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2-D Hexagonal Sampling

$\begin{picture}(120,50) \multiput(24,33)(8,0){8}{\circle{8}} \multiput(20,25)(8,... ...1,-2){4}} \put(90, 25){$ \Omega_1 $} \put(44,45){$ \Omega_2 $} \end{picture}$

$\begin{displaymath} \underline{U_1}=\left[\begin{array}{c}W \\ \sqrt{3}W\end{ar... ...e{U_2}=\left[\begin{array}{c}W\\ -\sqrt{3}W\end{array}\right] \end{displaymath}$

$\begin{displaymath} \underline{U}=\left[\begin{array}{cc}W&W\\ \sqrt{3}W&-\sqrt... ...frac{\pi}{\sqrt{3}W}&\frac{\pi}{-\sqrt{3}W} \end{array}\right] \end{displaymath}$

Sampling Density = $\frac{w^2\sqrt{3}}{2{\pi}^2}$

Brian L. Evans