Gravitational-Wave Data Analysis. Formalism and Sample Applications: The Gaussian Case

The article reviews the statistical theory of signal detection in application to analysis of deterministic gravitational-wave signals in the noise of a detector. Statistical foundations for the theory of signal detection and parameter estimation are presented. Several tools needed for both theoretical evaluation of the optimal data analysis methods and for their practical implementation are introduced. They include optimal signal-to-noise ratio, Fisher matrix, false alarm and detection probabilities, \F-statistic, template placement, and fitting factor. These tools apply to the case of signals buried in a stationary and Gaussian noise. Algorithms to efficiently implement the optimal data analysis techniques are discussed. Formulas are given for a general gravitational-wave signal that includes as special cases most of the deterministic signals of interest.Comment: Revised version of 2006-07-26; published version available at http://www.livingreviews.org/lrr-2005-

Detection of gravitational waves from inspiraling compact binaries using a network of interferometric detectors

We formulate the data analysis problem for the detection of the Newtonian waveform from an inspiraling compact-binary by a network of arbitrarily oriented and arbitrarily distributed laser interferometric gravitational wave detectors. We obtain for the first time the relation between the optimal statistic and the magnitude of the network correlation vector, which is constructed from the matched network-filter. This generalizes the calculation reported in an earlier work (gr-qc/9906064), where the detectors are taken to be coincident.Comment: 6 pages, RevTeX. Based on talk given at GWDAW-99, Rom

Constraint Likelihood analysis for a network of gravitational wave detectors

We propose a coherent method for the detection and reconstruction of gravitational wave signals for a network of interferometric detectors. The method is derived using the likelihood functional for unknown signal waveforms. In the standard approach, the global maximum of the likelihood over the space of waveforms is used as the detection statistic. We identify a problem with this approach. In the case of an aligned pair of detectors, the detection statistic depends on the cross-correlation between the detectors as expected, but this dependence dissappears even for infinitesimally small misalignments. We solve the problem by applying constraints on thelikelihood functional and obtain a new class of statistics. The resulting method can be applied to the data from a network consisting of any number of detectors with arbitrary detector orientations. The method allows us reconstruction of the source coordinates and the waveforms of two polarization components of a gravitational wave. We study the performance of the method with numerical simulation and find the reconstruction of the source coordinates to be more accurate than in the standard approach.Comment: 13 pages, 6 figure

Detecting Galactic Binaries with LISA

One of the main sources of gravitational waves for the LISA space-borne interferometer are galactic binary systems. The waveforms for these sources are represented by eight parameters, of which four are extrinsic, and four are intrinsic to the system. Geometrically, these signals exist in an 8-d parameter space. By calculating the metric tensor on this space, we calculate the number of templates needed to search for such sources. We show in this study that below a particular monochromatic frequency, we can ignore one of the intrinsic parameters and search over a 7-d space. Beyond this frequency, we have a sudden change in dimensionality of the parameter space from 7 to 8 dimensions, which results in a change in the scaling of the growth of template number as a function of monochromatic frequency.Comment: 7 pages-2 figures. One figure added and typos corrected. Accepted for the proceedings of GWDAW 9, special edition of Classical and Quantum Gravit

Quantum-mechanical communication theory

Optimum signal reception using quantum-mechanical communication theor

The application of prolate spheroidal wave functions to the detection and estimation of bandlimited signals

Prolate spheroidal wave functions for solution of Fredholm equation for bandlimited signal detectio

The Cauchy convergence of T and P-approximant templates for test-mass Kerr binary systems

In this work we examine the Cauchy convergence of both post-Newtonian (T-approximant) and re-summed post-Newtonian (P-approximant) templates for the case of a test-mass orbiting a Kerr black hole along a circular equatorial orbit. The Cauchy criterion demands that the inner product between the $n$ and $n+1$ order approximation approaches unity, as we increase the order of approximation. In previous works, it has been shown that we achieve greater fitting factors and better parameter estimation using the P-approximant templates for both Schwarzschild and Kerr black holes. In this work, we show that the P-approximant templates also display a faster Cauchy convergence making them a superior template to the standard post-Newtonian templates.Comment: 5 pages, Replaced with shortened published versio