TY - CHAP

T1 - The Estimation of Frequency

AU - Quinn, Barry G.

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84861377713&partnerID=8YFLogxK

U2 - 10.1016/B978-0-444-53858-1.00021-1

DO - 10.1016/B978-0-444-53858-1.00021-1

M3 - Chapter

AN - SCOPUS:84861377713

SN - 9780444538581

VL - 30

T3 - Time Series Analysis: Methods and Applications

SP - 585

EP - 621

BT - Handbook of Statistics

A2 - Subba Rao, Tata

A2 - Subba Rao , Suhasini

A2 - Rao, C.R.

PB - Elsevier

CY - Amsterdam, Netherlands

ER -