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, 2000 Despite the previous few chapters, the term “wavelets” usually refers to wavelets on ℝ, examples of which we construct in this chapter. The first two sections present the basics of Fourier analysis on ℝ.
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Discrete Wavelets and Fast Wavelet Transform
1991The wavelet analysis, introduced by J. MORLET and Y. MEYER in the middle of the eighties, is a processus of time-frequency (or time-scale) analysis which consists of decomposing a signal into a basis of functions (o jk ) called wavelets. These wavelets are in turn deduced from the analyzing wavelet o by dilatations and translations. More precisely:
Bonnet, Pierre, Rémond, Didier
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Foundations of Wavelet Networks and Applications, 2018
Many applications of signal processing entail detecting, extracting and classifying specific elements from high-dimensional data. These may be particular sounds from acoustical signals, or shapes from visual scenes, and may most certainly present ...
M. Moraud
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Many applications of signal processing entail detecting, extracting and classifying specific elements from high-dimensional data. These may be particular sounds from acoustical signals, or shapes from visual scenes, and may most certainly present ...
M. Moraud
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Wavelets and wavelet thresholding
2001Every theory starts from an idea. The wavelet idea is simple and clear. At a first confrontation, the mathematics that work out this idea might appear strange and difficult. Nevertheless, after a while, this theory leads to insight in the mechanism in wavelet based algorithms in a variety of applications.
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Multiple Wavelet Coefficients Fusion in Deep Residual Networks for Fault Diagnosis
IEEE transactions on industrial electronics (1982. Print), 2019Wavelet transform, an effective tool to decompose signals into a series of frequency bands, has been widely used for vibration-based fault diagnosis in machinery.
Minghang Zhao +3 more
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ACM Transactions on Graphics, 2005
Noise functions are an essential building block for writing procedural shaders in 3D computer graphics. The original noise function introduced by Ken Perlin is still the most popular because it is simple and fast, and many spectacular images have been made with it. Nevertheless, it is prone to problems with aliasing and detail loss.
Tony DeRose, Robert L. Cook
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Noise functions are an essential building block for writing procedural shaders in 3D computer graphics. The original noise function introduced by Ken Perlin is still the most popular because it is simple and fast, and many spectacular images have been made with it. Nevertheless, it is prone to problems with aliasing and detail loss.
Tony DeRose, Robert L. Cook
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Fast wavelet transforms and numerical algorithms I
, 1991A class of algorithms is introduced for the rapid numerical application of a class of linear operators to arbitrary vectors. Previously published schemes of this type utilize detailed analytical information about the operators being applied and are ...
G. Beylkin, R. Coifman, V. Rokhlin
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IEEE Transactions on Neural Networks, 1992
A wavelet network concept, which is based on wavelet transform theory, is proposed as an alternative to feedforward neural networks for approximating arbitrary nonlinear functions. The basic idea is to replace the neurons by ;wavelons', i.e., computing units obtained by cascading an affine transform and a multidimensional wavelet.
Qinghua Zhang, Albert Benveniste
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A wavelet network concept, which is based on wavelet transform theory, is proposed as an alternative to feedforward neural networks for approximating arbitrary nonlinear functions. The basic idea is to replace the neurons by ;wavelons', i.e., computing units obtained by cascading an affine transform and a multidimensional wavelet.
Qinghua Zhang, Albert Benveniste
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2009
Publisher Summary This chapter highlights the use of wavelets and wavelet transforms as an alternative method of spectral analysis. It also discusses a number of common wavelets and introduces Wavelet Toolbox of the MATLAB® software. A wavelet is a function that satisfies at least the following two criteria: the integral of the function O(x) over all ...
Nicholas G. Hatsopoulos +5 more
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Publisher Summary This chapter highlights the use of wavelets and wavelet transforms as an alternative method of spectral analysis. It also discusses a number of common wavelets and introduces Wavelet Toolbox of the MATLAB® software. A wavelet is a function that satisfies at least the following two criteria: the integral of the function O(x) over all ...
Nicholas G. Hatsopoulos +5 more
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Wavelet Transforms and Wavelet Approximations
1994We summarize properties of classical wavelet transforms and Wavelet Stieltjes transforms. Wavelet approximation problems are also considered for Wavelet Stieltjes transforms. This will give rise to some characterizations of general signals.
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