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This page is a copy of research/systems_and_control/signalproc/topics/ISdata (Wed, 31 Aug 2022 15:09:07)

Spectral analysis for irregularly sampled data

Spectral analysis of regularly-sampled (RS) data (also called evenly-sampled or uniformly-sampled data) is a mature topic, and there is a large set of useful RS methods from which to choose the one that is most appropriate for a given scenario. The literature on spectral analysis of irregularly-sampled (IS) data (also called unevenly-sampled or nonuniformly-sampled data) is also considerable. The motivation for the significant interest in the latter topic lies in the fact that data collected in many applications, such as engineering, physics, biomedicine, economics, seismology, and, particularly, astronomy is IS rather than RS. In fact if one had the possibility of choosing a sampling scheme to extract as much information (spectral or otherwise) as possible from a data set, one would rarely choose a RS strategy (unless there is a total lack of prior information about the data properties, or limitations of the available hardware require RS). However, in spite of its unquestionable importance and of the plethora of papers on the subject, the spectral analysis of IS data is a somewhat under-developed topic.

Example application

Ice-core drilling can provide information about paleoclimatic properties of historical glacial-interglacial periods including local temperature, wind strength, aerosol fluxes, changes in atmospheric trace-gas composition etc. The data considered in this example was obtained at the Russian Vostok station in East Antarctica and includes measurements covering approximately the past 420 000 years. The recorded data contain 283 samples. Previous reports show that there is a strong correlation between Antarctical temperature and atmospheric concentrations of several greenhouse gases. We will consider the measurements of CO2 concentrations in this example.

The data sequence is shown in Fig. 1 where the recorded concentration of CO2 is shown in parts per million by volume (p.p.m.v.). The time differences between two successive samples are ranging from 50 to 7000 years. In Fig. 2 we present the estimated spectra obtained using the IS versions of the periodogram (PER) and Capon (CAP) together with the frequency estimates obtained using the IS versions of ESPRIT and MUSIC assuming that the number of sinusoidal components in the data is equal to 6.

vostok_1.jpg

Fig. 1

vostok_3.jpg

Fig. 2

Selected publications

  1. New method of sparse parameter estimation in separable models and its use for spectral analysis of irregularly sampled data. Peter Stoica, Prabhu Babu, and Jian Li. In IEEE Transactions on Signal Processing, volume 59, number 1, pp 35-47, 2011. (DOI).
  2. Spectral analysis of nonuniformly sampled data — a review. Prabhu Babu and Peter Stoica. In Digital signal processing (Print), volume 20, number 2, pp 359-378, 2010. (DOI).
  3. Spectral Estimation of Irregularly Sampled Exponentially Decaying Signals with Applications to RF Spectroscopy. Erik Gudmundson, Peter Stoica, Jian Li, Andreas Jakobsson, Michael D. Rowe, John A. S. Smith, and Jun Ling. In Journal of magnetic resonance, volume 203, number 1, pp 167-176, 2010. (DOI).
  4. Spectral analysis of nonuniformly sampled data: a new approach versus the periodogram. Peter Stoica, Jian Li, and Hao He. In IEEE Transactions on Signal Processing, volume 57, number 3, pp 843-858, 2009. (DOI).
  5. Missing data recovery via a nonparametric iterative adaptive approach. Peter Stoica, Jian Li, and Jun Ling. In IEEE Signal Processing Letters, volume 16, number 4, pp 241-244, 2009. (DOI).
  6. Spectral Analysis of Irregularly-Sampled Data: Paralleling the regularly-sampled data approaches. Peter Stoica and Niclas Sandgren. In Digital signal processing (Print), volume 16, number 6, pp 712-734, 2006. (DOI).

Updated  2022-08-31 15:09:07 by Victor Kuismin.