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Optimal State Space Descriptions

  • Sandro A. P. Haddad
  • Wouter A. Serdijn
Part of the Analog Circuits and Signal Processing book series (ACSP)

This chapter describes the next step towards the implementation of wavelet filters. Departing from the transfer functions defined in Chapter 4, we derive a state space description of the wavelet filter. Since state space descriptions are not unique representations of a dynamical system, they allow the designer to find an implementation that fits best to the requirements imposed, e.g. coefficients that are readily implemented, a prescribed circuit topology, or maximum dynamic range. The description is transformed into the desired form by state space transforms or similarity transforms. In the context of low-power, low-voltage analogue integrated circuits, the most important requirements are dynamic range, sensitivity, and sparsity, all of which are treated in Chapter 5.

Keywords

Transfer Function State Space Canonical Form Continue Fraction Expansion State Space Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    T. Kailath, Linear Systems, Prentice Hall, Englewood Cliffs, NJ, 1980. MATHGoogle Scholar
  2. [2]
    B. P. Lathi, Linear Systems and Signals, Oxford University Press, New York, 2002. Google Scholar
  3. [3]
    P. M. DeRusso, R. J. Roy, C. M. Close and A. A. Desrochers, State Variables for Engineers, 2nd edn, Wiley, New York, 1998. Google Scholar
  4. [4]
    J. D. Aplevich, The Essentials of Linear State-Space Systems, Wiley, New York, 2000. Google Scholar
  5. [5]
    W. M. Snelgrove and A. S. Sedra, Synthesis and analysis of state-space active filters using intermediate transfer function, IEEE Transactions on Circuits and Systems, vol. 33, no. 3, pp. 287-301, March 1986. CrossRefMathSciNetGoogle Scholar
  6. [6]
    D. P. W. M. Rocha, Optimal design of analogue low-power systems, A strongly directional hearing-aid adapter, PhD thesis, Delft University of Technology, April 2003. Google Scholar
  7. [7]
    G. Groenewold, Optimal dynamic range integrators, IEEE Transactions on Circuits and Systems I, vol. 39, no. 8, pp. 614-627, August 1992. CrossRefGoogle Scholar
  8. [8]
    W. K. Chen (Editor-in-Chief), The Circuits and Filters Handbook, CRC Press and IEEE Press, Boca Raton, FL, 1995. MATHGoogle Scholar
  9. [9]
    D. A. Johns, W. M. Snelgrove and A. S. Sedra, Orthonormal ladder filters, IEEE Transactions on Circuits and Systems, vol. 36, no. 3, pp. 337-343, March 1989. CrossRefMathSciNetGoogle Scholar
  10. [10]
    L. Thiele, On the sensitivity of linear state-space systems, IEEE Transactions on Circuits and Systems, vol. 33, no. 5, pp. 502-510, May 1986. MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science + Business Media B.V. 2009

Authors and Affiliations

  1. 1.Freescale SemiconductorCampinas-SPBrazil
  2. 2.Electronics Research Lab.Delft University of TechnologyDelftThe Netherlands

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