To following is based on sections and .
Using the definition () for the scalar product
we can rewrite the expectation value () of the signal to
noise ratio (SNR) as

The function gives the reduction of the SNR due to a nonoptimal template . It is commonly called the

As was mentioned in section every signal is a linear combination of two orthogonal modes and (we suppress the index for now), where . We can filter for any linear combination by using the template

Using , the ambiguity function becomes

The sample program `plot_ambig` produces a file containing
as a function of the chirp mass
and the mass ratio
. The templates are taken to
be the 2 pN spin-less wave forms and the signal is one of the modes calculated from
perturbation theory.
The output is saved to the file `scan.dat`.
Includes/plot_ambig.tex