Fast Multitaper Spectral Estimation

Thomson’s multitaper method using discrete prolate spheroidal sequences (DPSSs) is a widely used technique for spectral estimation. For a signal of length N, Thomson’s method requires selecting a bandwidth parameter W, and then uses K ≈ 2NW tapers. The computational cost of evaluating the multitaper estimate at N grid frequencies is O(KN log N). It has been shown that the choice of W and K which minimizes the MSE of the multitaper estimate is W = O(N
^−1/5
) and K = O(N
⁴
/
⁵
). This choice would require a computational cost of O(N
^9/5
log N). We demonstrate an ϵ-approximation to the multitaper estimate which can be evaluated at N grid frequencies using $O\left( {N{{\log }^2}N\log \frac{1}{\varepsilon }} \right)$ operations.