{"paper":{"title":"Prolate Spheroidal Wave Functions and the Accuracy and Dimensionality of Spectral Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["eess.SP","math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Timothy Stroschein","submitted_at":"2024-09-25T03:24:48Z","abstract_excerpt":"The main result of this thesis is an efficient protocol to determine the frequencies of a signal $C(t)= \\sum_k |a_k|^2 e^{i \\omega_k t}$, which is given for a finite time, to a high degree of precision. Specifically, we develop a theorem that provides a fundamental precision guarantee. Additionally, we establish an approximation theory for spectral analysis through low-dimensional subspaces that can be applied to a wide range of problems. The signal processing routine relies on a symmetry between harmonic analysis and quantum mechanics. In this context, prolate spheroidal wave functions (PSWF)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.16584","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2409.16584/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}