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Denoising with compactly supported B-spline wavelets

Susumu Sakakibara
Organization: Tokyo Denki University
Department: Department of Information Environment Integration and Design
Journal / Anthology

Mathematics with Vision: Proceedings of the First International Mathematica Symposium
Year: 1995
Page range: 325-332

In finding a continuous function of time from time series data, one must eliminate noise that arise in measurements. Denoising is particularly important when one wants to compute the time derivative of the function, which is very sensitive to noise. The compactly supported B-spline wavelet provides us with an ideal method of finding a continuous function from such data. We have developed a Mathematica package SplineWavelet.m for wavelet analysis, with which one can estimate a smooth function from noisy time series data. Some details of the implementation are discussed, and an example time series data are analyzed using the package, focusing our attention to the time derivative of the function.

*Applied Mathematics > Numerical Methods > Approximation Theory > Wavelets
*Mathematics > Probability and Statistics