Abstract
The Wiener filter, named after its inventor, has been an extremely useful tool since its invention in the early 1930s. This optimal filter is not only popular in different aspects of speech processing but also in many other applications. This chapter presents the most fundamental results of the Wiener theory with an emphasis on the Wiener-Hopf equations, which are not convenient to solve in practice. An alternative approach to solving these equations directly is the use of an adaptive filter, which is why this work also describes the most classical adaptive algorithms that are able to converge, in a reasonable amount of time, to the optimal Wiener filter.
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