Gaussian Window

The Gaussian Window in its general form is defined by

$$\textrm{Gauss}(x,\tau,\sigma)=\left \{ \begin{array}{cl} 2^{... ...\vert x\vert < \tau$}\\ 0 & \textrm{else} \end{array} \right.$$ (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 $\pi$.