2,961 research outputs found
Improving the efficiency of the detection of gravitational wave signals from inspiraling compact binaries: Chebyshev interpolation
Inspiraling compact binaries are promising sources of gravitational waves for
ground and space-based laser interferometric detectors. The time-dependent
signature of these sources in the detectors is a well-characterized function of
a relatively small number of parameters; thus, the favored analysis technique
makes use of matched filtering and maximum likelihood methods. Current analysis
methodology samples the matched filter output at parameter values chosen so
that the correlation between successive samples is 97% for which the filtered
output is closely correlated. Here we describe a straightforward and practical
way of using interpolation to take advantage of the correlation between the
matched filter output associated with nearby points in the parameter space to
significantly reduce the number of matched filter evaluations without
sacrificing the efficiency with which real signals are recognized. Because the
computational cost of the analysis is driven almost exclusively by the matched
filter evaluations, this translates directly into an increase in computational
efficiency, which in turn, translates into an increase in the size of the
parameter space that can be analyzed and, thus, the science that can be
accomplished with the data. As a demonstration we compare the present "dense
sampling" analysis methodology with our proposed "interpolation" methodology,
restricted to one dimension of the multi-dimensional analysis problem. We find
that the interpolated search reduces by 25% the number of filter evaluations
required by the dense search with 97% correlation to achieve the same
efficiency of detection for an expected false alarm probability. Generalized to
higher dimensional space of a generic binary including spins suggests an order
of magnitude increase in computational efficiency.Comment: 23 pages, 5 figures, submitted to Phys. Rev.
A direct method to compute the galaxy count angular correlation function including redshift-space distortions
In the near future, cosmology will enter the wide and deep galaxy survey area
allowing high-precision studies of the large scale structure of the universe in
three dimensions. To test cosmological models and determine their parameters
accurately, it is natural to confront data with exact theoretical expectations
expressed in the observational parameter space (angles and redshift). The
data-driven galaxy number count fluctuations on redshift shells, can be used to
build correlation functions on and between shells which
can probe the baryonic acoustic oscillations, the distance-redshift distortions
as well as gravitational lensing and other relativistic effects. Transforming
the model to the data space usually requires the computation of the angular
power spectrum but this appears as an artificial and
inefficient step plagued by apodization issues. In this article we show that it
is not necessary and present a compact expression for
that includes directly the leading density and redshift space distortions terms
from the full linear theory. It can be evaluated using a fast integration
method based on Clenshaw-Curtis quadrature and Chebyshev polynomial series.
This new method to compute the correlation functions without any Limber
approximation, allows us to produce and discuss maps of the correlation
function directly in the observable space and is a significant step towards
disentangling the data from the tested models
Concepts for on-board satellite image registration, volume 1
The NASA-NEEDS program goals present a requirement for on-board signal processing to achieve user-compatible, information-adaptive data acquisition. One very specific area of interest is the preprocessing required to register imaging sensor data which have been distorted by anomalies in subsatellite-point position and/or attitude control. The concepts and considerations involved in using state-of-the-art positioning systems such as the Global Positioning System (GPS) in concert with state-of-the-art attitude stabilization and/or determination systems to provide the required registration accuracy are discussed with emphasis on assessing the accuracy to which a given image picture element can be located and identified, determining those algorithms required to augment the registration procedure and evaluating the technology impact on performing these procedures on-board the satellite
Fast computation of the Gauss hypergeometric function with all its parameters complex with application to the Poschl-Teller-Ginocchio potential wave functions
The fast computation of the Gauss hypergeometric function 2F1 with all its
parameters complex is a difficult task. Although the 2F1 function verifies
numerous analytical properties involving power series expansions whose
implementation is apparently immediate, their use is thwarted by instabilities
induced by cancellations between very large terms. Furthermore, small areas of
the complex plane are inaccessible using only 2F1 power series formulas, thus
rendering 2F1 evaluations impossible on a purely analytical basis. In order to
solve these problems, a generalization of R.C. Forrey's transformation theory
has been developed. The latter has been successful in treating the 2F1 function
with real parameters. As in real case transformation theory, the large
canceling terms occurring in 2F1 analytical formulas are rigorously dealt with,
but by way of a new method, directly applicable to the complex plane. Taylor
series expansions are employed to enter complex areas outside the domain of
validity of power series analytical formulas. The proposed algorithm, however,
becomes unstable in general when |a|,|b|,|c| are moderate or large. As a
physical application, the calculation of the wave functions of the analytical
Poschl-Teller-Ginocchio potential involving 2F1 evaluations is considered.Comment: 29 pages; accepted in Computer Physics Communication
The exponentially convergent trapezoidal rule
It is well known that the trapezoidal rule converges geometrically when applied to analytic functions on periodic intervals or the real line. The mathematics and history of this phenomenon are reviewed and it is shown that far from being a curiosity, it is linked with computational methods all across scientific computing, including algorithms related to inverse Laplace transforms, special functions, complex analysis, rational approximation, integral equations, and the computation of functions and eigenvalues of matrices and operators
Metastable energy strata in numerical discretizations of weakly nonlinear wave equations
The quadratic nonlinear wave equation on a one-dimensional torus with small
initial values located in a single Fourier mode is considered. In this
situation, the formation of metastable energy strata has recently been
described and their long-time stability has been shown. The topic of the
present paper is the correct reproduction of these metastable energy strata by
a numerical method. For symplectic trigonometric integrators applied to the
equation, it is shown that these energy strata are reproduced even on long time
intervals in a qualitatively correct way.Comment: 28 pages, 9 figure
The Discrete–Continuous Correspondence for Frequency-Limited Arma Models and the Hazards of Oversampling
Discrete-time ARMA processes can be placed in a one-to-one correspondence with a set of continuous-time processes that are bounded in frequency by the Nyquist value of ? radians per sample period. It is well known that, if data are sampled from a continuous process of which the maximum frequency exceeds the Nyquist value, then there will be a problem of aliasing. However, if the sampling is too rapid, then other problems will arise that will cause the ARMA estimates to be severely biased. The paper reveals the nature of these problems and it shows how they may be overcome. It is argued that the estimation of macroeconomic processes may be compromised by a failure to take account of their limits in frequency.Stochastic Differential Equations; Band-Limited Stochastic Processes; Oversampling
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