  Welch's method provides an estimator of the power spectral density that is
statistically consistent. This is achieved by averaging over periodograms
calculated from overlapping segments of a time series. For a finite length time
series, while the variance of the estimator decreases as the number of segments
increase, the magnitude of the estimator's bias increases: a bias-variance
trade-off ensues when setting the segment number. We address this issue by
providing a novel method for debiasing Welch's method which maintains the
computational complexity and asymptotic consistency, and leads to improved
finite-sample performance. Theoretical results are given for fourth-order
stationary processes with finite fourth-order moments and absolutely convergent
fourth-order cumulant function. The significant bias reduction is demonstrated
with numerical simulation and an application to real-world data. Our estimator
also permits irregular spacing over frequency and we demonstrate how this may
be employed for signal compression and further variance reduction. Code
accompanying this work is available in R and python.
