Choice of filters for the detection of gravitational waves from coalescing binaries. 2: Detection in coloured noise

The problem of detecting gravitational wave signals embedded in colored noise from coalescing binary systems is discussed. The signal is assumed to be Newtonian and matched filtering techniques are employed to filter out the signal. The problem is discussed at first for a general power spectral density of the noise and then specific numerical results are obtained for the standard recycling case. Since the signal parameters are unknown, a bank of filters is needed to carry out the signal detection. The number of filters in a bank, the spacing between filters etc. is obtained for different values of the minimum strength of the signal relative to the threshold. An approximate analytical formula which relates the spacing between filters to the minimum strength is also presented. Finally, we discuss the problem of detection probabilities given a data train.