170 research outputs found
Predictability of band-limited, high-frequency, and mixed processes in the presence of ideal low-pass filters
Pathwise predictability of continuous time processes is studied in
deterministic setting. We discuss uniform prediction in some weak sense with
respect to certain classes of inputs. More precisely, we study possibility of
approximation of convolution integrals over future time by integrals over past
time. We found that all band-limited processes are predictable in this sense,
as well as high-frequency processes with zero energy at low frequencies. It
follows that a process of mixed type still can be predicted if an ideal
low-pass filter exists for this process.Comment: 10 page
Predictability on finite horizon for processes with exponential decrease of energy on higher frequencies
The paper presents sufficient conditions of predictability for continuous
time processes in deterministic setting. We found that processes with
exponential decay on energy for higher frequencies are predictable in some weak
sense on some finite time horizon defined by the rate of decay. Moreover, this
predictability can be achieved uniformly over classes of processes. Some
explicit formulas for predictors are suggested.Comment: 11 page
Detectability of Extrasolar Planets in Radial Velocity Surveys
Radial velocity surveys are beginning to reach the time baselines required to
detect Jupiter analogs, as well as sub-Saturn mass planets in close orbits.
Therefore it is important to understand the sensitivity of these surveys at
long periods and low amplitudes. In this paper, I derive analytic expressions
for the detectability of planets at both short and long periods, for circular
and eccentric orbits. I suggest an extension of the Lomb-Scargle periodogram
for Keplerian orbits, and describe how to estimate the false alarm probability
associated with a Keplerian fit. Using this to investigate the detectability of
eccentric orbits shows that there are significant selection effects against
eccentric orbits for e>0.6, and the small number of highly eccentric planets
discovered so far may reflect this. Finally, I present a Bayesian approach to
the periodogram, which emphasises the equivalence of least squares and
periodogram techniques.Comment: MNRAS, in press (12 pages, 13 figures
Random template placement and prior information
In signal detection problems, one is usually faced with the task of searching
a parameter space for peaks in the likelihood function which indicate the
presence of a signal. Random searches have proven to be very efficient as well
as easy to implement, compared e.g. to searches along regular grids in
parameter space. Knowledge of the parameterised shape of the signal searched
for adds structure to the parameter space, i.e., there are usually regions
requiring to be densely searched while in other regions a coarser search is
sufficient. On the other hand, prior information identifies the regions in
which a search will actually be promising or may likely be in vain. Defining
specific figures of merit allows one to combine both template metric and prior
distribution and devise optimal sampling schemes over the parameter space. We
show an example related to the gravitational wave signal from a binary inspiral
event. Here the template metric and prior information are particularly
contradictory, since signals from low-mass systems tolerate the least mismatch
in parameter space while high-mass systems are far more likely, as they imply a
greater signal-to-noise ratio (SNR) and hence are detectable to greater
distances. The derived sampling strategy is implemented in a Markov chain Monte
Carlo (MCMC) algorithm where it improves convergence.Comment: Proceedings of the 8th Edoardo Amaldi Conference on Gravitational
Waves. 7 pages, 4 figure
A Characterization of the Brightness Oscillations During Thermonuclear Bursts From 4U 1636-536
The discovery of nearly coherent brightness oscillations during thermonuclear
X-ray bursts from six neutron-star low-mass X-ray binaries has opened up a new
way to study the propagation of thermonuclear burning, and may ultimately lead
to greater understanding of thermonuclear propagation in other astrophysical
contexts, such as in Type Ia supernovae. Here we report detailed analyses of
the ~580 Hz brightness oscillations during bursts from 4U 1636-536. We
investigate the bursts as a whole and, in more detail, the initial portions of
the bursts. We analyze the ~580 Hz oscillations in the initial 0.75 seconds of
the five bursts that were used in a previous search for a brightness
oscillation at the expected ~290 Hz spin frequency, and find that if the same
frequency model describes all five bursts there is insufficient data to require
more than a constant frequency or, possibly, a frequency plus a frequency
derivative. Therefore, although it is appropriate to use an arbitrarily
complicated model of the ~580 Hz oscillations to generate a candidate waveform
for the ~290 Hz oscillations, models with more than two parameters are not
required by the data. For the bursts as a whole we show that the
characteristics of the brightness oscillations vary greatly from burst to
burst. We find, however, that in at least one of the bursts, and possibly in
three of the four that have strong brightness oscillations throughout the
burst, the oscillation frequency reaches a maximum several seconds into the
