# B-spline scaling equation

• May 3rd 2010, 11:35 AM
surjective
B-spline scaling equation
Hello all,

I would greatly appriciate some assistance with the following.

I am considering a centered B-spline $B_{m}$ $(m\in \mathbb{N})$. I would like to determine the function $H_{0}$ such that:

$\widehat{B_{m}}(2\gamma)=H_{0}\widehat{B_{m}}(\gam ma) \hspace{0,5cm}, \hspace{0,5cm} \forall \gamma \in \mathbb{R}$

Thanks.
• May 3rd 2010, 02:16 PM
surjective
B-spline
Hey,

So far I've got the following:

$H_{0}(x)=\left(\frac{\sin(2\pi\gamma)}{2\sin(\pi\g amma)}\right)^{m}$

Could this be simplified?

Thanks.
• May 3rd 2010, 02:33 PM
Drexel28
Quote:

Originally Posted by surjective
Hey,

So far I've got the following:

$H_{0}(x)=\left(\frac{\sin(2\pi\gamma)}{2\sin(\pi\g amma)}\right)^{m}$

Could this be simplified?

Thanks.

$\sin(2x)=2\sin(x)\cos(x)$