We define a new wavelet transform that is based on a recently defined family of scaling functions: the fractional B-splines. The interest of this family is that they interpolate between the integer degrees of polynomial B-splines and that they allow a fractional order of approximation. The orthogonal fractional spline wavelets essentially behave as a fractional differentiators. This property seems promising for the analysis of $ 1/f ^{ \alpha } $ ; noise that can be whitened by an appropriate choice of the degree of the spline transform. We present a practical FFT-based algorithm for the implementation of these fractional wavelet transforms, and give some examples of processing.
Type
conference paper
Publication date
2000
Publisher
Published in
Proceedings of the Twenty-Fifth IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'00)
Issue
Istanbul, Turkey
Start page
512
End page
515
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
September 18, 2015
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