Optimum filtering and sensitivity for resonant gravitational-wave antennas.

The optimum filter algorithm based on the Wiener-Kolmogorov theory for the linear mean-square estimation of signals in the presence of noise is applied to the data provided by a gravitational-wave antenna. The conditions for reaching the ultimate sensitivity limit are studied in terms of the coupling constant (ratio of the energy in the electromechanical transducer to the total energy available in the antenna), the merit factor of the antenna, the antenna temperature, the antenna mass and the transducer intrinsic temperature. The electromechanical transducer is assumed to be linear. It is shown that the SNR for the filtered data is independent of the data-sampling time and the electronic circuit used. When the quantum limited noise is reached, the only way to improve the sensitivity of the antenna is to increase its mass. It is shown that the use of a large mass (above 1000 kg) might be necessary for detecting the supernovae in the Virgo cluster.