Minimum-bias windows for high-resolution spectral estimates

The class of window pairs
w(t) \leftrightarrowW(\\omega)
is considered such that
w(t) = 0
for
\mid t \mid > M
and
W(\omega) \geq 0
. It is shown that in this class, the window \begin{equation} w_o(t) = \frac{1}{\pi} \biggl| \sin \frac{\pi t}{M} \biggr| + \biggl( 1- \frac{\midt \mid}{M} \biggr) \cos \frac{\pi t}{M}, \qquad \mid t \mid \leq M \end{equation} yields spectral estimates with minimum bias. Furthermore, the variance of the resulting estimate is smaller than that obtained with the known windows of the same size.