Toward Early-Warning Detection of Gravitational Waves from Compact Binary Coalescence

Rapid detection of compact binary coalescence (CBC) with a network of advanced gravitational-wave detectors will offer a unique opportunity for multi-messenger astronomy. Prompt detection alerts for the astronomical community might make it possible to observe the onset of electromagnetic emission from (CBC). We demonstrate a computationally practical filtering strategy that could produce early-warning triggers before gravitational radiation from the final merger has arrived at the detectors.Comment: 16 pages, 7 figures, published in ApJ. Reformatted preprint with emulateap

Recent Advances in Theory and Methods for Nonstationary Signal Analysis

Cataloged from PDF version of article.All physical processes are nonstationary. When analyzing time series, it should be remembered that nature can be amazingly complex and that many of the theoretical constructs used in stochastic process theory, for example, linearity, ergodicity, normality, and particularly stationarity, are mathematical fairy tales. There are no stationary time series in the strict mathematical sense; at the very least, everything has a beginning and an end. Thus, while it is necessary to know the theory of stationary processes, one should not adhere to it dogmatically when analyzing data from physical sources, particularly when the observations span an extended period. Nonstationary signals are appropriate models for signals arising in several fields of applications including communications, speech and audio, mechanics, geophysics, climatology, solar and space physics, optics, and biomedical engineering. Nonstationary models account for possible time variations of statistical functions and/or spectral characteristics of signals. Thus, they provide analysis tools more general than the classical Fourier transform for finite-energy signals or the power spectrum for finite-power stationary signals. Nonstationarity, being a “nonproperty” has been analyzed from several different points of view. Several approaches that generalize the traditional concepts of Fourier analysis have been considered, including time-frequency, time-scale, and wavelet analysis, and fractional Fourier and linear canonical transforms

Recent Advances in Theory and Methods for Nonstationary Signal Analysis

Cataloged from PDF version of article.All physical processes are nonstationary. When analyzing time series, it should be remembered that nature can be amazingly complex and that many of the theoretical constructs used in stochastic process theory, for example, linearity, ergodicity, normality, and particularly stationarity, are mathematical fairy tales. There are no stationary time series in the strict mathematical sense; at the very least, everything has a beginning and an end. Thus, while it is necessary to know the theory of stationary processes, one should not adhere to it dogmatically when analyzing data from physical sources, particularly when the observations span an extended period. Nonstationary signals are appropriate models for signals arising in several fields of applications including communications, speech and audio, mechanics, geophysics, climatology, solar and space physics, optics, and biomedical engineering. Nonstationary models account for possible time variations of statistical functions and/or spectral characteristics of signals. Thus, they provide analysis tools more general than the classical Fourier transform for finite-energy signals or the power spectrum for finite-power stationary signals. Nonstationarity, being a “nonproperty” has been analyzed from several different points of view. Several approaches that generalize the traditional concepts of Fourier analysis have been considered, including time-frequency, time-scale, and wavelet analysis, and fractional Fourier and linear canonical transforms

Comparing compact binary parameter distributions I: Methods

Being able to measure each merger's sky location, distance, component masses, and conceivably spins, ground-based gravitational-wave detectors will provide a extensive and detailed sample of coalescing compact binaries (CCBs) in the local and, with third-generation detectors, distant universe. These measurements will distinguish between competing progenitor formation models. In this paper we develop practical tools to characterize the amount of experimentally accessible information available, to distinguish between two a priori progenitor models. Using a simple time-independent model, we demonstrate the information content scales strongly with the number of observations. The exact scaling depends on how significantly mass distributions change between similar models. We develop phenomenological diagnostics to estimate how many models can be distinguished, using first-generation and future instruments. Finally, we emphasize that multi-observable distributions can be fully exploited only with very precisely calibrated detectors, search pipelines, parameter estimation, and Bayesian model inference