The principles of pulse signal recovery from gravitational antennas

The general engineering problem of pulse signal recovery from a reactive (i.e. energy-storing) transducer is considered. It is shown that by using active filters (i.e. filters which are not subject to the constraints imposed upon passive systems by the second law of thermodynamics), pulses of energy less than k¿/2 (where ¿ is the absolute temperature) are detectable. The arguments are then extended to apply to the situation involving a resonant detector ¿ this is relevant to the gravitational wave detectors which are currently being engineered. In the resonant case the appropriate system function is centred on the resonance frequency ¿0/2¿ rather than on zero frequency. Expressions for the signal/noise ratio and the minimum detectable energy are obtained for a detector in terms of the Q values of the bar and the transducer, and ß, a parameter representing the degree of electro-mechanical coupling. Under optimum operating conditions the split bar is found to be more sensitive than the single bar by a factor of about 10; if, however, a time resolution of a few milliseconds is required for coincidence measurements the single bar shows a penalty of nearly 3000 compared with the split bar.