Choice of filters for the detection of gravitational waves from coalescing binaries. II. Detection in colored noise

Coalescing systems of compact binary stars are one of the most important sources for the future laser interferometric gravitational wave detectors. The signal from such a source will, in general, be completely swamped out by the photon-counting noise in the interferometer. However, since the wave form can be modeled quite accurately, it is possible to filter the signal out of the noise by the well known technique of matched filtering. The filtering procedure involves correlating the detector output with a copy of the expected signal called a matched filter or a template. When the signal parameters are unknown, as in the case of the coalescing binary signal, it is necessary to correlate the output through a number of filters each with a different set of values for the parameters. The ranges in which the values of the parameters lie are determined from astrophysical considerations and the set of filters must together span the entire ranges of the parameters. In this paper, we show how a choice of filters can be made so as not to miss any signal of amplitude larger than a certain minimum value, called the minimal strength. The number of filters and the spacing between filters in the parameter space are obtained for different values of the minimal strength of the signal. We also present an approximate analytical formula which relates the spacing between filters to the minimal strength. We discuss the problem of detection and false dismissal probabilities for a given data output and how a given set of filters determines these probabilities.