In applied mathematics, fbsp wavelets are frequency B-spline wavelets. ''fbsp m-fb-fc'' These frequency B-spline wavelets are complex wavelets whose spectrum are spline. :

fbsp^(t) :=  .\operatorname^m \left( \frac   \right). e^

where

sinc function In mathematics, physics and engineering, the sinc function, denoted by , has two forms, normalized and unnormalized.. In mathematics, the historical unnormalized sinc function is defined for by \operatornamex = \frac. Alternatively, the ...

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 Clearly,

Shannon wavelet In functional analysis, the Shannon wavelet (or sinc wavelets) is a decomposition that is defined by signal analysis by ideal bandpass filters. Shannon wavelet may be either of real or complex type. Shannon wavelet is not well-localized(noncompact ...

(sinc wavelet) is a particular 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. Continuous wavelets {{mathanalysis-stub