Reduction of Gibbs Overshoot in Continuous Wavelet Transform

Handa CHEN; Yasuhiro KAWAI; Hajime MAEDA

Reduction of Gibbs Overshoot in Continuous Wavelet Transform

Handa CHEN, Yasuhiro KAWAI, Hajime MAEDA

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In this paper we propose two methods, named the time smoothing and the scale smoothing respectively, to reduce the Gibbs overshoot in continuous wavelet transform. In is shown that for a large kind of wavelets the scale smoothing cannot remove the Gibbs overshoot completely as in the case of Fourier analysis, but it is possible to reduce the overshoot for any wavelets by choosing the smoothing window functions properly. The frequency behavior of scale smoothing is similar to that of the time smoothing. According to its frequency behavior we give the empirical conditions for selecting the smoothing window functions. Numerical examples are given for illustrations.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E80-A No.8 pp.1352-1361

Publication Date: 1997/08/25

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Type of Manuscript: Special Section PAPER (Special Section on Digital Signal Processing)

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Handa CHEN, Yasuhiro KAWAI, Hajime MAEDA, "Reduction of Gibbs Overshoot in Continuous Wavelet Transform" in IEICE TRANSACTIONS on Fundamentals, vol. E80-A, no. 8, pp. 1352-1361, August 1997, doi: .
Abstract: In this paper we propose two methods, named the time smoothing and the scale smoothing respectively, to reduce the Gibbs overshoot in continuous wavelet transform. In is shown that for a large kind of wavelets the scale smoothing cannot remove the Gibbs overshoot completely as in the case of Fourier analysis, but it is possible to reduce the overshoot for any wavelets by choosing the smoothing window functions properly. The frequency behavior of scale smoothing is similar to that of the time smoothing. According to its frequency behavior we give the empirical conditions for selecting the smoothing window functions. Numerical examples are given for illustrations.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/e80-a_8_1352/_p

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@ARTICLE{e80-a_8_1352,
author={Handa CHEN, Yasuhiro KAWAI, Hajime MAEDA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Reduction of Gibbs Overshoot in Continuous Wavelet Transform},
year={1997},
volume={E80-A},
number={8},
pages={1352-1361},
abstract={In this paper we propose two methods, named the time smoothing and the scale smoothing respectively, to reduce the Gibbs overshoot in continuous wavelet transform. In is shown that for a large kind of wavelets the scale smoothing cannot remove the Gibbs overshoot completely as in the case of Fourier analysis, but it is possible to reduce the overshoot for any wavelets by choosing the smoothing window functions properly. The frequency behavior of scale smoothing is similar to that of the time smoothing. According to its frequency behavior we give the empirical conditions for selecting the smoothing window functions. Numerical examples are given for illustrations.},
keywords={},
doi={},
ISSN={},
month={August},}

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TY - JOUR
TI - Reduction of Gibbs Overshoot in Continuous Wavelet Transform
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1352
EP - 1361
AU - Handa CHEN
AU - Yasuhiro KAWAI
AU - Hajime MAEDA
PY - 1997
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E80-A
IS - 8
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - August 1997
AB - In this paper we propose two methods, named the time smoothing and the scale smoothing respectively, to reduce the Gibbs overshoot in continuous wavelet transform. In is shown that for a large kind of wavelets the scale smoothing cannot remove the Gibbs overshoot completely as in the case of Fourier analysis, but it is possible to reduce the overshoot for any wavelets by choosing the smoothing window functions properly. The frequency behavior of scale smoothing is similar to that of the time smoothing. According to its frequency behavior we give the empirical conditions for selecting the smoothing window functions. Numerical examples are given for illustrations.
ER -