Estimating Frequency by Interpolation using Fourier Coefficients

Barry G. Quinn*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

370 Citations (Scopus)


The periodogram of a time series that contains a sinusoidal component provides a crude estimate of its frequency parameter, the maximizer over the Fourier frequencies being within 0(T-l) of the frequency as the sample size T increases. In this correspondence, a technique for obtaining an estimator that has root mean square error of order T-3/2 is presented, which involves only the Fourier components of the time series at three frequencies. The asymptotic variance of the estimator varies between, roughly, the asymptotic variance of the maximizer of the periodogram over all frequencies (the Cramer-Rao lower bound) and three times this variance. The advantage of the new estimator is its computational simplicity.

Original languageEnglish
Pages (from-to)1264-1268
Number of pages5
JournalIEEE Transactions on Signal Processing
Issue number5
Publication statusPublished - 1994
Externally publishedYes


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