Fbsp wavelet

In applied mathematics, fbsp wavelets are frequency <a href="/facts/Spline_wavelet/b6k6wH6e">B-spline wavelets</a>.
These frequency B-spline wavelets are complex wavelets whose spectrum are <a href="/facts/Spline_(mathematics)/yafkQtqp">spline</a>.

fbsp
          
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          sinc
          
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    {\displaystyle \operatorname {fbsp} ^{(m-\mathrm {fb} -f_{c})}(t):={\sqrt {\mathrm {fb} }}\operatorname {sinc} ^{m}\left({\frac {t}{\mathrm {fb} ^{m}}}\right)e^{j2\pi f_{c}t}}

where <a href="/facts/Sinc_function/lSvDtHy0">sinc function</a> that appears in <a href="/facts/Shannon_sampling_theorem/JYlVrvc5">Shannon sampling theorem</a>.

<ul><li>m > 1 is the order of the spline</li>
<li>fb is a bandwidth parameter</li>
<li>fc is the wavelet center frequency</li></ul>
The <a href="/facts/Shannon_wavelet/TsvKFNQq">Shannon wavelet</a> (sinc wavelet) is then clearly a special case of fbsp.

<ul><li>S.G. Mallat, A Wavelet Tour of Signal Processing, Academic Press, 1999, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-12-466606-X</li>
<li><a href="/facts/C._Sidney_Burrus/E4tsUg4S">C.S. Burrus</a>, R.A. Gopinath, H. Guo, Introduction to Wavelets and Wavelet Transforms: A Primer, Prentice-Hall, 1988, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-13-489600-9.</li>
<li>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.</li>
<li>M. Unser, Ten Good Reasons for Using Spline Wavelets, Proc. SPIE, Vol.3169, Wavelets Applications in Signal and Image Processing, 1997, pp. 422–431.</li></ul>

Fbsp wavelet open-in-new

Fbsp wavelet