will have to be bandpassed with a low frequency seismic cutoff, $f_s$, and a high frequency cutoff, $f_c$. We use the power spectral density expected for the initial LIGO as given in [@LIGO]. Accordingly, we choose $f_s = 40$ Hz and $ f_c = 800$ Hz.

In the absence of the signal the output will contain only noise drawn from a stochastic process which can be described by a probability distribution on the vector space $\cal V$. We assume that the noise has its mean zero, or that is, $\overline{n^a} = 0$, where the overbar denotes an ensemble average. Then the covariance matrix of the noise ${\cal C}^{ab}$ is defined as, $${\cal C}^{ab} = \overline{n^a n^b}.$$ If the noise is assumed to be stationary and ergodic then there exists a noise autocorrelation function $K(t)$ such that ${\cal C}^{ab} = 
K(|a-b|\Delta)$. In the Fourier basis it can be shown that the components of the noise vector are statistically independent [@HEL] and the covariance matrix in the Fourier basis will contain only diagonal terms whose values will be strictly positive: $\tilde{\cal C}^{aa} = \overline{\tilde n^a\tilde n^{*a}}$. This implies that the covariance matrix has strictly positive eigenvalues. The diagonal elements of this matrix 