102,457 research outputs found
Real-time fundamental frequency estimation by least-square fitting
For real-time applications, a fundamental frequency estimation algorithm must be able to obtain accurate estimates from short signal segments. Characterization of the error function of fitting a sinusoid to the signal segment allows its spectrum to be deduced and the algorithm to be implemented efficiently. Musical signals are discussed in particular.published_or_final_versio
Millisecond and Binary Pulsars as Nature's Frequency Standards. II. Effects of Low-Frequency Timing Noise on Residuals and Measured Parameters
Pulsars are the most stable natural frequency standards. They can be applied
to a number of principal problems of modern astronomy and time-keeping
metrology. The full exploration of pulsar properties requires obtaining
unbiased estimates of the spin and orbital parameters. These estimates depend
essentially on the random noise component being revealed in the residuals of
time of arrivals (TOA). In the present paper, the influence of low-frequency
("red") timing noise with spectral indices from 1 to 6 on TOA residuals,
variances, and covariances of estimates of measured parameters of single and
binary pulsars are studied. In order to determine their functional dependence
on time, an analytic technique of processing of observational data in time
domain is developed which takes into account both stationary and non-stationary
components of noise. Our analysis includes a simplified timing model of a
binary pulsar in a circular orbit and procedure of estimation of pulsar
parameters and residuals under the influence of red noise. We reconfirm that
uncorrelated white noise of errors of measurements of TOA brings on gradually
decreasing residuals, variances and covariances of all parameters. On the other
hand, we show that any red noise causes the residuals, variances, and
covariances of certain parameters to increase with time. Hence, the low
frequency noise corrupts our observations and reduces experimental
possibilities for better tests of General Relativity Theory. We also treat in
detail the influence of a polynomial drift of noise on the residuals and
fitting parameters. Results of the analitic analysis are used for discussion of
a statistic describing stabilities of kinematic and dynamic pulsar time scales.Comment: 40 pages, 1 postscript figure, 1 picture, uses mn.sty, accepted to
Mon. Not. Roy. Astron. So
Determining global parameters of the oscillations of solar-like stars
Helioseismology has enabled us to better understand the solar interior, while
also allowing us to better constrain solar models. But now is a tremendous
epoch for asteroseismology as space missions dedicated to studying stellar
oscillations have been launched within the last years (MOST and CoRoT). CoRoT
has already proved valuable results for many types of stars, while Kepler,
which was launched in March 2009, will provide us with a huge number of seismic
data very soon. This is an opportunity to better constrain stellar models and
to finally understand stellar structure and evolution. The goal of this
research work is to estimate the global parameters of any solar-like
oscillating target in an automatic manner. We want to determine the global
parameters of the acoustic modes (large separation, range of excited pressure
modes, maximum amplitude, and its corresponding frequency), retrieve the
surface rotation period of the star and use these results to estimate the
global parameters of the star (radius and mass).To prepare the analysis of
hundreds of solar-like oscillating stars, we have developed a robust and
automatic pipeline. The pipeline consists of data analysis techniques, such as
Fast Fourier Transform, wavelets, autocorrelation, as well as the application
of minimisation algorithms for stellar-modelling. We apply our pipeline to some
simulated lightcurves from the asteroFLAG team and the Aarhus-asteroFLAG
simulator, and obtain results that are consistent with the input data to the
simulations. Our strategy gives correct results for stars with magnitudes below
11 with only a few 10% of bad determinations among the reliable results. We
then apply the pipeline to the Sun and three CoRoT targets.In particular we
determine the parameters of the Sun, HD49933, HD181906, and HD181420.Comment: 15 pages, 17 figures, accepted for publication in A&
On line power spectra identification and whitening for the noise in interferometric gravitational wave detectors
In this paper we address both to the problem of identifying the noise Power
Spectral Density of interferometric detectors by parametric techniques and to
the problem of the whitening procedure of the sequence of data. We will
concentrate the study on a Power Spectral Density like the one of the
Italian-French detector VIRGO and we show that with a reasonable finite number
of parameters we succeed in modeling a spectrum like the theoretical one of
VIRGO, reproducing all its features. We propose also the use of adaptive
techniques to identify and to whiten on line the data of interferometric
detectors. We analyze the behavior of the adaptive techniques in the field of
stochastic gradient and in the
Least Squares ones.Comment: 28 pages, 21 figures, uses iopart.cls accepted for pubblication on
Classical and Quantum Gravit
On the Spectral Properties of Matrices Associated with Trend Filters
This paper is concerned with the spectral properties of matrices associated
with linear filters for the estimation of the underlying trend of a time
series. The interest lies in the fact that the eigenvectors can be interpreted
as the latent components of any time series that the filter smooths through the
corresponding eigenvalues. A difficulty arises because matrices associated with
trend filters are finite approximations of Toeplitz operators and therefore
very little is known about their eigenstructure, which also depends on the
boundary conditions or, equivalently, on the filters for trend estimation at
the end of the sample. Assuming reflecting boundary conditions, we derive a
time series decomposition in terms of periodic latent components and
corresponding smoothing eigenvalues. This decomposition depends on the local
polynomial regression estimator chosen for the interior. Otherwise, the
eigenvalue distribution is derived with an approximation measured by the size
of the perturbation that different boundary conditions apport to the
eigenvalues of matrices belonging to algebras with known spectral properties,
such as the Circulant or the Cosine. The analytical form of the eigenvectors is
then derived with an approximation that involves the extremes only. A further
topic investigated in the paper concerns a strategy for a filter design in the
time domain. Based on cut-off eigenvalues, new estimators are derived, that are
less variable and almost equally biased as the original estimator, based on all
the eigenvalues. Empirical examples illustrate the effectiveness of the method
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