29,031 research outputs found

    A unique polar representation of the hyperanalytic signal

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    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

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    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

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    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

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    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

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    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 L^(t)\mathbf{\hat{L}}(t) can be calculated from the gravitational-wave signal. This is done by calculating the direction that maximises the quadrupolar (ℓ=2,∣m∣=2)(\ell=2,|m|=2) emission. The direction depends on whether we use the Weyl scalar ψ4\psi_4 or the gravitational-wave strain hh, but these directions are nonetheless invariant for a given binary configuration. We treat the ψ4\psi_4-based direction as a proxy to L^(t)\mathbf{\hat{L}}(t). We investigate how well the the binary's orbital phase, ϕorb(t)\phi_{\rm orb}(t), can also be estimated from the signal. For this purpose we define a quantity Φ(t)\Phi(t) that agrees well with ϕorb(t)\phi_{\rm orb}(t). 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

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    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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