$L_2 $ Spectral Estimation
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The problem of estimating the power spectrum given a finite number of correlations is considered. A new spectral estimation is developed that minimizes the $L_p $ norm where $1 < p < \infty $. This estimate is of the form max $(P(k),0)^{1(p - 1)} $ where P is a trigonometric polynomial. This solution is shown to exist in some applications where a solution of the form $1/P$ fails to exist, where P is a positive trigonometric polynomial.