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Gaussian Window

The Gaussian Window in its general form is defined by

\textrm{Gauss}(x,\tau,\sigma)=\left \{ \begin{array}{cl}
...\vert x\vert < \tau$}\\
0 & \textrm{else}
\end{array} \right.
\end{displaymath} (12)

with $\sigma$ being the standard deviation. The higher $\sigma$ gets, the wider gets the Gaussian window and, on the other hand, the more severe gets the truncation. Several Gaussian windows with different standard deviations are depicted in Fig. 2 in the third row. The higher $\sigma$ the better the frequency response approximates the ideal one below $\pi$ but also the more distinctive are the bumps above $\pi$.