Frequency-domain P-approximant filters for time-truncated inspiral gravitational wave signals from compact binaries

Frequency-domain filters for time-windowed gravitational waves from inspiraling compact binaries are constructed which combine the excellent performance of our previously developed time-domain P approximants with the analytic convenience of the stationary phase approximation without a serious loss in event rate. These Fourier-domain representations incorporate the “edge oscillations” due to the (assumed) abrupt shutoff of the time-domain signal caused by the relativistic plunge at the last stable orbit. These new analytic approximations, the SPP approximants, are not only effectual for detection and faithful for parameter estimation, but are also computationally inexpensive to generate (and are faster by factors up to 10, as compared to the corresponding time-domain templates). The SPP approximants should provide data analysts the Fourier-domain templates for massive black hole binaries of total mass $m\lesssim {40M}_{\odot },$ the most likely sources for LIGO and VIRGO.