Computaion of Realizable Optimum Filter for Additive and Multiplicative Noises

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  • Computation of Realizable Optimum Filter for Additive and Multiplicative Noises
  • Computaion of Realizable Optimum Filter

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Abstract

This paper describes a realizable optimum filter under the mean square error criterion. First of all, the Wiener-Hoph equation is deduced for the system which contains additive and multiplicative noises. Under several assumptions, we find that both noise factors appear in the Wiener-Hoph equation as the sum of two noise terms. Next, we deal with several signal power spectrum densities which are not limited rational functions in the s-plane. Therefore, we cannot apply the method of spectrum factorization. So the impulse responses of this filter are computed by solving simultaneous equations which approximate the Wiener-Hoph equation. Some computed impulse responses for two noises and other parameters are illustrated, and the accuracy of this approximation is evaluated.

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