FILTERING COALESCING BINARY SIGNALS - ISSUES CONCERNING NARROW BANDING, THRESHOLDS, AND OPTIMAL SAMPLING

When the raw output of a gravitational wave detector is correlated wit h the matched filter of a coalescing binary wave form the filtered out put shows a periodic behavior - it rings at a certain frequency. This phenomenon could be worrisome since the signal peak in the filtered ou tput might be reduced if it falls in the ''trough'' of the sinusoid. I n this paper we address this question and present a detailed examinati on of the ringing which is caused by the effective narrow banding by t he matched filter of detector noise. We first solve the problem for an idealized ''box'' filter and show that the ringing frequency is rough ly the central frequency of the box if the box is not too wide. For an idealized coalescing binary filter we show that the expected value of this frequency is 1.27 f(s) where f(s) is the seismic noise cutoff of the detector. The ringing implies that there is some redundancy in th e filtered ouput. Also the autocorrelation function of the filtered ou tput resembles the sinc function, and hence adjacent sample points are correlated, i.e., the filtered output is colored. These two phenomena are related and have a bearing on the setting up of thresholds and al so suggest that we resample the filtered output at a coarser rate. We investigate the problem of thresholds when the filtered output is colo red and obtain relations between the false alarm probabilities and thr eshold levels. Finally we suggest optimal sampling rates so that the r esampled filtered output is uncorrelated.