{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/frequency-time-analysis-low-rank","title":"Frequency-time analysis, low-rank reconstruction and denoising of turbulent flows using SPOD","arxiv_id":"2011.03644","date":"2020-11-07","proceeding":null,"authors":["Akhil Nekkanti","Oliver T. Schmidt"],"abstract":"Four different applications of spectral proper orthogonal decomposition (SPOD): low-rank reconstruction, denoising, frequency-time analysis, and prewhitening are demonstrated on large-eddy simulation data of a turbulent jet. SPOD-based low-rank reconstruction can be performed by direct inversion of a truncated SPOD. This spectral inversion problem, however, is ambiguous since SPOD relies on spectral estimation. We demonstrate SPOD-based flow field reconstruction using direct inversion of the SPOD algorithm (frequency-domain approach) and propose an alternative approach based on projection of the time series data onto the modes (time-domain approach). While the SPOD optimally represents the flow in a statistical sense, the time-domain approach seeks an optimal reconstruction of each instantaneous flow field. We further propose a SPOD-based denoising strategy that is based on hard-thresholding of the SPOD eigenvalues. The proposed strategy achieves significant noise reduction while facilitating drastic data compression. In contrast to standard methods of frequency-time analysis such as wavelet transform, a proposed SPOD-based approach yields a spectrogram that characterizes the temporal evolution of spatially coherent flow structures. In the frequency-domain, time-varying expansion coefficients can be obtained by basing the SPOD on a sliding window. This approach, however, is computationally intractable, and an alternative strategy based on convolution in the time-domain is presented. When applied to the turbulent jet data, SPOD-based frequency-time analysis reveals that the intermittent occurrence of large-scale coherent structures is directly associated with high-energy events. This work suggests that the time-domain approach is preferable for low-rank reconstruction of individual snapshots, and the frequency-domain approach for denoising and frequency-time analysis.","url_abs":"https://arxiv.org/abs/2011.03644v2","url_pdf":"https://arxiv.org/pdf/2011.03644v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"frequency-time-analysis-low-rank","repo_url":"https://github.com/SpectralPOD/spod_matlab","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}