Elliptical tiling method to generate a 2-dimensional set of templates for gravitational wave search

Searching for a signal depending on unknown parameters in a noisy background with matched filtering techniques always requires an analysis of the data with several templates in parallel in order to ensure a proper match between the filter and the real waveform. The key feature of such an implementation is the design of the filter bank which must be small to limit the computational cost while keeping the detection efficiency as high as possible. This paper presents a geometrical method that allows one to cover the corresponding physical parameter space by a set of ellipses, each of them being associated with a given template. After the description of the main characteristics of the algorithm, the method is applied in the field of gravitational wave (GW) data analysis, for the search of damped sine signals. Such waveforms are expected to be produced during the deexcitation phase of black holes-the so-called "ringdown" signals-and are also encountered in some numerically computed supernova signals. First, the number of templates N computed by the method is similar to its analytical estimation, despite the overlaps between neighbor templates and the border effects. Moreover, N is small enough to test for the first time the performances of the set of templates for different choices of the minimal match MM, the parameter used to define the maximal allowed loss of signal-to-noise ratio (SNR) due to the mismatch between real signals and templates. The main result of this analysis is that the fraction of SNR recovered is on average much higher than MM, which dramatically decreases the mean percentage of false dismissals. Indeed, it goes well below its estimated value of 1-MM3 used as input of the algorithm. Thus, as this feature should be common to any tiling algorithm, it seems possible to reduce the constraint on the value of MM-and indeed the number of templates and the computing power-without losing as many events as expected on average. This should be of great interest for the inspiraling binaries case where the number of templates can reach some hundreds of thousands for the whole parameter space.