{ "article_id": 1096, "public_id": "2882ef64-3125-4247-9930-d38bc8e65b04", "internal_identifier": null, "source_identifier": "42:101", "status": "published", "type": "research_article", "title": "Simple and Accurate Bias and Variance Expressions of Some Instantaneous Frequency Estimators including the DESAs", "title_secondary": null, "abstract": "Instantaneous estimation of the frequency of a real sinusoid in noise from a small number of data samples is an important problem in the signal processing area. Several frequency estimators are proposed for this problem in the literature. In this paper, some of the popular ones including the discrete energy separation algorithms (DESAs) are considered. Using a Taylor series expansion technique, very simple and yet accurate closed form expressions for the bias and the variance of the estimators are derived. Computer simulations are included to validate the theoretical results.", "language": "en", "english_title": null, "english_abstract": null, "doi": null, "doi_url": null, "resource_url": "https://www.set-science.com/a/2882ef64-3125-4247-9930-d38bc8e65b04", "pdf_url": "https://www.set-science.com/a/2882ef64-3125-4247-9930-d38bc8e65b04/pdf", "og_image": "https://www.set-science.com/assets/img/og-card-v2.png", "authors": [ { "public_id": "99d9ce4a-d857-4716-afb6-acbd19f6eea4", "given": "Sewim Hazal  ", "family": "Uz ", "full": "Sewim Hazal   Uz ", "literal": null, "orcid": null, "orcid_url": null, "email": "dilaver@uludag.edu.tr", "corresponding": false, "sequence": "first", "affiliations": [ { "name": "Bursa Uludağ University  ", "department": null, "country": null, "country_code": null, "ror": null, "ror_url": null } ] }, { "public_id": "39b76f95-c649-4bdf-9db8-13bba18d5109", "given": "Erdoğan ", "family": "Dilaveroğlu  ", "full": "Erdoğan  Dilaveroğlu  ", "literal": null, "orcid": null, "orcid_url": null, "email": "dilaver@uludag.edu.tr", "corresponding": true, "sequence": "additional", "affiliations": [ { "name": "Bursa Uludağ University  ", "department": null, "country": null, "country_code": null, "ror": null, "ror_url": null } ] } ], "keywords": [ "Instantaneous frequency estimation; Real sinusoid; DESAs; Bias and variance analysis." ], "translations": [ { "language": "en", "title": "Simple and Accurate Bias and Variance Expressions of Some Instantaneous Frequency Estimators including the DESAs", "abstract": "Instantaneous estimation of the frequency of a real sinusoid in noise from a small number of data samples is an important problem in the signal processing area. Several frequency estimators are proposed for this problem in the literature. In this paper, some of the popular ones including the discrete energy separation algorithms (DESAs) are considered. Using a Taylor series expansion technique, very simple and yet accurate closed form expressions for the bias and the variance of the estimators are derived. Computer simulations are included to validate the theoretical results.", "keywords": [ "Instantaneous frequency estimation; Real sinusoid; DESAs; Bias and variance analysis." ] } ], "subjects": [], "subject_names": [], "published_date": "2019-06-01", "published_year": "2019", "received_date": null, "accepted_date": null, "volume": "4", "issue": null, "page_first": "537", "page_last": "540", "article_number": null, "conference": { "short_name": "ISAS2019-ENS", "full_title": "3rd International Symposium on Innovative Approaches in Scientific Studies (Engineering and Natural Sciences)", "name": "3rd International Symposium on Innovative Approaches in Scientific Studies (Engineering and Natural Sciences)", "acronym": "ISAS2019-ENS", "location": "Ankara, Türkiye", "start_date": "2019-04-19", "end_date": null, "public_id": "ed3b36e9-38cf-4aeb-a135-833c969cc89f" }, "proceedings": { "title": "3rd International Symposium on Innovative Approaches in Scientific Studies (Engineering and Natural Sciences)", "series_title": "Setsci conference indexing system", "publisher": "SET Technology", "isbn": null, "eisbn": null, "issn": "2618-6446", "eissn": null, "doi": null, "doi_prefix": null, "slug": "setsci-volume-4-2019-legacy-42", "public_id": "24d215ef-a545-4351-9725-6e9bdb167b3c", "url": "https://www.set-science.com/p/setsci-volume-4-2019-legacy-42" }, "license": { "name": "CC BY 4.0", "url": "https://creativecommons.org/licenses/by/4.0/", "code": "CC-BY-4.0", "open_access": true }, "copyright": { "holder": "SET Technology", "year": "2019" }, "funding_statement": null, "funders": [], "references": [ { "order": 1, "raw": "P. Maragos, J. F. Kaiser, and T. F. Quatieri, “On separating amplitude from frequency modulations using energy operators,” in Proc. ICASSP-92, vol. 2, pp. 1-4.", "doi": null, "title": null, "authors": null, "source": null, "year": null, "volume": null, "pages": null }, { "order": 2, "raw": "L. B. Fertig and J. H. McClellan, “Instantaneous frequency estimation using linear prediction with comparisons to the DESAs,” IEEE Signal Processing Letters, vol. 3, no. 2, pp. 54-56, February 1996.", "doi": null, "title": null, "authors": null, "source": null, "year": null, "volume": null, "pages": null }, { "order": 3, "raw": "A. Papoulis, Probability, Random Variables, and Stochastic Processes, 3rd ed., New York: McGraw-Hill, 1991.", "doi": null, "title": null, "authors": null, "source": null, "year": null, "volume": null, "pages": null }, { "order": 4, "raw": "H. C. So, Y. T. Chan, K. C. Ho, and Yuan Chen, “Simple formulas for bias and mean square error computation,” IEEE Signal Processing Magazine, vol. 30, no. 4, pp. 162-165, July 2013.", "doi": null, "title": null, "authors": null, "source": null, "year": null, "volume": null, "pages": null } ], "statements": { "acknowledgements": null, "conflict_of_interest": null, "data_availability": null, "ai_disclosure": null }, "credit": [], "history": { "published": "2019-06-01" } }