Spectral Proper Orthogonal Decomposition using Multitaper Estimates

TL;DR

This paper investigates the use of multitaper spectral estimates in proper orthogonal decomposition, demonstrating improved variance control and resolution in turbulent flow data analysis over traditional methods.

Contribution

It introduces multitaper-Welch estimators for SPOD, combining orthogonal tapers with overlapping segments to enhance spectral estimation accuracy.

Findings

Multitaper-Welch estimators reduce variance at fixed resolution.

They achieve higher frequency resolution with similar variance.

The method is validated on experimental and numerical turbulent flow data.

Abstract

The use of multitaper estimates for spectral proper orthogonal decomposition (SPOD) is explored. Multitaper and multitaper-Welch estimators that use discrete prolate spheroidal sequences (DPSS) as orthogonal data windows are compared to the standard SPOD algorithm that exclusively relies on weighted overlapped segment averaging, or Welch's method, to estimate the cross-spectral density matrix. Two sets of turbulent flow data, one experimental and the other numerical, are used to discuss the choice of resolution bandwidth and the bias-variance tradeoff. Multitaper-Welch estimators that combine both approaches by applying orthogonal tapers to overlapping segments allow for flexible control of resolution, variance, and bias. At additional computational cost but for the same data, Multitaper-Welch estimators provide lower variance estimates at fixed frequency resolution or higher frequency resolution at similar variance compared to the standard algorithm.