Matched filter for multitransducer resonant gravitational wave antennas

We analyze two kinds of matched filters for data output of a spherical resonant GW detector. In order to filter the data of a real sphere, a strategy is proposed, firstly using an omnidirectional inline filter, which is supposed to select periodograms with excitations, secondly by performing a directional filter on such selected periodograms, finding the wave arrival time, direction and polarization. We point out that, as the analytical simplifications occurring in the ideal 6 transducers TIGA sphere do not hold for a real sphere, using a 5 transducers configuration could be a more convenient choice.

Figure 1

Direction dependence of $s$ on the cylindrical coordinates ${\theta }^{\prime }$, ${\varphi }^{\prime }$. ${\theta }^{\prime }$ is the radial coordinate, and ${\varphi }^{\prime }$ the angular coordinate. We have fixed $\theta =0$, $\varphi =0$, $\psi =\pi /4$, ${\tilde{h}}_{+}^{\mathrm{fil}}=1$, ${\tilde{h}}_{\times }^{\mathrm{fil}}=0$ and plot $s$ for ${\theta }^{\prime }\in [0,\pi /2]$ and ${\varphi }^{\prime }\in [0,2\pi ]$. In order to avoid a mulitvalued function at ${\theta }^{\prime }=0$ we have corrected the polarization angle setting ${\psi }^{\prime }=\psi +{\varphi }^{\prime }$. We use the sphere model with capacitive transducers described in 12.

Figure 2

Strain sensitivity computed for directional filter. We use the 1 [m] radius sphere model with capacitive transducers of 12 and display the different noise contributions. We have used a $\delta$-filter.

Figure 3

Under the same conditions than Fig. 1 we plot the direction dependence of $\sqrt{s_E}$. Note that $\sqrt{s_E}$ vary only between $\sim 1/2$ and 1.

Figure 4

Strain sensitivity obtained for the energy filter. This computation is performed for the same sphere model as in Fig. 2.