  Periodogram methods are widely used for the estimation of power- and
cross-spectra, of which Welch's method is the most popular. Previous studies
have analyzed the variance of the power spectra estimates and developed
analytical probability functions, showing that the approach is unbiased when
applied to white-noise signals or in the limit of infinite window lengths.
However, no explicit expression for the estimation bias is available for more
complex signals when finite windows are used. In this study, we show that, for
finite window lengths, Welch's method is biased for all signals other than the
white-noise signal. A novel two-window approach that is unbiased when applied
to signals with bounded correlation lengths is proposed. Numerical experiments
are used to illustrate the advantages of the novel approach.
