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L p -spectral estimation with anL ∞-upper bound

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Abstract

Given the constraint 0≤f≤B, whereB is in the interior of the positive cone ofL ∞, and given a finite number of correlations off, we wish to estimatef. Since only a finite number of correlations are given, this does not uniquely determinef. We estimatef by picking the unique function Φ0 satisfying the constraints and minimizing theL p -norm with 1<p<∞. Under suitable conditions, the form of the solution is shown to be

$$\Phi _0 (f) = \min \{ B(x), \max \{ 0,P(x)\} ^{1/(p - 1)} \} ,$$

whereP is a linear combination of the correlation functions.

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Author notes

  1. R. E. Cole (Staff Member)

    Present address: Department of Mathematics, University of Colorado, Boulder, Colorado

Authors and Affiliations

  1. Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, Massachusetts

    R. E. Cole (Staff Member)

  2. Department of Mathematics, University of Colorado, Boulder, Colorado

    R. K. Goodrich (Professor)

Authors
  1. R. E. Cole
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  2. R. K. Goodrich
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Communicated by D. G. Luenberger

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Cole, R.E., Goodrich, R.K. L p -spectral estimation with anL ∞-upper bound. J Optim Theory Appl 76, 321–355 (1993). https://doi.org/10.1007/BF00939611

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