The resolution of closely adjacent spectral lines

E. J. Hannan*, B. G. Quinn

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

25 Citations (Scopus)


Abstract. The problem is that of determining the parameters in a trigonometric polynomial when it is observed with added stationary noise. The frequencies, in particular, must be determined and the situation especially considered is that where these are close together. A similar problem arises if an angular frequency is close to zero or π. The method of estimation is the maximization of the regression sum of squares as a function of the unknown frequencies. In the asymptotic theory, the closely adjacent frequencies are separated by an amount that is of the order T‐1, where T is the length of the series. Simulations show that this asymptotic treatment gives a better approximation in cases where the separation is of this magnitude than that obtained by treating the frequencies as fixed.

Original languageEnglish
Pages (from-to)13-31
Number of pages19
JournalJournal of Time Series Analysis
Issue number1
Publication statusPublished - 1989
Externally publishedYes


  • frequency estimation
  • maximum entropy
  • regularity
  • spectral line
  • Trigonometric regression
  • weak mixing


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