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Wiener and Adaptive Filters

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Springer Handbook of Speech Processing

Part of the book series: Springer Handbooks ((SHB))

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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Abbreviations

DFT:

discrete Fourier transform

FIR:

finite impulse response

IIR:

infinite impulse response

IPNLMS:

improved PNLMS

LMS:

least mean square

MIMO:

multiple-input multiple-output

MMSE:

minimum mean-square error

MSE:

mean-square error

NLMS:

normalized least-mean-square

PNLMS:

proportionate NLMS

SIMO:

single-input multiple-output

SISO:

single-input single-output

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Author information

Authors and Affiliations

  1. INRS-EMT, University of Quebec, 800 de la Gauchetiere Ouest, H5A 1K6, Montreal, Quebec, Canada

    Jacob Benesty Prof.

  2. Alcatel-Lucent, Bell Laboratories, 600 Mountain Avenue, 07974, Murray Hill, NJ, USA

    Yiteng (Arden) Huang Dr.

  3. Alcatel-Lucent, Bell Laboratories, 600 Mountain Ave, 07974, Murray Hill, NJ, USA

    Jingdong Chen Dr.

Authors
  1. Jacob Benesty Prof.
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  2. Yiteng (Arden) Huang Dr.
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  3. Jingdong Chen Dr.
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Corresponding authors

Correspondence to Jacob Benesty Prof. , Yiteng (Arden) Huang Dr. or Jingdong Chen Dr. .

Editor information

Editors and Affiliations

  1. INRS-EMT, University of Quebec, 800 de la Gauchetiere Ouest, H5A 1K6, Montreal, Quebec, Canada

    Jacob Benesty Dr.

  2. Avayalabs Research, 233 Mount Airy Road, 07920, Basking Ridge, NJ, USA

    M. Mohan Sondhi Ph.D.

  3. Alcatel-Lucent, Bell Laboratories, 600 Mountain Avenue, 07974, Murray Hill, NJ, USA

    Yiteng Arden Huang Dr.

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© 2008 Springer-Verlag Berlin Heidelberg

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Benesty, J., Huang, Y.(., Chen, J. (2008). Wiener and Adaptive Filters. In: Benesty, J., Sondhi, M.M., Huang, Y.A. (eds) Springer Handbook of Speech Processing. Springer Handbooks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-49127-9_6

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  • DOI: https://doi.org/10.1007/978-3-540-49127-9_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-49125-5

  • Online ISBN: 978-3-540-49127-9

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