where, the Hermitian property of the Fourier transform of a real function has been used to restrict the domain of integration to positive frequencies. $S_n(f)$ is the power spectral density of the noise. The Fourier domain is convenient since stationarity of the noise has been assumed. The norm of a vector ${\bf z}$ will be denoted by $\|{\bf z}\| = \left\langle{\bf z},{\bf z}\right\rangle^{1/2}$. In eqn. (\[FT\]) we had left $\cal N$ undefined. We choose the value of $\cal N$ such that $\|{\bf s}(\bbox{\mu})\| = A$. From the definition of the scalar product in eqn. (\[scal\]) and from eqn. (\[FT\]) it follows that, $$\label{normdef}
\frac{1}{{\cal N}^2} = 2\int\limits_0^\infty \frac{f^{-7/3}}{S_n(f)}df.$$ The integrand in the above equation, $I(f)$ is plotted in Fig. \[fig1\]. This function peaks at around $f=135$Hz and a major contribution to the integral comes from a region around $135$Hz.

We shall use normalized matched filters, that is,we set ${\bf h}(\mu^j) =  {\bf s}(\bbox{\mu})/A$. Henceforth we shall use the symbols $a,b,\ldots$ to indicate indices whose range of values includes $0$ which as a index denotes the amplitude parameter, [*i.e. $\mu^0 = A$*]{}. Indices $i,j,\ldots$ will not include the amplitude parameter and will never take the value $0$.

The output called the 