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A class of filter problems, II: Solution for absolutely continuous kernels

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Abstract

A variational problem generated by a class of filter problems in which the autocorrelation function of the noise is assumed to be expressible as a convolution of a functionK with itself is considered. The variational problem involves the minimization of the square of theL 1[0, ∞] norm of a functiony plus the square of theL 2[0, ∞] norm of a functionG. The functionsy andG are related by a renewal equation which also involvesK. Existence and uniqueness of the solution was established earlier. In this paper, the solution is shown to have compact support.

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References

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Additional information

This research was supported by NSF Grants Nos. MCS-79-27137 and MCS-78-01106.

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Berkovitz, L.D. A class of filter problems, II: Solution for absolutely continuous kernels. J Optim Theory Appl 37, 387–399 (1982). https://doi.org/10.1007/BF00935278

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Key Words

  • Optimal filters
  • variational problems
  • renewal equations
  • solutions with compact support