{"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/sinusoidal-frequency-estimation-by-gradient","title":"Sinusoidal Frequency Estimation by Gradient Descent","arxiv_id":"2210.14476","date":"2022-10-26","proceeding":null,"authors":["Ben Hayes","Charalampos Saitis","György Fazekas"],"abstract":"Sinusoidal parameter estimation is a fundamental task in applications from spectral analysis to time-series forecasting. Estimating the sinusoidal frequency parameter by gradient descent is, however, often impossible as the error function is non-convex and densely populated with local minima. The growing family of differentiable signal processing methods has therefore been unable to tune the frequency of oscillatory components, preventing their use in a broad range of applications. This work presents a technique for joint sinusoidal frequency and amplitude estimation using the Wirtinger derivatives of a complex exponential surrogate and any first order gradient-based optimizer, enabling end to-end training of neural network controllers for unconstrained sinusoidal models.","url_abs":"https://arxiv.org/abs/2210.14476v2","url_pdf":"https://arxiv.org/pdf/2210.14476v2.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":"sinusoidal-frequency-estimation-by-gradient","repo_url":"https://github.com/ben-hayes/sinusoidal-gradient-descent","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"time-series-1","task_name":"Time Series"},{"task_slug":"time-series","task_name":"Time Series Analysis"},{"task_slug":"time-series-forecasting","task_name":"Time Series Forecasting"},{"task_slug":"parameter-estimation","task_name":"parameter estimation"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2210.14476","atlas_url":"https://app.syntology.ai/?focus=2210.14476","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2210.14476"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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