On the Reconstruction of Irregularly Sampled Time Series

Vio, R.; Strohmer, Thomas; Wamsteker, W.

doi:10.1086/316495

Cited by 30 publications

(19 citation statements)

References 21 publications

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“…In turn, this implies some ambiguities in the definition of the Nyquist frequency that, loosely speaking, corresponds to the highest frequencies that contain information on the signal of interest (e.g. see Vio et al 2000;Koen 2006). As a consequence, Eq.…”

Section: Periodogram Analysis In the Case Of Uneven Samplingmentioning

confidence: 99%

Unevenly-sampled signals: a general formalism for the Lomb-Scargle periodogram

Vio¹,

Andreani²,

Biggs³

2010

A&A

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The periodogram is a popular tool that tests whether a signal consists only of noise or if it also includes other components. The main issue of this method is to define a critical detection threshold that allows identification of a component other than noise, when a peak in the periodogram exceeds it. In the case of signals sampled on a regular time grid, determination of such a threshold is relatively simple. When the sampling is uneven, however, things are more complicated. The most popular solution in this case is to use the Lomb-Scargle periodogram, but this method can be used only when the noise is the realization of a zero-mean, white (i.e. flat-spectrum) random process. In this paper, we present a general formalism based on matrix algebra, which permits analysis of the statistical properties of a periodogram independently of the characteristics of noise (e.g. colored and/or non-stationary), as well as the characteristics of sampling.

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Section: Periodogram Analysis In the Case Of Uneven Samplingmentioning

confidence: 99%

Unevenly-sampled signals: a general formalism for the Lomb-Scargle periodogram

Vio¹,

Andreani²,

Biggs³

2010

A&A

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“…Daylight periods and adverse nighttime weather conditions prevent regular data collection (see, e.g., [111] and the references therein).…”

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confidence: 99%

Nonuniform Sampling and Reconstruction in Shift-Invariant Spaces

Aldroubi¹,

Gröchenig²

2001

SIAM Rev.

626

541

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Abstract. This article discusses modern techniques for nonuniform sampling and reconstruction of functions in shift-invariant spaces. It is a survey as well as a research paper and provides a unified framework for uniform and nonuniform sampling and reconstruction in shiftinvariant spaces by bringing together wavelet theory, frame theory, reproducing kernel Hilbert spaces, approximation theory, amalgam spaces, and sampling. Inspired by applications taken from communication, astronomy, and medicine, the following aspects will be emphasized: (a) The sampling problem is well defined within the setting of shift-invariant spaces. (b) The general theory works in arbitrary dimension and for a broad class of generators. (c) The reconstruction of a function from any sufficiently dense nonuniform sampling set is obtained by efficient iterative algorithms. These algorithms converge geometrically and are robust in the presence of noise. (d) To model the natural decay conditions of real signals and images, the sampling theory is developed in weighted L p -spaces.

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“…Both sets of 87 Sr͞ 86 Sr data were first averaged in nonoverlapping time windows of 10 My. The resulting unevenly spaced record was then transformed (20) to an evenly spaced record with time increments of approximately 10 My and no contributions to the power spectral density at periods less than 21 My.…”

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confidence: 99%

Atmospheric carbon dioxide levels for the last 500 million years

Rothman

2002

Proc. Natl. Acad. Sci. U.S.A.

110

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The last 500 million years of the strontium-isotope record are shown to correlate significantly with the concurrent record of isotopic fractionation between inorganic and organic carbon after the effects of recycled sediment are removed from the strontium signal. The correlation is shown to result from the common dependence of both signals on weathering and magmatic processes. Because the long-term evolution of carbon dioxide levels depends similarly on weathering and magmatism, the relative fluctuations of CO 2 levels are inferred from the shared fluctuations of the isotopic records. The resulting CO 2 signal exhibits no systematic correspondence with the geologic record of climatic variations at tectonic time scales.

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On the Reconstruction of Irregularly Sampled Time Series

Cited by 30 publications

References 21 publications

Unevenly-sampled signals: a general formalism for the Lomb-Scargle periodogram

Unevenly-sampled signals: a general formalism for the Lomb-Scargle periodogram

Nonuniform Sampling and Reconstruction in Shift-Invariant Spaces

Atmospheric carbon dioxide levels for the last 500 million years

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