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Abstract

Wiener theory, formulated by Norbert Wiener, forms the foundation of data-dependent linear least squared error filters. Wiener filters play a central role in a wide range of applications such as linear prediction, signal coding, echo cancellation, signal restoration, channel equalisation, system identification etc. The coefficients of a Wiener filter are calculated to minimise the average squared distance between the filter output and a desired signal. In its basic form, the Wiener theory assumes that the signals are stationary processes. However, if the filter coefficients are periodically recalculated, for every block of N samples, then the filter adapts to the average characteristics of the signals within the blocks and becomes block-adaptive. A block-adaptive filter can be used for signals that can be considered stationary over the duration of the block. In this chapter we study the theory of Wiener filters, and consider alternative methods of formulation of the Wiener filter problem. We consider the application of Wiener filters in channel equalisation, time-delay estimation, and additive noise suppression. A case study of the frequency response of a Wiener filter, for additive noise reduction, provides useful insight into the operation of the filter. We also deal with some implementation issues of Wiener filters.

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Copyright information

© John Wiley & Sons Ltd. and B.G. Teubner 1996

Authors and Affiliations

  • Saeed V. Vaseghi
    • 1
  1. 1.Queen’s UniversityBelfastUK

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