## Optimal filtering of square-integrable signals in Gaussian noise.(English. Russian original)Zbl 0452.94003

Probl. Inf. Transm. 16, 120-133 (1980); translation from Probl. Peredachi Inf. 16, No. 2, 52-68 (1980).
Summary: Expressions are considered for the optimal mean-square error $$\delta^2$$ of restoration of signals from $$L_2(0,T)$$, in Gaussian noise $$\xi_1(t)$$, the exact asymptotic form of $$\delta^2$$ is obtained for the case in which $$\xi_1(t)=\varepsilon\xi_(t)$$, $$\varepsilon^2\to 0$$, while $$\theta(t)\in\mathfrak A$$, $$\mathfrak A$$ is an ellipsoid in $$L_2(0,T)$$, and also when $$T\to\infty$$. It is shown that the linear estimates are asymptotically optimal.

### MSC:

 94A12 Signal theory (characterization, reconstruction, filtering, etc.) 93E11 Filtering in stochastic control theory 60G15 Gaussian processes
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