burst and then decreases. This behavior has not been reported previously for
burst brightness oscillations, and it poses a challenge to the standard burning
layer expansion explanation for the frequency changes.Comment: 18 pages including three figures, uses aaspp4.sty, submitted to The
Astrophysical Journal on April
Searching for Gravitational Waves from Binary Inspirals with LIGO
We describe the current status of the search for gravitational waves from
inspiralling compact binary systems in LIGO data. We review the result from the
first scientific run of LIGO (S1). We present the goals of the search of data
taken in the second scientific run (S2) and describe the differences between
the methods used in S1 and S2.Comment: 9 pages, 2 figures. Published in proceedings of the 8th Gravitational
Wave Data Analysis Workshop, Milwaukee, WI, USA, 17-20 December 200
Discrimination of signal and noise events on seismic recordings by linear threshold estimation theory
The object of this study is the investigation of a linear threshold element technique for identifying surface multiples on a single seismic trace. Traces of seismic events were generated which contained primaries, surface multiples, and various levels of Gaussian random noise. Since it was necessary to separate the events as much as possible, the traces were subjected to pulse-compression deconvolution processing prior to LTE analysis. Mean frequency, peak frequency, amplitude spectrum variance, periodicity, and polarity were employed as pattern parameters. A set of weights was found that would maximize the moment of inertia of the S line distribution of the patterns subject to the constraint that the sum of the squared values of the weights was minimized. It is shown that the problem of the maximization of the moment of inertia reduces to the solution of a simple eigenvalue problem. Furthermore, the optimum set of weights is the eigenvector corresponding to the largest eigenvalue of a matrix proportional to the autocovariance matrix of the pattern vectors. The classes of patterns representing primaries and multiples on traces with high signal-to-noise ratios were clustered and separated, making identification by inspection a simple procedure. Clustering and separation of classes on traces with low signal-to-noise ratios was less than optimum --Abstract, page ii
Gravitational waves from inspiraling compact binaries: Second post-Newtonian waveforms as search templates
We ascertain the effectiveness of the second post-Newtonian approximation to
the gravitational waves emitted during the adiabatic inspiral of a compact
binary system as templates for signal searches with kilometer-scale
interferometric detectors. The reference signal is obtained by solving the
Teukolsky equation for a small mass moving on a circular orbit around a large
nonrotating black hole. Fitting factors computed from this signal and these
templates, for various types of binary systems, are all above the 90% mark.
According to Apostolatos' criterion, second post-Newtonian waveforms should
make acceptably effective search templates.Comment: LaTeX, one eps figure. Hires and color versions are available from
http://jovian.physics.uoguelph.ca/~droz/uni/papers/search.htm
Gravitational waves from inspiralling compact binaries: Parameter estimation using second-post-Newtonian waveforms
The parameters of inspiralling compact binaries can be estimated using
matched filtering of gravitational-waveform templates against the output of
laser-interferometric gravitational-wave detectors. Using a recently calculated
formula, accurate to second post-Newtonian (2PN) order [order , where
is the orbital velocity], for the frequency sweep () induced by
gravitational radiation damping, we study the statistical errors in the
determination of such source parameters as the ``chirp mass'' , reduced
mass , and spin parameters and (related to spin-orbit and
spin-spin effects, respectively). We find that previous results using template
phasing accurate to 1.5PN order actually underestimated the errors in ,
, and . For two inspiralling neutron stars, the measurement errors
increase by less than 16 percent.Comment: 14 pages, ReVTe
Pulsar timing arrays as imaging gravitational wave telescopes: angular resolution and source (de)confusion
Pulsar timing arrays (PTAs) will be sensitive to a finite number of
gravitational wave (GW) "point" sources (e.g. supermassive black hole
binaries). N quiet pulsars with accurately known distances d_{pulsar} can
characterize up to 2N/7 distant chirping sources per frequency bin \Delta
f_{gw}=1/T, and localize them with "diffraction limited" precision \delta\theta
\gtrsim (1/SNR)(\lambda_{gw}/d_{pulsar}). Even if the pulsar distances are
poorly known, a PTA with F frequency bins can still characterize up to
(2N/7)[1-(1/2F)] sources per bin, and the quasi-singular pattern of timing
residuals in the vicinity of a GW source still allows the source to be
localized quasi-topologically within roughly the smallest quadrilateral of
quiet pulsars that encircles it on the sky, down to a limiting resolution
\delta\theta \gtrsim (1/SNR) \sqrt{\lambda_{gw}/d_{pulsar}}. PTAs may be
unconfused, even at the lowest frequencies, with matched filtering always
appropriate.Comment: 7 pages, 1 figure, matches Phys.Rev.D versio
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