Multitaper spectral estimation

Thomson's multitaper method estimates the spectrum by tapering the same data segment with several orthogonal Slepian sequences, computing an eigenspectrum from each, and averaging them. Because the tapers are designed to be maximally concentrated and mutually orthogonal, the individual eigenspectra are approximately statistically independent, so averaging K of them cuts the variance by about a factor of K while confining leakage to a controlled bandwidth 2W.

Compared with Welch's method, which reduces variance by splitting the record into overlapping segments, multitaper uses the whole record for each estimate and thus preserves more low-frequency information and gives better protection against leakage. It also supports principled error bars: a jackknife over the deletion of individual tapers yields approximate confidence intervals, and an F-test on the tapered coefficients detects sinusoidal line components. Its cost is the explicit choice of the time-bandwidth product and the smoothing it imposes.