improve the resolution in that direction. It aids the wave filtering by improving the separation of events in the τ-p domain. The p‐direction deconvolution is required for both th

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Sedeeg, Abdelilah Kamal, Zahra I. Mahamoud, and Rania Saadeh. "Using Double Integral Transform (Laplace-ARA Transform) in Solving Partial Differential Equations." Symmetry 14, no. 11 (2022): 2418. http://dx.doi.org/10.3390/sym14112418.

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The main goal of this research is to present a new approach to double transforms called the double Laplace–ARA transform (DL-ARAT). This new double transform is a novel combination of Laplace and ARA transforms. We present the basic properties of the new approach including existence, linearity and some results related to partial derivatives and the double convolution theorem. To obtain exact solutions, the new double transform is applied to several partial differential equations such as the Klein–Gordon equation, heat equation, wave equation and telegraph equation; each of these equations has

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Shah, Firdous, and Aajaz Teali. "Two-sided quaternion wave-packet transform and the quantitative uncertainty principles." Filomat 36, no. 2 (2022): 449–67. http://dx.doi.org/10.2298/fil2202449s.

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In this article, we introduce the notion of two-sided quaternion wave-packet transform which inherits the advantages of both the quaternion windowed Fourier and wavelet transforms with some additional promising features. The preliminary analysis encompasses the derivation of fundamental properties including, orthogonality relation, energy preserving relation, inversion formula and the range theorem by utilizing the machinery of two-sided quaternion Fourier transforms. Besides, we also derive the Heisenberg?s and logarithmic uncertainty principles for the proposed transform. We culminate our in

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Zimmerman, W. B., and G. W. Haarlemmer. "Internal gravity waves: Analysis using the periodic, inverse scattering transform." Nonlinear Processes in Geophysics 6, no. 1 (1999): 11–26. http://dx.doi.org/10.5194/npg-6-11-1999.

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Abstract. The discrete periodic inverse scattering transform (DPIST) has been shown to provide the salient features of nonlinear Fourier analysis for surface shallow water waves whose dynamics are governed by the Korteweg-de Vries (KdV) equation - (1) linear superposition of components with power spectra that are invariants of the motion of nonlinear dispersive waves and (2) nonlinear filtering. As it is well known that internal gravity waves also approximately satisfy the KdV equation in shallow stratified layers, this paper investigates the degree to which DPIST provides a useful nonlinear s

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Oleinik, Phelype Haron, Gabriel Pereira Tavares, Bianca Neves Machado, and Liércio André Isoldi. "Transformation of Water Wave Spectra into Time Series of Surface Elevation." Earth 2, no. 4 (2021): 997–1005. http://dx.doi.org/10.3390/earth2040059.

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Spectral wave modelling is widely used to simulate large-scale wind–wave processes due to its low computation cost and relatively simpler formulation, in comparison to phase-resolving or hydrodynamic models. However, some applications require a time-domain representation of sea waves. This article proposes a methodology to transform the wave spectrum into a time series of water surface elevation for applications that require a time-domain representation of ocean waves. The proposed method uses a generated phase spectrum and the inverse Fourier transform to turn the wave spectrum into a time se

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Su, Shanjie, Feng Gao, Zekai Wang, and Menglin Du. "Applications of the Fourier-like integral transform in the wave and heat-transfer problems." Thermal Science 23, Suppl. 3 (2019): 703–9. http://dx.doi.org/10.2298/tsci180520084s.

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In this article, some new properties of a novel integral transform termed the Fourier-Yang are explored. The Fourier-Yang integral transforms of several basic functions are given firstly. With the aid of the new integral transform, a 1-D wave equation and 2-D heat transfer equation are solved. The results show that the Fourier-Yang integral transform is efficient in solving PDE.

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Hu, Chen, and Ke Ding. "Thin Plate Damage Analysis Based on Transient Displacement Response." Academic Journal of Science and Technology 15, no. 1 (2025): 249–58. https://doi.org/10.54097/v2k3e487.

