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Band-ensemble spectral proper orthogonal decomposition with frequency attribution

Jakob G. R. von Saldern*

Oliver T. Schmidt

Philipp Godbersen

J. Moritz Reumschüssel

Tim Colonius

  • *Contact author: j.vonsaldern@tu-berlin.de
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Phys. Rev. Fluids 11, 104905 – Published 23 October, 2026

DOI: https://doi.org/10.1103/b9hq-xvpx

Abstract

This study presents band-ensemble spectral proper orthogonal decomposition (bSPOD). The approach is inspired by frequency smoothing, a method used to reduce estimator variance in power spectral density estimates, and is here extended to SPOD. The algorithm estimates SPOD modes from consecutive Fourier coefficients obtained from a single Fourier transform of the full-time record and thus avoids time segmentation. In this study, bSPOD is applied to artificial test data and to a particle image velocimetry data set of a broadband-tonal cavity flow. Compared to the more commonly used Welch-based SPOD formulation, bSPOD reduces spectral leakage, permits increased frequency resolution, and retains frequency information of tonal components at comparable computational cost. These features enable reduced estimator variance while maintaining low bias for tonal components, making bSPOD particularly effective for broadband-tonal flows.

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Phys. Rev. Fluids 11, 104905– Published 23 October, 2026
  • Received 6 February 2026
  • Accepted 15 September 2026
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