Fbsp wavelet

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

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

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

where 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.