Fbsp wavelet

File:Complex fbsp wavelet.PNG

Frequency B-spline wavelets: cubic spline fbsp 3-1-2 complex wavelet.

In applied mathematics, fbsp wavelets are frequency B-spline wavelets.

These frequency B-spline wavelets are complex wavelets whose spectrum are spline.

${\mathrm{fbsp}}^{(m-\mathrm{f}\mathrm{b}-f_c)}(t):=\sqrt{\mathrm{f}\mathrm{b}}{\mathrm{sinc}}^m\left(\frac{t}{{\mathrm{f}\mathrm{b}}^m}\right)e^{j2\pi f_{c}t}$

where sinc function that appears in Shannon sampling theorem.

• m > 1 is the order of the spline
• fb is a bandwidth parameter
• f_c 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.