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Thread: B-spline scaling equation

  1. May 3rd 2010, 11:35 AM #1
    surjective
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    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.
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  2. May 3rd 2010, 02:16 PM #2
    surjective
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    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.
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  3. May 3rd 2010, 02:33 PM #3
    Drexel28
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    Quote Originally Posted by surjective View Post
    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)
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