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Lebedev–Skalskaya Transform Related Continuous Wavelet Transform
Results in MathematicsThe paper deals with the continuous wavelet transform (CWT) in the context of the Lebedev-Skalskaya transform (LS-transform). The authors propose the definition of the CTW, where the translation operator is specific to the LS-transform. The basic properties of the novel CWT are checked (linearity, convolution, etc.).
Ajay K. Gupt +2 more
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2010
The WFT localizes a signal simultaneously in time and frequency by "looking" at it through a window that is translated in time, then translated in frequency (i.e., modulated in time). These two operations give rise to the "notes" gω,t(u). The signal is then reconstructed as a superposition of such notes, with the WFT ƒ(tω,t) as the coefficient function.
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The WFT localizes a signal simultaneously in time and frequency by "looking" at it through a window that is translated in time, then translated in frequency (i.e., modulated in time). These two operations give rise to the "notes" gω,t(u). The signal is then reconstructed as a superposition of such notes, with the WFT ƒ(tω,t) as the coefficient function.
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Inverse continuous wavelet transform “Deconvolution”
SEG Technical Program Expanded Abstracts 2011, 2011Most deconvolution algorithms try to transform the seismic wavelet into spikes by designing inverse filters that attempts to remove an estimated seismic wavelet from seismic data. Considering that seismic trace singularities are associated with acoustic impedance contrasts, and can be characterized by wavelet transform modulus maxima lines (WTMML), we ...
Marcilio Castro de Matos +1 more
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Continuous Wavelet Transform Involving Linear Canonical Transform
National Academy Science Letters, 2018The main objective of this paper is to study the continuous wavelet transform involving linear canonical transform (LCT) and some of its basic properties. The inversion formula and the Parseval’s relation of continuous wavelet transform are discussed. Moreover, discrete wavelet transform based on LCT is defined and studied its basic properties.
Akhilesh Prasad, Z. A. Ansari
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Hardy’s theorem for the continuous wavelet transform
Journal of Pseudo-Differential Operators and Applications, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Radha, R., Sarvesh, K.
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Optical implementation of the continuous wavelet transform
Applied Optics, 1998A simple optical implementation for the one-dimensional wavelet transform (WT) is proposed. In contrast with previous WT optical implementations, the obtained WT is continuous along both axes (dilation and shift). An optical implementation to the inverse WT is proposed as well. Thus an optical continuous WT processor can be implemented.
G, Shabtay, D, Mendlovic, Z, Zalevsky
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BRIDGE INTEGRITY ASSESSMENT BY CONTINUOUS WAVELET TRANSFORMS
International Journal of Structural Stability and Dynamics, 2009The potential of continuous wavelet transforms for damage assessment of existing bridges is investigated herein. Different types of continuous wavelet transforms have been under investigation and the most effective ones have been introduced in a toolbox to automate the damage assessment procedure.
Alvandi, A. +3 more
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The continuous wavelet transform in n-dimensions
International Journal of Wavelets, Multiresolution and Information Processing, 2016Daubechies 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 ...
Pandey, J. N., Jha, N. K., Singh, O. P.
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Wavelet transforms and downward continuation
1994Applications of wavelet theory [5, 6] to the numerical solution of partial differential equations and integral operators is a rapidly developing topic of research [1]. For a large class of integral operators, with smooth slowly decaying kernels, the matrices approximating these operators which are dense in the natural basis become sparser for the same ...
Ronan Bras, George Mellman
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Continuous Wavelet and Gabor Transforms
1998The continuous wavelet transform (CWT) as well as the continuous Gabor transform (CGT) (also known as the short-time Fourier transform) and their inverses are presented in this chapter. Both the CGT and the CWT take a one-dimensional time signal to a two-dimensional function of time and frequency.
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