Builds on Welch’s method to provide an improved power spectral density (PSD) estimate. Instead of using bandpass filters that are essentially rectangular windows (as in the periodogram method), the multitaper method uses a bank of optimal bandpass filters to compute the estimate. These optimal FIR filters are derived from a set of sequences known as discrete prolate spheroidal sequences (DPSSs, also known as Slepian sequences). These weights or tapers (Slepian tapers) are selected to optimally minimize broad-band bias, the tendency for power from strong peaks to spread into neighboring frequency intervals of lower power (also known as spectral leakage). Each of the tapered copies of the data is Fourier transformed and a weighted average is computed to obtain a low variance result while maintaining a high-resolution estimate.

## Multitaper

In practice only a few tapers need to be computed, depending on the resolution of the spectrum desired. The user chooses a bandwidth W over which the spectrum is smoothed, thus for an N-long sequence ﬁxing the value NW known as the time-bandwidth product. The standard number of tapers K that need to be computed is K = 2 * NW - 1, although this is left for the user to decide and will depend on the particular study or type of data available.

For the kth Slepian taper vk, we have

The kth eigencomponent, which is the complex-valued Fourier transform of the N -long data sequence y(n) after being multiplied by vk(n). Here we assume unit sampling. Note that Yk(f)2 is a standard single-taper spectrum estimate

G.A. Prieto, R.L. Parker, F.L. Vernon III, 2008. A Fortran 90 library for multitaper spectrum analysis, Computers & Geosciences 35 (2009) 1701–1710

Spectral analysis involves a tradeoff between resolving comparable strength components with similar frequencies and resolving disparate strength components with dissimilar frequencies. That tradeoff occurs when the window function is chosen.

For the kth Slepian taper vk, we have

The kth eigencomponent, which is the complex-valued Fourier transform of the N -long data sequence y(n) after being multiplied by vk(n). Here we assume unit sampling. Note that Yk(f)2 is a standard single-taper spectrum estimate

G.A. Prieto, R.L. Parker, F.L. Vernon III, 2008. A Fortran 90 library for multitaper spectrum analysis, Computers & Geosciences 35 (2009) 1701–1710

Spectral analysis involves a tradeoff between resolving comparable strength components with similar frequencies and resolving disparate strength components with dissimilar frequencies. That tradeoff occurs when the window function is chosen.