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A Practical Guide to Wavelet Analysis
, 1998
"... A practical stepbystep guide to wavelet analysis is given, with examples taken from time series of the El Nio Southern Oscillation (ENSO). The guide includes a comparison to the windowed Fourier transform, the choice of an appropriate wavelet basis function, edge effects due to finitelength t ..."
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Cited by 869 (3 self)
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A practical stepbystep guide to wavelet analysis is given, with examples taken from time series of the El Nio Southern Oscillation (ENSO). The guide includes a comparison to the windowed Fourier transform, the choice of an appropriate wavelet basis function, edge effects due to finite
From the Wavelet Series to the Discrete Wavelet Transform  the Initialization
 IEEE Trans. Signal Processing
, 1996
"... Discrete wavelet transform (DWT) is computed by subband filters bank and often used to approximate wavelet series (WS) and continuous wavelet transform (CWT). The approximation is often inaccurate because of the improper initialized discretization of the continuoustime signal. In this paper, the pr ..."
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Cited by 6 (0 self)
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Discrete wavelet transform (DWT) is computed by subband filters bank and often used to approximate wavelet series (WS) and continuous wavelet transform (CWT). The approximation is often inaccurate because of the improper initialized discretization of the continuoustime signal. In this paper
Adapting to unknown smoothness via wavelet shrinkage
 JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 1995
"... We attempt to recover a function of unknown smoothness from noisy, sampled data. We introduce a procedure, SureShrink, which suppresses noise by thresholding the empirical wavelet coefficients. The thresholding is adaptive: a threshold level is assigned to each dyadic resolution level by the princip ..."
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Cited by 1006 (18 self)
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on the choice of mother wavelet. We know from a previous paper by the authors that traditional smoothing methods  kernels, splines, and orthogonal series estimates  even with optimal choices of the smoothing parameter, would be unable to perform
From multifractal measures to multifractal wavelet series
 THE JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
, 2004
"... Given a positive locally finite Borel measure µ on R, a natural way to construct multifractal wavelet series Fµ(x) = ∑ j≥0,k∈Z dj,kψj,k(x) is to set dj,k  =2 −j(s0−1/p0) −j −j 1/p0 µ([k2, (k + 1)2)) , where s0,p0 ≥ 0, s0 − 1/p0> 0. Indeed, under suitable conditions, it is shown that the funct ..."
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Cited by 22 (10 self)
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Given a positive locally finite Borel measure µ on R, a natural way to construct multifractal wavelet series Fµ(x) = ∑ j≥0,k∈Z dj,kψj,k(x) is to set dj,k  =2 −j(s0−1/p0) −j −j 1/p0 µ([k2, (k + 1)2)) , where s0,p0 ≥ 0, s0 − 1/p0> 0. Indeed, under suitable conditions, it is shown
Bayesian methods for wavelet series in singleindex models
 J. Comp. Graph. Statist
, 2005
"... Singleindex models have found applications in econometrics and biometrics, where multidimensional regression models are often encountered. This article proposes a nonparametric estimation approach that combines wavelet methods for nonequispaced designs with Bayesian models. We consider a wavelet se ..."
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Cited by 3 (2 self)
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series expansion of the unknown regression function and set prior distributions for the wavelet coefficients and the other model parameters. To ensure model identifiability, the direction parameter is represented via its polar coordinates. We employ ad hoc hierarchical mixture priors that perform
Shannon wavelets theory,”
 Mathematical Problems in Engineering,
, 2008
"... Recommended by Cristian Toma Shannon wavelets are studied together with their differential properties known as connection coefficients . It is shown that the Shannon sampling theorem can be considered in a more general approach suitable for analyzing functions ranging in multifrequency bands. This ..."
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Cited by 371 (2 self)
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of a finite hypergeometric series. These coefficients make it possible to define the wavelet reconstruction of the derivatives of the C functions.
X.P. ZHANGETAL, FROM THE WAVELET SERIES TO THE DISCRETE WAVELET TRANSFORM 1 From the Wavelet Series to the Discrete Wavelet Transform  the Initialization
, 1999
"... Discrete wavelet transform (DWT) is computed by subband lters bank and often used to approximate wavelet series (WS) and continuous wavelet transform (CWT). The approximation is often inaccurate because of the improper initialized discretization of the continuoustime signal. In this paper, the prob ..."
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Discrete wavelet transform (DWT) is computed by subband lters bank and often used to approximate wavelet series (WS) and continuous wavelet transform (CWT). The approximation is often inaccurate because of the improper initialized discretization of the continuoustime signal. In this paper
Compressed sensing
, 2004
"... We study the notion of Compressed Sensing (CS) as put forward in [14] and related work [20, 3, 4]. The basic idea behind CS is that a signal or image, unknown but supposed to be compressible by a known transform, (eg. wavelet or Fourier), can be subjected to fewer measurements than the nominal numbe ..."
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Cited by 3625 (22 self)
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We study the notion of Compressed Sensing (CS) as put forward in [14] and related work [20, 3, 4]. The basic idea behind CS is that a signal or image, unknown but supposed to be compressible by a known transform, (eg. wavelet or Fourier), can be subjected to fewer measurements than the nominal
MINIMIZATION OF CIRCUIT DESIGN USING PERMUTATION OF HAAR WAVELET SERIES
, 2004
"... The paper discusses complexity of circuit realization through Haar wavelet series. The efficiency in circuit synthesis using a method for minimization of the number of nonzero Haar coefficients by permutation of binary coordinates of indices of Haar functions is considered. Some applications of Haar ..."
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The paper discusses complexity of circuit realization through Haar wavelet series. The efficiency in circuit synthesis using a method for minimization of the number of nonzero Haar coefficients by permutation of binary coordinates of indices of Haar functions is considered. Some applications
Random wavelet series based on a treeindexed Markov chain
 Comm. Math. Phys
, 2008
"... Abstract. We study the global and local regularity properties of random wavelet series whose coefficients exhibit correlations given by a treeindexed Markov chain. We determine the law of the spectrum of singularities of these series, thereby performing their multifractal analysis. We also show tha ..."
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Cited by 9 (4 self)
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Abstract. We study the global and local regularity properties of random wavelet series whose coefficients exhibit correlations given by a treeindexed Markov chain. We determine the law of the spectrum of singularities of these series, thereby performing their multifractal analysis. We also show
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