{
    "article_id": 1095,
    "public_id": "49c5b530-3a52-48f0-970c-b13670b172bd",
    "internal_identifier": null,
    "source_identifier": "42:100",
    "status": "published",
    "type": "research_article",
    "title": "An Exact Variance Expression of Pisarenko’s Method for Frequency Estimation of a Single Real Sinusoid: Random Phase Case",
    "title_secondary": null,
    "abstract": "Several statistical analyses of the Pisarenko harmonic decomposition (PHD) method for frequency estimation of a single real sinusoid in noise have been carried out in the literature. However, all of the analyses consider the phase of the sinusoid as a constant parameter which does not change from one snapshot to another. In this paper, it is assumed that the phase is a random variable uniformly distributed in an interval of length 2 . With the use of a simple variance analysis technique, an exact expression of the PHD frequency variance is derived. An approximate PHD variance formula for sufficiently large data lengths and signal-to-noise ratios is also given. Computer simulations are included to validate the theoretical development",
    "language": "en",
    "english_title": null,
    "english_abstract": null,
    "doi": null,
    "doi_url": null,
    "resource_url": "https://www.set-science.com/a/49c5b530-3a52-48f0-970c-b13670b172bd",
    "pdf_url": "https://www.set-science.com/a/49c5b530-3a52-48f0-970c-b13670b172bd/pdf",
    "og_image": "https://www.set-science.com/assets/img/og-card-v2.png",
    "authors": [
        {
            "public_id": "1c690f2f-2a08-44d8-a15d-4644ee0935d5",
            "given": "Betofe Mboyo ",
            "family": "Keyta  ",
            "full": "Betofe Mboyo  Keyta  ",
            "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": [
        "Frequency estimation; Real sinusoid; Pisarenko’s method; Variance analysis"
    ],
    "translations": [
        {
            "language": "en",
            "title": "An Exact Variance Expression of Pisarenko’s Method for Frequency Estimation of a Single Real Sinusoid: Random Phase Case",
            "abstract": "Several statistical analyses of the Pisarenko harmonic decomposition (PHD) method for frequency estimation of a single real sinusoid in noise have been carried out in the literature. However, all of the analyses consider the phase of the sinusoid as a constant parameter which does not change from one snapshot to another. In this paper, it is assumed that the phase is a random variable uniformly distributed in an interval of length 2 . With the use of a simple variance analysis technique, an exact expression of the PHD frequency variance is derived. An approximate PHD variance formula for sufficiently large data lengths and signal-to-noise ratios is also given. Computer simulations are included to validate the theoretical development",
            "keywords": [
                "Frequency estimation; Real sinusoid; Pisarenko’s method; 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": "533",
    "page_last": "536",
    "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": "H. Sakai, “Statistical analysis of Pisarenko’s method for sinusoidal frequency estimation,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 32, no. 1, pp. 95-101, February 1984.",
            "doi": null,
            "title": null,
            "authors": null,
            "source": null,
            "year": null,
            "volume": null,
            "pages": null
        },
        {
            "order": 2,
            "raw": "K. W. Chan and H. C. So, “An exact analysis of Pisarenko’s singletone frequency estimation algorithm,” Signal Processing, vol. 83, no.3, pp. 685-690, March 2003.",
            "doi": null,
            "title": null,
            "authors": null,
            "source": null,
            "year": null,
            "volume": null,
            "pages": null
        },
        {
            "order": 3,
            "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
        },
        {
            "order": 4,
            "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
        }
    ],
    "statements": {
        "acknowledgements": null,
        "conflict_of_interest": null,
        "data_availability": null,
        "ai_disclosure": null
    },
    "credit": [],
    "history": {
        "published": "2019-06-01"
    }
}