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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 Lₚ norm where 1 < p < ∞. 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.
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Goodrich et al. (1986) studied this question.
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