{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T00:00:14Z","timestamp":1768694414575,"version":"3.49.0"},"reference-count":65,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,9,12]],"date-time":"2023-09-12T00:00:00Z","timestamp":1694476800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"FEDER funds (Fundo Europeu de Desenvolvimento Regional)","award":["POCI-01-0145-FEDER-029308"],"award-info":[{"award-number":["POCI-01-0145-FEDER-029308"]}]},{"DOI":"10.13039\/501100001871","name":"FCT (Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["POCI-01-0145-FEDER-029308"],"award-info":[{"award-number":["POCI-01-0145-FEDER-029308"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Acoustics"],"abstract":"<jats:p>The estimation of the frequency of sinusoids has been the object of intense research for more than 40 years. Its importance in classical fields such as telecommunications, instrumentation, and medicine has been extended to numerous specific signal processing applications involving, for example, speech, audio, and music processing. In many cases, these applications run in real-time and, thus, require accurate, fast, and low-complexity algorithms. Taking the normalized Cram\u00e9r\u2013Rao lower bound as a reference, this paper evaluates the relative performance of nine non-iterative discrete Fourier transform-based individual sinusoid frequency estimators when the target sinusoid is affected by full-bandwidth quasi-harmonic interference, in addition to stationary noise. Three levels of the quasi-harmonic interference severity are considered: no harmonic interference, mild harmonic interference, and strong harmonic interference. Moreover, the harmonic interference is amplitude-modulated and frequency-modulated reflecting real-world conditions, e.g., in singing and musical chords. Results are presented for when the Signal-to-Noise Ratio varies between \u221210 dB and 70 dB, and they reveal that the relative performance of different frequency estimators depends on the SNR and on the selectivity and leakage of the window that is used, but also changes drastically as a function of the severity of the quasi-harmonic interference. In particular, when this interference is strong, the performance curves of the majority of the tested frequency estimators collapse to a few trends around and above 0.4% of the DFT bin width.<\/jats:p>","DOI":"10.3390\/acoustics5030049","type":"journal-article","created":{"date-parts":[[2023,9,12]],"date-time":"2023-09-12T21:41:12Z","timestamp":1694554872000},"page":"845-869","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["One-Step Discrete Fourier Transform-Based Sinusoid Frequency Estimation under Full-Bandwidth Quasi-Harmonic Interference"],"prefix":"10.3390","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2460-8825","authenticated-orcid":false,"given":"Jo\u00e3o Miguel","family":"Silva","sequence":"first","affiliation":[{"name":"Department of Electrical and Computer Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"},{"name":"INESC TEC, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3161-1109","authenticated-orcid":false,"given":"Marco Ant\u00f3nio","family":"Oliveira","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-0798-2328","authenticated-orcid":false,"given":"Andr\u00e9 Ferraz","family":"Saraiva","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"},{"name":"Forensic Science Laboratory, Judiciary Police, Rua Gomes Freire, 1169-007 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7278-6749","authenticated-orcid":false,"given":"An\u00edbal J. S.","family":"Ferreira","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"},{"name":"INESC TEC, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1109\/MSP.2007.361611","article-title":"Fast, Accurate Frequency estimators","volume":"24","author":"Jacobsen","year":"2007","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Klapuri, A., and Davy, M. (2006). Signal Processing Methods for Music Transcription, Springer. 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