{"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/testing-for-high-frequency-features-in-a","title":"Testing for high frequency features in a noisy signal","arxiv_id":"1911.12719","date":"2019-11-28","proceeding":null,"authors":[],"abstract":"Given nonstationary data, one generally wants to extract the trend from the\nnoise by smoothing or filtering. However, it is often important to delineate a\nthird intermediate category, that we call high frequency (HF) features: this is\nthe case in our motivating example, which consists in experimental measurements\nof the time-dynamics of depolymerising protein fibrils average size. One may\nintuitively visualise HF features as the presence of fast, possibly\nnonstationary and transient oscillations, distinct from a slowly-varying trend\nenvelope. The aim of this article is to propose an empirical definition of HF\nfeatures and construct estimators and statistical tests for their presence\naccordingly, when the data consists of a noisy nonstationary 1-dimensional\nsignal. We propose a parametric characterization in the Fourier domain of the\nHF features by defining a maximal amplitude and distance to low frequencies of\nsignificant energy. We introduce a data-driven procedure to estimate these\nparameters, and compute a p-value proxy based on a statistical test for the\npresence of HF features. The test is first conducted on simulated signals where\nthe ratio amplitude of the HF features to the level of the noise is controlled.\nThe test detects HF features even when the level of noise is five times larger\nthan the amplitude of the oscillations. In a second part, the test is conducted\non experimental data from Prion disease experiments and it confirms the\npresence of HF features in these signals with significant confidence.","url_abs":"http://arxiv.org/abs/1911.12719v1","url_pdf":"http://arxiv.org/pdf/1911.12719v1.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":"abstracts"},"code_links":[{"paper_slug":"testing-for-high-frequency-features-in-a","repo_url":"https://github.com/mmezache/HFFTest","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"high","task_name":"Vocal Bursts Intensity Prediction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}