Advertisement

Analog and digital computing

  • Roger W. Brockett
V. Signal Processing, Control, and Manufacturing Automation
Part of the Lecture Notes in Computer Science book series (LNCS, volume 653)

Abstract

It is clear that digital signal processing is growing in importance, fulfilling functions that were once carried out exclusively by analog means. At the same time the analog point of view, as represented by neural networks and adaptive control is also developing in new directions. Prompted by these considerations, this paper attempts to put into perspective recent work on analog computing. Some basic definitions are proposed and used to classify some examples from the literature.

Keywords

Digital Computer Strange Attractor Digital System Floquet Multiplier Pulse Frequency Modulation 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    John von Neumann, The Computer and the Brain, Yale University Press, New Haven, 1958.MATHGoogle Scholar
  2. 2.
    John von Neumann, Theory of Self-Reproducing Automata, University of Illinois Press, Urbana, IL, 1966.Google Scholar
  3. 3.
    W. S. McCulloch and W. Pitts, “A logical calculus of the ideas immanent in nervous activity”, Bulletin of Math. Biophysics, Vol. 5, (1943) pp. 115–133.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Norbert Wiener, Extrapolation, Interpolation and Smoothing of Stationary Time Series, MIT Press, Cambridge, MA and John Wiley, New York, 1949.MATHGoogle Scholar
  5. 5.
    C. E. Shannon, “A Mathematical Theory of Communication”, Bell Systems Technical Journal, Vol. 27, (1948), pp. 379–423 (part I) and pp. 623–656, (part II).MathSciNetGoogle Scholar
  6. 6.
    D. O. Hebb, The Organization of Behavior, John Wiley, New York, 1949.Google Scholar
  7. 7.
    R. M. Gray and A. Gresho, Adaptive Quantization, John Wiley, New York, 1991.Google Scholar
  8. 8.
    R. W. Brockett, “Smooth Dynamical Systems Which Realize Arithmetical and Logical Operations,” in Lecture Notes in Control and Information Sciences. Three Decades of Mathematical Systems Theory. (H. Nijmeijer and J. M. Schumacher, eds.) Springer-Verlag, Berlin, 1989, pp. 19–30.Google Scholar
  9. 9.
    G. B. Clayton, Data Converters, John Wiley, New York, 1992.Google Scholar
  10. 10.
    E. A. Guillemin, Passive Network Synthesis, John Wiley, New York, 1965.Google Scholar
  11. 11.
    B. Widrow and Stearns, Adaptive Signal Processing, Prentice-Hall, Englewood Cliffs, New Jersey, 1985.MATHGoogle Scholar
  12. 12.
    R. W. Brockett, “Dynamical Systems That Learn Subspaces,” Mathematical System Theory: The Influence of R. E. Kalman, (A.C. Antoulas, Ed.) Springer Verlag, Berlin, 1991, pp. 579–592.Google Scholar
  13. 13.
    R. W. Brockett, “Dynamical Systems That Sort Lists, Diagonalize Matrices and Solve Linear Programming Problems,” Linear Algebra and its Applications, Vol 146, pp. 79–91, 1991, (also Proceedings of the 1988 IEEE Conference on Decision and Control, (1988) pp. 799–803.)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    R. W. Brockett, “Least Squares Matching Problems,” Linear Algebra and Its Applications, Vols. 122/123/124, pp. 761–777, 1989.CrossRefMathSciNetGoogle Scholar
  15. 15.
    R. W. Brockett, “Sorting With the Dispersionless Limit of the Toda Lattice,” in Hamiltonian Systems, Transformation Groups and Spectral Transform Methods, CRM, (J. Harnad and J.E. Marsden, Eds.) Université de Montréal, Montréal, Canada, pp. 103–112 (with A. M. Bloch)Google Scholar
  16. 16.
    R. W. Brockett, “An Estimation Theoretic Basis for the Design of Sorting and Classification Networks”, in Neural Networks, (R. Mammone and Y. Zeevi, Eds) Academic Press, 1991, pp. 23–41.Google Scholar
  17. 17.
    R. W. Brockett, “A Gradient Flow for the Assignment Problem”, Progress in System and Control Theory (G. Conte and B. Wyman, Eds.) Birkhauser, 1991 (with Wing Wong) pp. 170–177.Google Scholar
  18. 18.
    R. W. Brockett, “Differential Geometry and the Design of Gradient Algorithms”, in Differential Geometry (Robert Green and S.T. Yau, Eds.) AMS, 1992. (to appear)Google Scholar
  19. 19.
    Misha Mahowald and Rodney Douglas, “A Silicon Neuron”, Nature, Vol. 354, pp. 515–518, Dec. 1991.CrossRefGoogle Scholar
  20. 20.
    Carver Mead, Analog VLSI and Neural Systems, Addison-Wesley, Reading, MA, 1989.MATHGoogle Scholar
  21. 21.
    A.L. Hodgkin and A.F. Huxley, Propagation of Pulses, J. of Physiology, (London), Vol. 117, pp. 500–544, 1952.Google Scholar
  22. 22.
    R. W. Brockett, “Pulse Driven Dynamical Systems”, in Dynamics, Control and Feedback, (Alberto Isidori and T. J. Tarn, Eds.), Birkhäuser, Boston, 1992.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Roger W. Brockett
    • 1
  1. 1.Division of Applied SciencesHarvard UniversityCambridge

Personalised recommendations