`int num:`In order to deal with templates ``wholesale" it is useful to number them. The numbering system is up to you; we typically give each template a number, starting from 0 and going up to the number of templates minus one!`float f_lo:`This is the starting (low) frequency of template, in units of .`float f_hi:`This is the ending (high) frequency of the template, in units of`float tau0:`The Newtonian time to coalescence, in seconds, starting from the moment when the frequency of the waveform is f_lo.`float tau1:`First post-Newtonian correction to .`float tau15:`3/2 PN correction`float tau20:`second order PN correction`float pha0:`Newtonian phase to coalescence, radians`float pha1:`First post-Newtonian correction to pha0`float pha15:`3/2 PN correction`float pha20:`second order PN correction`float mtotal:`total mass , in solar masses`float mchirp:`chirp mass , in solar masses`float mred:`the reduced mass , in solar masses`float eta:`reduced mass/total mass , dimensionless`float m1:`the smaller of the two masses, in solar masses.`float m2:`the larger of the two masses, in solar masses.

One may use the technique of *matched filtering* to search for
chirps. The (noisy) signal is compared with templates, each formed
from a chirp with a particular values of , , and a ``start
frequency" of the waveform at the time that it enters the
bandpass of the gravitational wave detector. Several theoretical
studies [4,5] have shown how the template filtering
technique performs when the detector is not ideal, but is contaminated by
instrument noise.

In the presence of detector noise, one can never be entirely certain that a given chirp (determined by ) will be detected by a particular template, even one with the exact same mass parameters. However one can make statistical statements about a template, such as ``if the masses and of the chirp lie in region of parameter space, then with 97% probability, they will be detected if their amplitude exceeds value ". Thus, associated with each chirp, and a specified level of uncertainty, is a region of parameter space.

It turns out that if we use the correct choice of coordinates on the
parameter space then these regions are quite simple.
If we demand that the uncertainty associated with each template be
fairly small, then these regions are ellipses. Moreover, to a good
approximation, the shape of the ellipses is determined only by the
noise power spectrum of the detector, and does not change significantly
as we move about in the parameter space. These ``nice" coordinates
have units of time, and are defined by

and

The symbol

(9.1.192) |

(9.1.193) |

We are generally interested in a region of parameter space corresponding to binary systems, each of whose masses lie in some given range, say from to solar masses. The region of parameter space is determined by a minimum and maximum mass; we show an example of this in Figure .

- (1) The equal mass line. Along this line .
- (2) The minimum mass line. Along this line, one of the masses has its smallest value.
- (3) The maximum mass line. Along this line, one of the masses has its largest value.