Approximate spectral analysis by least-squares fit

Vaníček, Petr

doi:10.1007/bf00651344

Cited by 170 publications

(110 citation statements)

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“…In this way the problem of model parameter estimation can be converted to the problem of solving the global minimum or minima of LSS. This approach has been applied to astronomical data already by Vaniček (1969Vaniček ( , 1971 and Taylor & Hamilton (1972), or more recently by Martinez & Koen (1994), Wilcox & Wilcox (1995) and Bossi & La Franceschina (1995). The LSS analysis is not trivial for semirandomly distributed observations, like the astronomical data that often contain periodic gaps.…”

Section: Three Stage Period Analysis (Tspa)mentioning

confidence: 99%

Three stage period analysis and complementary methods

Jetsu

Pelt

1999

Astron. Astrophys. Suppl. Ser.

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Abstract. We generalize the multistage period search and analysis method for the case when the data error estimates (i.e. statistical weights) are available. Adjustment of model parameters allows us to detect complex wave forms in noisy data. Complementary statistical tests are also presented to estimate the significance of the detected periodicities, to verify the modelling reliability, and to separate real periodicities from spurious ones. The application of these methods is illustrated on different samples of real photometric data.

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Section: Three Stage Period Analysis (Tspa)mentioning

confidence: 99%

Three stage period analysis and complementary methods

Jetsu

Pelt

1999

Astron. Astrophys. Suppl. Ser.

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“…The oversampling factor for a particular bandpass with spectral range ∆λ, and spectral resolution δλ is given by c = Mδλ/(2∆λ), where c = 1 corresponds to critical (Nyquist) sampling. The input spectrum, x, can be retrieved as the FFT of a critically-sampled interferogram, or by non-uniform Fourier-transform (NFFT) of an oversampled interferogram [16,19]. Without loss of information, the number of spectral points in x is necessarily half the number of MZIs since the FFT requires a solution to both the amplitude and phase of each spectral component.…”

Section: Resultsmentioning

confidence: 99%

Athermal planar-waveguide Fourier-transform spectrometer for methane detection

Podmore¹,

Scott²,

Cheben³

et al. 2017

Opt. Express

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Vous avez des questions? Nous pouvons vous aider. Pour communiquer directement avec un auteur, consultez la première page de la revue dans laquelle son article a été publié afin de trouver ses coordonnées. Si vous n'arrivez pas à les repérer, communiquez avec nous à PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca. Questions? Contact the NRC Publications Archive team atPublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca. If you wish to email the authors directly, please see the first page of the publication for their contact information. NRC Publications Archive Archives des publications du CNRCThis publication could be one of several versions: author's original, accepted manuscript or the publisher's version. / La version de cette publication peut être l'une des suivantes : la version prépublication de l'auteur, la version acceptée du manuscrit ou la version de l'éditeur. For the publisher's version, please access the DOI link below./ Pour consulter la version de l'éditeur, utilisez le lien DOI ci-dessous. Abstract:We demonstrate a passively thermally-stabilized planar waveguide Fourier-transform spectrometer for remote detection of atmospheric methane. The device is implemented as a spatial heterodyne spectrometer using an array of 100 Mach-Zehnder interferometers (MZIs) on an integrated photonic chip. The spectrometer is buffered against temperature fluctuations by using waveguides with a carefully engineered, athermal geometry. The achieved waveguide thermooptic optic coefficient is 3.5 × 10 −6 K −1 . Effective entrance aperture is increased over dispersive element spectrometers, without sacrificing spectral resolution, by coupling light independently to each of the 100 MZIs. The output of each MZI is sampled in quadrature, to compensate for non-uniform illumination across the MZI input apertures. The spectrometer is validated using a methane reference cell in a benchtop setup: an interferogram is inverted via least-squares spectral analysis (LSSA) to retrieve multiple absorption lines at a spectral resolution of 50 pm over a 1 nm free spectral range (FSR) centered at λ 0 = 1666.5 nm. The retrieved spectrum is compared against the Beer-Lambert absorption law and is found to provide a correct measurement of the volume mixing ratio (VMR) in the optical path. 44(10), 761-765 (1954 Florjańczyk, and M. Vachon, "High-resolution Fourier-transform spectrometer chip with microphotonic silicon spiral waveguides," Opt. Lett., 38(5), 706-708 (2013). 13. M. Yang, M. Li, and J.-J. He, "Static FT imaging spectrometer based on a modified waveguide MZI array," Opt.

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“…The least squares' spectral analysis is a modeling method for approximate behavior of natural and physical behaviors [7]. To determine the included part a limited number of 1 periodic component to observe periodic sinuous and cosine base functions were used for modeling [8].…”

Section: Least Square Spectral Analysismentioning

confidence: 99%

“…Though the traditional method of Fourier analysis maintains some limitations we can refer dependency of this method to using co-distanced data that most of the observations are dispersed and are not at the same distance that are sensitive to information gap [8]. To overcome such limitations [7], the spectral analysis method according to estimation of the least squares can be developed. This method is known widely as spectral analysis of the least squares [9]- [11].…”

Section: Least Square Spectral Analysismentioning

confidence: 99%

The Time Series Spectral Analysis of Satellite Altimetry and Coastal Tide Gauges and Tide Modeling in the Coast of Caspian Sea

Pirooznia¹,

Emadi²,

Alamdari³

2016

OJMS

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This study endeavors to deal with the least square spectral analysis on the time series, to find present significant frequencies, to analyze 40 tide components using harmonic methods and to show relationship between discovered frequencies and 40 components of tide. For the purpose of collecting data of altimetry satellites of Topex/Poseidon (T/P), Jason 1, Jason 2 and coastal tide gauges of Bandar Anzali, Noshahr, and Nekah were utilized. In this time series formed by cross over points of altimetry satellite and then using least square spectral analysis on time series derived from altimetry satellite and coastal tide gauges the significant components were found and annual, biannual, and monthly components were discovered. Then, analysis of 40 tide components was conducted using harmonic method to find the amplitude and phase. It represented that solar annual (Sa) plays the most significant role on Caspian Sea corresponded to the least square spectral analysis of the time series. The results shows that the annual (Sa) and semi-annual Solar (Ssa) constituents on all of the ports listed have the highest amplitude in comparison with the other constituents which are respectively 16 cm, 18 cm and 15 cm for annual constituent and 2.8 cm, 5.4 cm and 3.7 cm for semi-annual constituent.

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Approximate spectral analysis by least-squares fit

Cited by 170 publications

References 0 publications

Three stage period analysis and complementary methods

Three stage period analysis and complementary methods

Athermal planar-waveguide Fourier-transform spectrometer for methane detection

The Time Series Spectral Analysis of Satellite Altimetry and Coastal Tide Gauges and Tide Modeling in the Coast of Caspian Sea

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