Emerging Applications to Signal Processing

  • Nigel Boston
Chapter
Part of the SpringerBriefs in Computer Science book series (BRIEFSCOMPUTER)

Abstract

In this chapter we discuss some new applications of algebra to signal processing. The first way in which this arises is via the transfer function of a filter. This leads to questions about polynomials and rational functions, which can sometimes be solved by ideas from algebraic geometry, often with better results than through numerical methods. The second application of algebra is to image processing. We already saw how three-dimensional rotations can be simply described by quaternions – now we look at an application in face recognition.

Keywords

Manifold Expense Acoustics Fermat 

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References

  1. 1.
    Blondel, V.D.: Simultaneous stabilization of linear systems. Lecture Notes in Control and Information Sciences 191, Springer-Verlag (1994)Google Scholar
  2. 2.
    Boston, N.: Makhoul’s conjecture for p = 2. In: IEEE International Conference on Acoustics, Speech, and Signal Processing (2001)Google Scholar
  3. 3.
    Boston N (2005) Pipelined IIR filter architecture using pole-radius minimization. VLSI Signal Processing 39:323–331MATHCrossRefGoogle Scholar
  4. 4.
    Boston, N.: On the Belgian Chocolate Problem and output feedback stabilization: efficacy of algebraic methods. To be submitted.Google Scholar
  5. 5.
    Chang YJ, Sahinidis NV (2007) Global optimization in stabilizing controller design. Journal of Global Optimization 38:509–526MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Lin, W.-Y., Boston, N., Hu, Y.H.: Summation invariant and Its applications to shape recognition. IEEE International Conference on Acoustics, Speech, and Signal Processing (2005)Google Scholar
  7. 7.
    Makhoul J (2000) Conjectures on the peaks of all-pass signals. IEEE Signal Processing Magazine 17:8–11Google Scholar
  8. 8.
    Mason, R.C.: Diophantine equations over function fields. London Mathematical Society Lecture Note Series, 96 (1984)Google Scholar
  9. 9.
    Olver PJ (2005) A survey of moving frames. In: Computer Algebra and Geometric Algebra with Applications, Lecture Notes in Computer Science 3519:105–138CrossRefGoogle Scholar
  10. 10.
    Rajagopal,R., Wenzel, L.: Peak locations in all-pass signals - the makhoul conjecture challenge. In: Proceedings of the International Conference on Acoustics, Speech, and Signal Processing (ICASSP) 2001Google Scholar
  11. 11.
    Stothers, W.W.: Polynomial identities and Hauptmoduln. Quart. J. Math., Oxf. II. Ser. 32, 349–370 (1981)Google Scholar

Copyright information

© The Author(s) 2012

Authors and Affiliations

  • Nigel Boston
    • 1
  1. 1.University of WisconsinMadisonUSA

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