$A$, is the amplitude parameter depending on the distance to the binary, as well as the chirp mass and $\cal N$ is a normalization constant to be fixed by means of a scalar product to be introduced later, and $$\begin{aligned}
\label {eqs1}
\chi_1 & = & {f\over f_s}, \nonumber\\
\chi_2 & = & -1, \nonumber\\
\chi_3 & = & {f\over f_s}  -{ 8 \over 5}+ {3\over 5}
\left ( {f\over f_s} \right )^{-5/3},\nonumber\\
\chi_4 & = & {f\over f_s} - 2 + {f_s\over f}.\end{aligned}$$ For $f<0$ the Fourier transform is computed using the identity $\tilde
s(-f) = \tilde s^*(f)$ obeyed by real functions $s(t).$

The noise {#noise}
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The output of a gravitational wave detector such as the LIGO, will comprise of data segments, each of duration $T$ seconds, uniformly sampled with a sampling interval of $\Delta$, giving the number of samples in a single data train to be $N = T/\Delta$. Each data train can be considered as a $N$-tuple ${\bf x} \equiv \{x^0,x^1,\ldots,x^{N-1}\}$, $x^a$ being the value of the output of the detector at time $a\Delta$. The set of all such $N$-tuples constitutes an $N$-dimensional vector space $\cal V$ where the addition of two vectors is accomplished by 