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Minimum-bias windows for high-resolution spectral estimates

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The class of window pairsw(t) leftrightarrowW(\omega)is considered such thatw(t) = 0formid t mid > MandW(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.

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Information Theory, IEEE Transactions on  (Volume:19 ,  Issue: 1 )