Gravitational waves from inspiraling compact binaries: Validity of the stationary-phase approximation to the Fourier transform - art. no. 124016.

We prove that the oft-used stationary-phase method gives a very accurate ex pression for the Fourier transform of the gravitational-wave signal produce d by an inspiraling compact binary. We give three arguments. First, we anal ytically calculate the next-order correction to the stationary-phase approx imation, and show that it is small. This calculation is essentially an appl ication of the steepest-descent method to evaluate integrals. Second, we nu merically compare the stationary-phase expression to the results obtained b y fast Fourier transform. We show that the differences can be fully attribu ted to the windowing of the time series, and that they have nothing to do w ith an intrinsic failure of the stationary-phase method. And third, we show that these differences are negligible for the practical application of mat ched filtering. [S0556-2821(99)00414-2].