  It has long been known that the search for gravitational waves from
inspiraling binaries must be aided by signal processing methods, and that the
technique of matched filtering is the most likely to be used for the detection
of inspiral ``chirps''. This means that the output of an interferometer must be
cross- correlated with many waveform templates to dig out faint signals buried
in the noise. The templates are characterized by several parameters which vary
continuously over some finite range; but because the amount of computing power
available to perform the cross-correlations of the search templates with the
output is finite, the actual templates used must be picked with certain
discrete values of these parameters, which will have some finite spacing. If
the spacing is too small, the number of templates (and therefore the computing
power) needed to perform an on-line search becomes prohibitive; if the spacing
is too large, many chirps will not be detected because the values of their
parameters lie too far from those of the nearest template. In this paper I use
differential geometry to extend the earlier formalism of Sathyaprakash and
Dhurandhar to estimate the template spacing, number of templates, and computing
power required for a single-pass, on-line search of the output of a single
interferometer in terms of the fraction of events lost to parameter
discretization. My formalism obtains these results with little numerical
computation, and is valid for arbitrary noise spectra and template
parameterizations. I find that the computing power needed for the most
computationally intensive, reasonable search is of order several hundred
Gigaflops. This will be feasible by the time LIGO is operational, but it is
worth pursuing methods of reducing this number.
