** Up:** The art of fitting

The purpose of this appendix is to show that using a proper matrix
, the noise covariance matrix of Eq.
(37) given by:

| |
(A1) |

can have a diagonal form. The matrix can be
diagonalized and we can write.

| |
(A2) |

where is diagonal and is an orthogonal matrix (). Replacing Eq. (A2) into Eq. (A1), we have:

| |
(A3) |

Since is positive definite all its eigenvalues are
positive, therefore the square root of is defined.
Therefore if we apply the following transformation to the data:

| |
(A4) |

we can rewrite Eq. (A3) as:

| |
(A5) |

where is the identity matrix. So replacing in Eq.
(33) by will have the effect of removing
the artificial correlation due to the
noise, and also of performing a normalization. We should point out that
the transformation matrix that can achieve this
is not unique, and any multiplication by an orthogonal matrix will
achieve this. Nevertheless, we give a solution to the problem which
can be solved as an eigenvalue and eigenvector problem. The
transformation given above does not remove the artificial correlation
due the p modes but more or less preserve it. This can have some
useful application when one wants to produce spectra with uncorrelated
noise but with correlated p-mode signals.

** Up:** The art of fitting

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