2. Wiener filter

2.1 Problem position

We have a message m (t ) = s ₁ (t ) + b ₁ (t ) where signal and noise are two stationary random processes. The task is to find the stationary linear filter that gives the best approximation of s ₁ (t ) denoted $\hat{s} (t)$ . Signal and noise are two stationary random processes.

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Wiener filter

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Kalman filter

References

(1) - WIENER (N.) - Extrapolation, interpolation and smoothing of stationary time series - . MIT Press, 1949. Cambridge, Ma.
(2) - LEE (Y.W.) - Statistical theory of communication - . J. Wiley, 1960.
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