as given in [@CF94]: $$\label{psd}
S_n(f) = S_0 \left[\left(\frac{f}{200}\right)^{-4} + 2\left(1+\frac{f}{200}\right)^2\right].$$ The value of $S_0$ will not concern us since what matters is only the ratio of the signal amplitude to that of the noise, in other words the SNR. We shall set the value of $S_0$ to be unity and accordingly adjust the amplitude of the signal to get the required SNR.

The Matched Filter {#mf}
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In the absence of any prior information it must be assumed that all the parameter values, within their respective range, are equally likely to occur. In such a case, the method of maximum liklihood can be used. When the noise is a stationary Gaussian random process, the method of MLE reduces to the so called matched filtering technique. Matched filtering involves correlating the detector output with a bank of matched filters each of which corresponds to the signal waveform for a fixed set of parameters. To this end, we define a scalar product on $\cal V$. In the continuum limit the scalar product between two vectors ${\bf x}$ and ${\bf y}$ is given by, $$\label{scal}
\left\langle{\bf x},{\bf y}\right\rangle   = \int_{0}^{\infty}df\,{1\over S_n(f)}\, 
 \left( \, \tilde{x}(f)\, \tilde{y}^{\ast} (f)\, + \,\tilde{x}^{\ast}(f)
 \,\tilde{y}(f)\, \right) \; ,$$ 