Conventional Optimization

  • Jacob BenestyEmail author
  • Jingdong Chen
  • Chao Pan
Part of the SpringerBriefs in Electrical and Computer Engineering book series (BRIEFSELECTRIC)


With conventional optimization techniques, we can derive a large class of differential beamformers as it is shown in this chapter. From some classical quadratic criteria, we introduce the w-hypercardioid and the w-supercardioid of any order. We also propose robust versions of them. We reveal how to design the dipole and the cardioid of any order, by exploiting the fact that they have a unique null of maximum multiplicity but at different positions. We also present some other differential beamformers that can compromise between the white noise gain and the directivity factor.


  1. 1.
    Benesty J, Chen J, Huang Y (2008) Microphone array signal processing. Springer, BerlinGoogle Scholar
  2. 2.
    Seber GAF (2008) A matrix handbook for statisticians. John Wiley & Sons Inc., HobokenGoogle Scholar
  3. 3.
    Cox H, Zeskind RM, Kooij T (1986) Practical supergain. IEEE Trans Acoust Speech Signal Process ASSP-34:393–398Google Scholar
  4. 4.
    Cox H, Zeskind RM, Owen MM (1987) Robust adaptive beamforming. IEEE Trans Acoust Speech Signal Process ASSP-35:1365–1376Google Scholar
  5. 5.
    Franklin JN (1968) Matrix theory. Prentice-Hall, Englewood CliffsGoogle Scholar
  6. 6.
    Golub GH, Van Loan CF (1996) Matrix computations, 3rd edn. The Johns Hopkins University Press, BaltimoreGoogle Scholar
  7. 7.
    Chen J, Benesty J, Pan C (2014) On the design and implementation of linear differential microphone arrays. J Acoust Soc Am 136:3097–3113Google Scholar
  8. 8.
    Berkun R (2015) Quality Analysis and enhancement of reverberated speech using microphone arrays. Master Thesis, The Technion, Haifa, IsraelGoogle Scholar

Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.INRS-EMT, University of QuebecMontrealCanada
  2. 2.Northwestern Polytechnical UniversityXi’anChina

Personalised recommendations