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In applied mathematics, '''fbsp wavelets''' are '''frequency B-spline [[wavelet]]s'''.

''fbsp m-fb-fc''

These frequency B-spline wavelets are complex wavelets whose spectrum are [[spline (mathematics)|spline]].

: <math> fbsp^{(\operatorname{m-fb-fc}) }(t) := {\sqrt {fb}} .\operatorname{sinc}^m \left( \frac {t} {fb^m} \right). e^{j2 \pi fc t}   </math>

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

Clearly, [[Shannon wavelet]] (sinc wavelet) is a particular case of fbsp.

[[File:Complex fbsp wavelet.PNG|thumb|Frequency B-Spline wavelets: cubic spline fbsp 3-1-2 complex wavelet.]]

== References ==

* S.G. Mallat, ''A Wavelet Tour of Signal Processing'', Academic Press, 1999, ISBN 0-12-466606-X

* [[C. Sidney Burrus|C.S. Burrus]], R.A. Gopinath, H. Guo, ''Introduction to Wavelets and Wavelet Transforms: A Primer'', Prentice-Hall, 1988,  ISBN 0-13-489600-9.

* 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.&nbsp;123–151.

* M. Unser, Ten Good Reasons for Using Spline Wavelets, ''Proc. SPIE'', Vol.3169, Wavelets Applications in Signal and Image Processing, 1997, pp.&nbsp;422–431.

== References ==

* S.G. Mallat, ''A Wavelet Tour of Signal Processing'', Academic Press, 1999, ISBN 0-12-466606-X

* [[C. Sidney Burrus|C.S. Burrus]], R.A. Gopinath, H. Guo, ''Introduction to Wavelets and Wavelet Transforms: A Primer'', Prentice–Hall, 1988,  ISBN 0-13-489600-9.

* 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.&nbsp;123–151.

* M. Unser, Ten Good Reasons for Using Spline Wavelets, ''Proc. SPIE'', Vol.3169, Wavelets Applications in Signal and Image Processing, 1997, pp.&nbsp;422–431.

[[Category:Continuous wavelets]]
[[Category:Functional analysis]]