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This study systematically simulates and analyzes the dynamic response of a thin plate structure under different damage conditions based on a transient model, aiming to evaluate the performance of Wave Atom transform, wavelet packet transform, and Curvelet transform in damage detection. By applying random initial displacement excitations to the thin plate structure and using optimized load step settings, the impact of different damage severities, damage ranges, boundary damage, and damage spacing on the dynamic response of the structure is analyzed. The results show that both Wave Atom and Curv

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Serdyukov, Aleksander S., Aleksander V. Yablokov, Anton A. Duchkov, Anton A. Azarov, and Valery D. Baranov. "Slant f-k transform of multichannel seismic surface wave data." GEOPHYSICS 84, no. 1 (2019): A19—A24. http://dx.doi.org/10.1190/geo2018-0430.1.

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We have addressed the problem of estimating surface-wave phase velocities through the spectral processing of seismic data. This is the key step of the well-known near-surface seismic exploration method, called multichannel analysis of surface waves. To increase the accuracy and ensure the unambiguity of the selection of dispersion curves, we have developed a new version of the frequency-wavenumber ([Formula: see text]-[Formula: see text]) transform based on the S-transform. We obtain the frequency-time representation of seismic data. We analyze the obtained S-transform frequency-time represent

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Yoshikawa, Kogo, and Gen Nakamura. "Model Independent MRE Data Analysis." Computational and Mathematical Methods in Medicine 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/912920.

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For the diagnosing modality called MRE (magnetic resonance elastography), the displacement vector of a wave propagating in a human tissue can be measured. The average of the local wavelength from this measured data could be an index for the diagnosing, because the local wave length becomes larger when the tissue is stiffer. By assuming that the local form of the wave is given approximately as multiple complex plane waves, we identify the real part of the complex linear phase of the strongest plane wave of this multiple complex plane waves, by first applying the FBI transform (Fourier-Bros-Iago

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Abo-Seida, O. M., and R. J. Pirjola. "Transient behaviour of magnetic and electric fields at any height above an atmospheric duct." Canadian Journal of Physics 86, no. 9 (2008): 1103–7. http://dx.doi.org/10.1139/p08-048.

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We model the atmosphere by a surface duct underlying a half-space. A derivation is given for the electromagnetic field created by a vertical magnetic dipole, in the half-space above the duct, with an arbitrary time-varying moment. The method used for the solution is essentially based on the application of two functional transforms. Starting from the wave equation for the magnetic field and applying a Laplace transform in time, we obtain a two-dimensional Fourier transform in the horizontal spatial coordinates leading to an integral representation of the solution of the wave equation in the tra

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Veltcheva, Albena D., and C. Guedes Soares. "Analysis of Abnormal Wave Records by the Hilbert–Huang Transform Method." Journal of Atmospheric and Oceanic Technology 24, no. 9 (2007): 1678–89. http://dx.doi.org/10.1175/jtech2067.1.

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Abstract The Hilbert–Huang transform method is used in this work to analyze wave records from the North Sea, which include abnormal waves. The analysis of the characteristics of abnormal waves is based on the local decomposition of wave data by using the intrinsic mode functions. The variations of amplitude of intrinsic mode functions around the time of the occurrence of abnormal waves are examined in order to investigate the contribution of different intrinsic mode functions on the abnormal waves’ profile, in an attempt to find relationships between them. The changes of local frequency of eac

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Cho, H., G. A. Kardomateas, and C. S. Valle. "Elastodynamic Solution for the Thermal Shock Stresses in an Orthotropic Thick Cylindrical Shell." Journal of Applied Mechanics 65, no. 1 (1998): 184–93. http://dx.doi.org/10.1115/1.2789024.

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An elastodynamic solution for the thermal shock stresses in an orthotropic thick cylindrical shell is presented. The solution is achieved by the proper usage of integral transforms such as the finite Hankel transform and the Laplace transform. No restrictive assumptions on the shell thickness are placed. Results are presented for the well-formed wave propagation phenomenon of elastic stresses through the thickness of an orthotropic thick cylindrical shell. Thermal shock stresses become of significant magnitude due to stress wave propagation which is initiated at the boundaries by sudden therma

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Pinnegar, C. Robert, and Lalu Mansinha. "The S‐transform with windows of arbitrary and varying shape." GEOPHYSICS 68, no. 1 (2003): 381–85. http://dx.doi.org/10.1190/1.1543223.

