Choice of filters for the detection of gravitational waves from coalescing binaries

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Abstract
Coalescing binaries are one of the most promising candidates for the detection of gravitational waves with the advent of the new generation of laser interferometric gravitational-wave detectors. Signals from coalescing binaries will most probably not stand above the broadband noise of the detector. Their detection is possible by the use of special data analysis techniques such as matched filtering which takes advantage of the fact that the wave form can be fairly well predicted. The wave form of the coalescing binary signal is known very accurately. However, the parameters of the signal are not known priori and the signal needs to be correlated with several filters which are copies of the coalescing binary wave form for different values of the parameters. In this paper we present an algorithm to choose a lattice set of filters by a criterion that every signal of a certain minimal strength is picked up by at least one filter of the set. The wave form is characterized by three parameters: the time of arrival, the mass parameter, and the phase of the signal. We show that it is enough to have just two filters corresponding to the phase of the signal. Determination of the lattice for various values of the mass parameter involves a knowledge of the cross correlation function of two chirp wave forms with different values of the parameters. It is shown that for a considerable range of the mass parameter, the peak value of the correlation function, in a certain approximation, does not depend on the absolute values of the parameters but only on their difference. This leads to a very convenient way of constructing most of the lattice. The maximum possible distance up to which we can see is restricted by the threshold of the detector. There is a further limitation on this distance brought about by the fact that we can use only a finite number of filters. The number of filters which one can use depends on the available computing power. Hence, there is an empirical relation between computing power and the distance up to which we can see. In a restricted sense, the computing power decides the number of detectable events. Numerical experiments indicate that parallel processing is a promising new approach to on-line data analysis.