Response of resonant gravitational wave detectors to damped sinusoid signals

Till date, the search for burst signals with resonant gravitational wave (GW) detectors has been done using the delta-function approximation for the signal, which was reasonable due to the very small bandwidth of these detectors. However, now with increased bandwidth (of the order of 10 or more Hz) and with the possibility of comparing results with interferometric GW detectors (broad-band), it is very important to exploit the resonant detectors' capability to detect also signals with specific wave shapes. As a first step, we present a study of the response of resonant GW detectors to damped sinusoids with given frequency and decay time and report on the development of a filter matched to these signals. This study is a preliminary step towards the comprehension of the detector response and of the filtering for signals such as the excitation of stellar quasi-normal modes.