Maximizing the periodogram

Barry G. Quinn, Robby G. McKilliam, I. Vaughan L Clarkson

    Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionResearchpeer-review

    Abstract

    It has been well known for at least twenty years [1] that computing the maximizer of the periodogram, in order to estimate the unknown frequency in a noisy sinusoid, is problematic. In particular, because the periodogram is highly nonlinear, a grid size of order o (T) is needed to find the maximizer reliably, where T is the sample size, and that Newton's method may fail to find the zero of the first derivative of the periodogram closest to the maximizer of the periodogram calculated, for example, using the FFT. In this paper, we show that Newton's method does, in fact, work if it is applied to an appropriately chosen monotonic function of the periodogram.

    LanguageEnglish
    Title of host publication2008 IEEE Global Telecommunications Conference, GLOBECOM 2008
    EditorsRichard W. Miller
    Place of PublicationPiscataway, NJ
    PublisherInstitute of Electrical and Electronics Engineers (IEEE)
    Pages3478-3482
    Number of pages5
    ISBN (Print)9781424423248
    DOIs
    Publication statusPublished - 2008
    Event2008 IEEE Global Telecommunications Conference, GLOBECOM 2008 - New Orleans, LA, United States
    Duration: 30 Nov 20084 Dec 2008

    Other

    Other2008 IEEE Global Telecommunications Conference, GLOBECOM 2008
    CountryUnited States
    CityNew Orleans, LA
    Period30/11/084/12/08

    Fingerprint

    Newton-Raphson method
    Fast Fourier transforms
    Derivatives

    Bibliographical note

    Copyright 2008 IEEE. Reprinted from 2008 IEEE Global Telecommunications Conference : New Orleans, Louisiana, 30 November 2008-04 December 2008. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Macquarie University’s products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.

    Cite this

    Quinn, B. G., McKilliam, R. G., & Clarkson, I. V. L. (2008). Maximizing the periodogram. In R. W. Miller (Ed.), 2008 IEEE Global Telecommunications Conference, GLOBECOM 2008 (pp. 3478-3482). [4698443] Piscataway, NJ: Institute of Electrical and Electronics Engineers (IEEE). https://doi.org/10.1109/GLOCOM.2008.ECP.668
    Quinn, Barry G. ; McKilliam, Robby G. ; Clarkson, I. Vaughan L. / Maximizing the periodogram. 2008 IEEE Global Telecommunications Conference, GLOBECOM 2008. editor / Richard W. Miller. Piscataway, NJ : Institute of Electrical and Electronics Engineers (IEEE), 2008. pp. 3478-3482
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    Quinn, BG, McKilliam, RG & Clarkson, IVL 2008, Maximizing the periodogram. in RW Miller (ed.), 2008 IEEE Global Telecommunications Conference, GLOBECOM 2008., 4698443, Institute of Electrical and Electronics Engineers (IEEE), Piscataway, NJ, pp. 3478-3482, 2008 IEEE Global Telecommunications Conference, GLOBECOM 2008, New Orleans, LA, United States, 30/11/08. https://doi.org/10.1109/GLOCOM.2008.ECP.668

    Maximizing the periodogram. / Quinn, Barry G.; McKilliam, Robby G.; Clarkson, I. Vaughan L.

    2008 IEEE Global Telecommunications Conference, GLOBECOM 2008. ed. / Richard W. Miller. Piscataway, NJ : Institute of Electrical and Electronics Engineers (IEEE), 2008. p. 3478-3482 4698443.

    Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionResearchpeer-review

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    Quinn BG, McKilliam RG, Clarkson IVL. Maximizing the periodogram. In Miller RW, editor, 2008 IEEE Global Telecommunications Conference, GLOBECOM 2008. Piscataway, NJ: Institute of Electrical and Electronics Engineers (IEEE). 2008. p. 3478-3482. 4698443 https://doi.org/10.1109/GLOCOM.2008.ECP.668