The Estimation of Frequency

Barry G. Quinn*

*Corresponding author for this work

    Research output: Chapter in Book/Report/Conference proceedingChapter

    3 Citations (Scopus)

    Abstract

    Numerical methods have been used for fitting sinusoids to data since the middle of the 18th century. Since the discovery of the Fast Fourier Transform by Cooley and Tukey in 1965, the techniques for estimating frequency have become computationally feasible. This review examines various techniques for estimating the frequency or frequencies of sinusoids in additive noise. The techniques fall into two categories - those based on Fourier, or frequency-domain methods, and those derived from a consideration of a small number of sample autocovariances. The Fourier techniques invariably have asymptotic variances of order T -3, where T is the sample size, and are particularly useful when T is large and the signal is noisy, whereas the other techniques are usually statistically inefficient, with asymptotic variances of order T -1, and are often biased, but because of their computational efficiency, can be useful when T is small and the signal is relatively noise free.

    Original languageEnglish
    Title of host publicationHandbook of Statistics
    EditorsTata Subba Rao, Suhasini Subba Rao , C.R. Rao
    Place of PublicationAmsterdam, Netherlands
    PublisherElsevier
    Pages585-621
    Number of pages37
    Volume30
    ISBN (Print)9780444538581
    DOIs
    Publication statusPublished - 2012

    Publication series

    NameTime Series Analysis: Methods and Applications
    PublisherElsevier
    Volume30
    ISSN (Print)0169-7161

      Fingerprint

    Cite this

    Quinn, B. G. (2012). The Estimation of Frequency. In T. Subba Rao, S. Subba Rao , & C. R. Rao (Eds.), Handbook of Statistics (Vol. 30, pp. 585-621). (Time Series Analysis: Methods and Applications; Vol. 30). Amsterdam, Netherlands: Elsevier. Handbook of Statistics https://doi.org/10.1016/B978-0-444-53858-1.00021-1