Fbsp wavelet explained
In applied mathematics, fbsp wavelets are frequency B-spline wavelets.
These frequency B-spline wavelets are complex wavelets whose spectrum are spline.
| (m-fb-fc) |
| \operatorname{fbsp} | |
(t):={\sqrt{fb
}} \operatorname^m \left(\frac \right) e^
where sinc function that appears in Shannon sampling theorem.
- m > 1 is the order of the spline
- fb is a bandwidth parameter
- fc is the wavelet center frequency
The Shannon wavelet (sinc wavelet) is then clearly a special case of fbsp.
References
- S.G. Mallat, A Wavelet Tour of Signal Processing, Academic Press, 1999,
- C.S. Burrus, R.A. Gopinath, H. Guo, Introduction to Wavelets and Wavelet Transforms: A Primer, Prentice-Hall, 1988, .
- O. Cho, M-J. Lai, A Class of Compactly Supported Orthonormal B-Spline Wavelets in: Splines and Wavelets, Athens 2005, G Chen and M-J Lai Editors pp. 123–151.
- M. Unser, Ten Good Reasons for Using Spline Wavelets, Proc. SPIE, Vol.3169, Wavelets Applications in Signal and Image Processing, 1997, pp. 422–431.
