  The prior knowledge of the gravitational waveform from compact binary systems
makes matched filtering an attractive detection strategy. This detection method
involves the filtering of the detector output with a set of theoretical
waveforms or templates. One of the most important factors in this strategy is
knowing how many templates are needed in order to reduce the loss of possible
signals. In this study we calculate the number of templates and computational
power needed for a one-step search for gravitational waves from inspiralling
binary systems. We build on previous works by firstly expanding the
post-Newtonian waveforms to 2.5-PN order and secondly, for the first time,
calculating the number of templates needed when using P-approximant waveforms.
The analysis is carried out for the four main first-generation interferometers,
LIGO, GEO600, VIRGO and TAMA. As well as template number, we also calculate the
computational cost of generating banks of templates for filtering GW data. We
carry out the calculations for two initial conditions. In the first case we
assume a minimum individual mass of $1 M_{\odot}$ and in the second, we assume
a minimum individual mass of $5 M_{\odot}$. We find that, in general, we need
more P-approximant templates to carry out a search than if we use standard PN
templates. This increase varies according to the order of PN-approximation, but
can be as high as a factor of 3 and is explained by the smaller span of the
P-approximant templates as we go to higher masses. The promising outcome is
that for 2-PN templates the increase is small and is outweighed by the known
robustness of the 2-PN P-approximant templates.

General Relativity and Quantum Cosmology