Complex-valued tapers

The spectral estimation method based on the average of short, tapered periodograms is re-examined. The bias of such estimators is typically O(1/b(2)), where b is the length of the short blocks. Much of the current research on multitapering has been focusing on reducing the proportionality constant implicit in the term O(1/b(2)). In this letter, we show how-with the use of complex-valued tapers-the bias of the spectral estimator can be reduced by orders of magnitude becoming O(1/b(P)) for (possibly) high p. Expressions for the estimators' variance and MSE are presented with an aim toward optimal estimation. An automatic method of optimally choosing the block size b is given. Finally, the usage of multiple complex tapers is proposed in an effort to reduce sidelobe size and improve finite-sample performance.