Spectral proper orthogonal decomposition using multitaper estimates

• Published in: Theoretical and computational fluid dynamics Vol. 36; no. 5; pp. 741 - 754
• Main Author: Schmidt, Oliver T.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2022; Springer; Springer Nature B.V
• Subjects: Algorithms; Analysis; Bandwidths; Bias; Classical and Continuum Physics; Computational Science and Engineering; Decomposition; Eigenvalues; Engineering; Engineering Fluid Dynamics; Estimates; Estimators; Fourier transforms; Original Article; Proper Orthogonal Decomposition; Resolution; Segments; Spectral decomposition (Mathematics); Turbulent flow; United States; Spectral estimation; Particle image velocimetry; Proper orthogonal decomposition; Large eddy simulation; Multitaper; SPOD
• ISSN: 0935-4964; 1432-2250
• DOI: 10.1007/s00162-022-00626-x

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. Graphic abstract