P. Abry (1994). Transform'ees en ondelettes -- Analyses multir'esolutions et signaux de pression en turbulance. Th`ese de Doctorat. Universit'e Claude Bernard, Lyon, France. Home/Search Document Not in Database Summary Related Articles Check |
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Detecting Abrupt Changes by Wavelet Methods - Antoniadis, Gijbels (1997) (3 citations) (Correct)
....for a lower resolution are displayed as circles on the bottom panel. As one can see, the DWT, due to the lack of translation invariance, presents on the cusp location a weak coefficient. Moreover, Holder regularity characterization does not hold in general for the discrete wavelet transform (see Abry (1994)) This is due to the lack of translation invariance of the discrete wavelet transform. It is therefore imperative, in a discrete and practical setting, to use the continuous wavelet transform for estimating the location of the jump points. However, the use of the continuous wavelet transform ....
....the wavelet transform modulus on the dyadic scales at the finest grid (this means that we only have to look at jCWT f (2 Gammaj ; k)j) This type of transform is refered to as the continuous discrete wavelet transform, i.e. CDWT and can be shown to be time translation invariant. 6 Abry (1994) proposes a fast algorithm for calculating the CDWT. The proposed algorithm is based on the same ideas as Mallat s pyramidal algorithm and is a variant of the algorithm a trous . The computation time for the proposed algorithm is of order O(Mn) where M denotes the number of scales and n the ....
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P. Abry (1994). Transform'ees en ondelettes -- Analyses multir'esolutions et signaux de pression en turbulance. Th`ese de Doctorat. Universit'e Claude Bernard, Lyon, France.
Wavelet Analysis of Long Range Dependent Traffic - Abry, Veitch (1998) (87 citations) Self-citation (Abry) (Correct)
....S j jj j Gamma P j2 j=j1 S j j P j2 j=j1 S j j j P j2 j=j1 S j P j2 j=j1 S j j 2 Gamma ( P j2 j=j1 S j j) 2 1 # (2. 10) where j j = log 2 i 1 n j P k jd x (j; k)j 2 j and the weight S j = n ln 2 2) 2 j 1 is the inverse of the theoretical asymptotic variance of j j [1, 3]. Bias of H. The above definition for H holds provided that (2.1) holds for all frequencies and that (2.6) converges. We can relax the first condition since in (2.7) we are free to choose only the range of scales over which (2.1) does hold. Now consider the convergence of (2.9) In fact ....
....higher computational cost, the performance of the estimator using a redundant wavelet transform is not superior to that given by the DWT, neither theoretically nor practically, except in some specific situations. Within the DWT, another interesting question is the choice of the mother wavelet. In [1, 3] it was shown that for the estimation of H, the only property of the wavelet that matters is its number of vanishing moments. Whether the wavelets are symmetrical or not, form an orthonormal, semi or biorthonormal basis or not, makes no theoretical nor significant practical difference. The reason ....
[Article contains additional citation context not shown here]
P.Abry, Transform'ees en ondelettes - Analyses multir'esolution et signaux de pression en turbulence. Th`ese de doctorat, Universit'e Lyon I et Ecole Normale Sup'erieure de Lyon, (1994).
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