Gravitational waves from inspiraling compact binaries: Validity of the stationary-phase approximation to the Fourier transform

Serge Droz, Daniel J. Knapp, Eric Poisson, Benjamin J. Owen

Research output: Contribution to journalArticle

90 Scopus citations

Abstract

We prove that the oft-used stationary-phase method gives a very accurate expression for the Fourier transform of the gravitational-wave signal produced by an inspiraling compact binary. We give three arguments. First, we analytically calculate the next-order correction to the stationary-phase approximation, and show that it is small. This calculation is essentially an application of the steepest-descent method to evaluate integrals. Second, we numerically compare the stationary-phase expression to the results obtained by fast Fourier transform. We show that the differences can be fully attributed to the windowing of the time series, and that they have nothing to do with an intrinsic failure of the stationary-phase method. And third, we show that these differences are negligible for the practical application of matched filtering.

Original languageEnglish
Article number124016
Pages (from-to)1-8
Number of pages8
JournalPhysical Review D
Volume59
Issue number12
StatePublished - Jun 15 1999

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