Advances in Statistical Climatology, Meteorology and Oceanography
Advances in Statistical Climatology, Meteorology and Oceanography
ASCMO
Articles | Volume 12, issue 1
Articles | Volume 12, issue 1
https://doi.org/10.5194/ascmo-12-59-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/ascmo-12-59-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
Articles | Volume 12, issue 1
20 Feb 2026
 | 20 Feb 2026

Asymptotically-unbiased nonparametric estimation of the power spectral density from uniformly-spaced data with missing samples

Cédric Chavanne

Cited articles

Abry, P. and Sellan, F.: The wavelet-based synthesis for fractional Brownian motion proposed by F. Sellan and Y. Meyer: Remarks and fast implementation, Appl. Comput. Harmon. Anal., 3, 377–383, 1996. a
Babu, P. and Stoica, P.: Spectral analysis of nonuniformly sampled data – a review, Digit. Sig. Process., 20, 359–378, 2010. a
Bartlett, M. S.: Smoothing periodograms from time-series with continuous spectra, Nature, 161, 686–687, 1948. a
Bendat, J. S. and Piersol, A. G.: Random data: analysis and measurement procedures, John Wiley & Sons, Hoboken, NJ, 2011. a, b, c, d, e, f
Blackman, R. B. and Tukey, J. W.: The measurement of power spectra from the point of view of communications engineering – Part I, Bell Syst. Tech. J., 37, 185–282, 1958. a
More articles (35)
Download
Short summary
Standard algorithms for estimating the power spectral density of finite discrete data require interpolating missing samples, which usually produces biased estimates. An unbiased estimate can be obtained by taking the Fourier transform of the unbiased estimator of the circular autocorrelation, using only the available data. With missing samples, this estimator can produce negative power spectral densities, but converges to positive values when averaged over a sufficient number of realizations.
Read more
Share