Description
The goal of the Wiener filter is to filter out noise that has corrupted a signal. It is based on a statistical approach.
Typical filters are designed for a desired frequency response. However, the design of the Wiener filter takes a different approach. One is assumed to have knowledge of the spectral properties of the original signal and the noise, and one seeks the linear time-invariant filter whose output would come as close to the original signal as possible. Wiener filters are characterized by the following:
- Assumption: signal and (additive) noise are stationary linear stochastic processes with known spectral characteristics or known autocorrelation and cross-correlation
- Requirement: the filter must be physically realizable/causal (this requirement can be dropped, resulting in a non-causal solution)
- Performance criterion: minimum mean-square error (MMSE)
This filter is frequently used in the process of deconvolution; for this application, see Wiener deconvolution.
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