Analytic inversion of a class of covariance matrices

The sample covariance matrix arising out of finite memory linear least squares estimation over a set of equally spaced time points, is inverted by spectral methods (operationally referred to as the transform). It is shown that the complexity of the problem depends only upon the complexity of the input correlation function. The final solution is shown to reduce to the inversion of a triangular system of linear equations of an order less than half the degree of the denominator of the input power spectral density function.