Fast Multitaper Spectral Estimation
- Resource Type
- Conference
- Authors
- Karnik, Santhosh; Romberg, Justin; Davenport, Mark A.
- Source
- 2019 13th International conference on Sampling Theory and Applications (SampTA) Sampling Theory and Applications (SampTA), 2019 13th International conference on. :1-4 Jul, 2019
- Subject
- Signal Processing and Analysis
Eigenvalues and eigenfunctions
Estimation
Frequency estimation
Approximation algorithms
Computational efficiency
Bandwidth
Stochastic processes
- Language
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.