29,031 research outputs found
A unique polar representation of the hyperanalytic signal
The hyperanalytic signal is the straight forward generalization of the
classical analytic signal. It is defined by a complexification of two canonical
complex signals, which can be considered as an inverse operation of the
Cayley-Dickson form of the quaternion. Inspired by the polar form of an
analytic signal where the real instantaneous envelope and phase can be
determined, this paper presents a novel method to generate a polar
representation of the hyperanalytic signal, in which the continuously complex
envelope and phase can be uniquely defined. Comparing to other existing
methods, the proposed polar representation does not have sign ambiguity between
the envelope and the phase, which makes the definition of the instantaneous
complex frequency possible.Comment: 2014 IEEE International Conference on Acoustics, Speech, and Signal
Processing (ICASSP
Gravitational waves from BH-NS binaries: Effective Fisher matrices and parameter estimation using higher harmonics
Inspiralling black hole-neutron star (BH-NS) binaries emit a complicated
gravitational wave signature, produced by multiple harmonics sourced by their
strong local gravitational field and further modulated by the orbital plane's
precession. Some features of this complex signal are easily accessible to
ground-based interferometers (e.g., the rate of change of frequency); others
less so (e.g., the polarization content); and others unavailable (e.g.,
features of the signal out of band). For this reason, an ambiguity function (a
diagnostic of dissimilarity) between two such signals varies on many parameter
scales and ranges. In this paper, we present a method for computing an
approximate, effective Fisher matrix from variations in the ambiguity function
on physically pertinent scales which depend on the relevant signal to noise
ratio. As a concrete example, we explore how higher harmonics improve parameter
measurement accuracy. As previous studies suggest, for our fiducial BH-NS
binaries and for plausible signal amplitudes, we see that higher harmonics at
best marginally improve our ability to measure parameters. For non-precessing
binaries, these Fisher matrices separate into intrinsic (mass, spin) and
extrinsic (geometrical) parameters; higher harmonics principally improve our
knowledge about the line of sight. For the precessing binaries, the extra
information provided by higher harmonics is distributed across several
parameters. We provide concrete estimates for measurement accuracy, using
coordinates adapted to the precession cone in the detector's sensitive band.Comment: 19 pages, 11 figure
Detection of Coherent Vorticity Structures using Time-Scale Resolved Acoustic Spectroscopy
We describe here an experimental technique based on the acoustic scattering
phenomenon allowing the direct probing of the vorticity field in a turbulent
flow. Using time-frequency distributions, recently introduced in signal
analysis theory, for the analysis of the scattered acoustic signals, we show
how the legibility of these signals is significantly improved (time resolved
spectroscopy). The method is illustrated on data extracted from a highly
turbulent jet flow : discrete vorticity events are clearly evidenced. We claim
that the recourse to time-frequency distributions lead to an operational
definition of coherent structures associated with phase stationarity in the
time-frequency plane.Comment: 26 pages, 6 figures. Latex2e format Revised version : Added
references, figures and Changed conten
Bayesian Bounds on Parameter Estimation Accuracy for Compact Coalescing Binary Gravitational Wave Signals
A global network of laser interferometric gravitational wave detectors is
projected to be in operation by around the turn of the century. Here, the noisy
output of a single instrument is examined. A gravitational wave is assumed to
have been detected in the data and we deal with the subsequent problem of
parameter estimation. Specifically, we investigate theoretical lower bounds on
the minimum mean-square errors associated with measuring the parameters of the
inspiral waveform generated by an orbiting system of neutron stars/black holes.
Three theoretical lower bounds on parameter estimation accuracy are considered:
the Cramer-Rao bound (CRB); the Weiss-Weinstein bound (WWB); and the Ziv-Zakai
bound (ZZB). We obtain the WWB and ZZB for the Newtonian-form of the coalescing
binary waveform, and compare them with published CRB and numerical Monte-Carlo
results. At large SNR, we find that the theoretical bounds are all identical
and are attained by the Monte-Carlo results. As SNR gradually drops below 10,
the WWB and ZZB are both found to provide increasingly tighter lower bounds
than the CRB. However, at these levels of moderate SNR, there is a significant
departure between all the bounds and the numerical Monte-Carlo results.Comment: 17 pages (LaTeX), 4 figures. Submitted to Physical Review
Inferring black-hole orbital dynamics from numerical-relativity gravitational waveforms
Binary-black-hole dynamics cannot be related to the resulting
gravitational-wave signal by a constant retarded time. This is due to the
non-trivial dynamical spacetime curvature between the source and the signal. In
a numerical-relativity simulation there is also some ambiguity in the
black-hole dynamics, which depend on the gauge (coordinate) choices used in the
numerical solution of Einstein's equations. It has been shown previously that a
good approximation to the direction of the binary's time-dependent orbital
angular momentum can be calculated from the
gravitational-wave signal. This is done by calculating the direction that
maximises the quadrupolar emission. The direction depends on
whether we use the Weyl scalar or the gravitational-wave strain ,
but these directions are nonetheless invariant for a given binary
configuration. We treat the -based direction as a proxy to
. We investigate how well the the binary's orbital phase,
, can also be estimated from the signal. For this purpose we
define a quantity that agrees well with . One
application is to studies that involve injections of numerical-relativity
waveforms into gravitational-wave detector data.Comment: 12 pages with 10 figure
Improved filters for gravitational waves from inspiralling compact binaries
The order of the post-Newtonian expansion needed, to extract in a reliable
and accurate manner the fully general relativistic gravitational wave signal
from inspiralling compact binaries, is explored. A class of approximate wave
forms, called P-approximants, is constructed based on the following two inputs:
(a) The introduction of two new energy-type and flux-type functions e(v) and
f(v), respectively, (b) the systematic use of Pade approximation for
constructing successive approximants of e(v) and f(v). The new P-approximants
are not only more effectual (larger overlaps) and more faithful (smaller
biases) than the standard Taylor approximants, but also converge faster and
monotonically. The presently available O(v/c)^5-accurate post-Newtonian results
can be used to construct P-approximate wave forms that provide overlaps with
the exact wave form larger than 96.5% implying that more than 90% of potential
events can be detected with the aid of P-approximants as opposed to a mere
10-15 % that would be detectable using standard post-Newtonian approximants.Comment: Latex ([prd,aps,eqsecnum,epsf]{revtex}), 40 pages including 12
encapsulated figures. (The paper, together with all the figures and tables is
available from ftp://carina.astro.cf.ac.uk/pub/incoming/sathya/dis97.uu
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