Welch Window

Another quite simple window, which uses only polynomials, is the Welch window.

$$\textrm{Welch}(x,\tau)=\left \{ \begin{array}{cl} 1-\left(\f... ...\vert x\vert < \tau$}\\ 0 & \textrm{else} \end{array} \right.$$ (7)

Its frequency response is better than that of the Bartlett windowed cosc function below $\pi$, but it shows again a rather distinctive bump above.