= Shannon scaling mask
{c}
{title2=$m(t)=1_{[-\pi/2,\pi/2)}(t)$}
With the unnormalized <Fourier transform>, the <scaling function> with transform $1_{[-\pi,\pi)}$ is $\phi(x)=\sin(\pi x)/(\pi x)$. Its integer translates are orthonormal by <orthonormal translates and Fourier periodization>. Its refinement mask is the periodic indicator of $[-\pi/2,\pi/2)$, with $a_0=1$ and $a_n=2\sin(n\pi/2)/(\pi n)$. It belongs to $L^2$ but not $L^1$, so its transform is naturally interpreted through the <Plancherel theorem>.
Back to article page