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The S‐transform is an invertible time‐frequency spectral localization technique which combines elements of wavelet transforms and short‐time Fourier transforms. In previous usage, the frequency dependence of the analyzing window of the S‐transform has been through horizontal and vertical dilations of a basic functional form, usually a Gaussian. In this paper, we present a generalized S‐transform in which two prescribed functions of frequency control the scale and the shape of the analyzing window, and apply it to determining P‐wave arrival time in a noisy seismogram. The S‐transform is also us

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Yen, David H. Y. "Green's Function for the Damped Wave Equation on a Finite Interval Subject to Two Robin Boundary Conditions." Journal of Mechanics 19, no. 1 (2003): 257–62. http://dx.doi.org/10.1017/s1727719100004299.

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ABSTRACTThe Green's function for the damped wave equation on a finite interval subject to two Robin boundary conditions is studied. The problem for a semi-infinite interval with one Robin boundary is considered first by the Laplace transform method to establish the reflection principle at a Robin boundary. It is seen that the reflected wave generated by an exiting wave at a Robin boundary is a convolution involving the exiting wave and some kernel function. This generalizes the well known classical results for reflections at Dirichlet and Neumann boundaries. The reflection principle at a Robin

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Kumari, Kiranta, P. Gupta, and G. Shanker. "Coupling of Laplace Transform and Differential Transform for Wave Equations." Physical Science International Journal 9, no. 4 (2016): 1–10. http://dx.doi.org/10.9734/psij/2016/23357.

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Ma, Jianqing, and Qingchun Li. "Surface Wave Suppression with Joint S Transform and TT Transform." Procedia Earth and Planetary Science 3 (2011): 246–52. http://dx.doi.org/10.1016/j.proeps.2011.09.090.

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Li, Yuan-Min, and Deyun Wei. "The wave packet transform associated with the linear canonical transform." Optik 126, no. 21 (2015): 3168–72. http://dx.doi.org/10.1016/j.ijleo.2015.07.103.

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Hassan, Hany N., and Hassan K. Saleh. "The Solution of the Regularized Long Wave Equation Using the Fourier Leap-Frog Method." Zeitschrift für Naturforschung A 65, no. 4 (2010): 268–76. http://dx.doi.org/10.1515/zna-2010-0402.

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An efficient numerical method is developed for solving nonlinear wave equations by studying the propagation and stability properties of solitary waves (solitons) of the regularized long wave (RLW) equation in one space dimension using a combination of leap frog for time dependence and a pseudospectral (Fourier transform) treatment of the space dependence. Our schemes follow very accurately these solutions, which are given by simple closed formulas. Studying the interaction of two such solitons and three solitary waves interaction for the RLW equation. Our implementation employs the fast Fourie

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Hu, Liang‐Zie, and George A. McMechan. "Wave‐field transformations of vertical seismic profiles." GEOPHYSICS 52, no. 3 (1987): 307–21. http://dx.doi.org/10.1190/1.1442305.

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Vertical seismic profile (VSP) data may be partitioned in a variety of ways by application of wave‐field transformations. These transformations provide insights into the nature of the data and aid in the design of processing operations. Transformations are implemented in a reversible sequence that takes the observed VSP data from the depth‐time (z-t) domain through the slowness‐time intercept (p-τ) domain (by a slant stack), to the slowness‐frequency (p-ω) domain (by a 1-D Fourier transform over τ), to the wavenumber‐frequency (k-ω) domain (by resampling using the Fourier central‐slice theorem

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Brühl, Markus, and Hocine Oumeraci. "ANALYSIS OF SOLITON FISSION OVER A SUBMERGED STRUCTURE USING “NONLINEAR FOURIER TRANSFORM (NLFT)”." Coastal Engineering Proceedings 1, no. 32 (2011): 59. http://dx.doi.org/10.9753/icce.v32.waves.59.

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When a single incident solitary wave passes over a submerged reef, it disintegrates into a train of solitons (soliton fission), followed by a train of oscillatory waves. One of the major problems in the analysis of the recorded time series is the uncertain identification of the number of solitons N in the transmitted wave train behind the reef due to the difficulties to distinguish between solitons and oscillatory waves, especially in the case of breaking waves. With the “nonlinear Fourier transform (NLFT)”, an application of the inverse scattering transform (IST) of the Korteweg-de Vries equa

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Ghaani Farashahi, Arash. "Wave Packet Transform over Finite Fields." Electronic Journal of Linear Algebra 30 (February 8, 2015): 507–29. http://dx.doi.org/10.13001/1081-3810.2903.

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In this article we introduce the notion of finite wave packet groups over finite fields as the finite group of dilations, translations, and modulations. Then we will present a unified theoretical linear algebra approach to the theory of wave packet transform (WPT) over finite fields. It is shown that each vector defined over a finite field can be represented as a coherent sum of finite wave packet group elements as well.

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Duquet, Bertrand, and Kurt J. Marfurt. "Filtering coherent noise during prestack depth migration." GEOPHYSICS 64, no. 4 (1999): 1054–66. http://dx.doi.org/10.1190/1.1444613.

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We can often suppress short‐period multiples by predictive deconvolution. We can often suppress coherent noise with significantly different moveout by time‐invariant dip filtering on common‐shot, common‐receiver or NMO-corrected common‐midpoint gathers. Unfortunately, even time variant dip filtering on NMO-corrected data breaks down in the presence of strong lateral velocity variation where the underlying NMO correction breaks down. Underattenuated multiples, converted waves, and diffracted head waves can significantly impede and/or degrade prestack migration‐driven velocity analysis and ampli

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Kikuchi, Kazuyoshi, and Bin Wang. "Spatiotemporal Wavelet Transform and the Multiscale Behavior of the Madden–Julian Oscillation*." Journal of Climate 23, no. 14 (2010): 3814–34. http://dx.doi.org/10.1175/2010jcli2693.1.

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Abstract Meteorological and geophysical phenomena involve multiple-scale processes. Here the spatiotemporal wavelet transform (STWT) is applied to detect significant, nonstationary, wave propagation signals from a time–space domain. One of the major advantages of the STWT is the capability to localize the wave properties in both space and time, which facilitates the study of interactions among multiple-scale disturbances by providing relevant information about energy concentration at a given time and space. The global wavelet spectrum (scalogram) of the STWT, which gives an integrated view of

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Shah, Nehad Ali, Essam R. El-Zahar, Ali Akgül, Adnan Khan, and Jeevan Kafle. "Analysis of Fractional-Order Regularized Long-Wave Models via a Novel Transform." Journal of Function Spaces 2022 (June 6, 2022): 1–16. http://dx.doi.org/10.1155/2022/2754507.

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A new integral transform method for regularized long-wave (RLW) models having fractional-order is presented in this study. Although analytical approaches are challenging to apply to such models, semianalytical or numerical techniques have received much attention in the literature. We propose a new technique combining integral transformation, the Elzaki transform (ET), and apply it to regularized long-wave equations in this study. The RLW equations describe ion-acoustic waves in plasma and shallow water waves in seas. The results obtained are extremely important and necessary for describing var

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Askelson, Mark A., and Jerry M. Straka. "Response Functions for Arbitrary Weight Functions and Data Distributions. Part I: Framework for Interpreting the Response Function." Monthly Weather Review 133, no. 8 (2005): 2117–31. http://dx.doi.org/10.1175/mwr2961.1.

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Abstract The response function is a commonly used measure of analysis scheme properties. Its use in the interpretation of analyses of real-valued data, however, is unnecessarily complicated by the structure of the standard form of the Fourier transform. Specifically, interpretation using this form of the Fourier transform requires knowledge of the relationship between Fourier transform values that are symmetric about the origin. Here, these relationships are used to simplify the application of the response function to the interpretation of analysis scheme properties. In doing so, Fourier trans

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Wu, Ning, Yue Li, and Baojun Yang. "Surface wave attenuation of seismic records with the co-core trace transform filter." GEOPHYSICS 76, no. 6 (2011): V115—V128. http://dx.doi.org/10.1190/geo2010-0010.1.

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To remove surface waves from seismic records while preserving other seismic events of interest, we introduced a transform and a filter based on recent developments in image processing. The transform can be seen as a weighted Radon transform, in particular along linear trajectories. The weights in the transform are data dependent and designed to introduce large amplitude differences between surface waves and other events such that surface waves could be separated by a simple amplitude threshold. This is a key property of the filter and distinguishes this approach from others, such as convention

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Wei, Deyun, and Yijie Zhang. "A new fractional wave packet transform." Optik 231 (April 2021): 166357. http://dx.doi.org/10.1016/j.ijleo.2021.166357.

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