Skip to main content

Analog and digital computing

  • V. Signal Processing, Control, and Manufacturing Automation
  • Conference paper
  • First Online:
Future Tendencies in Computer Science, Control and Applied Mathematics (INRIA 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 653))

Included in the following conference series:

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.

This work was supported in part by the National Science Foundation under Engineering Research Center Program, NSF D CDR-8803012 and by the US Army Research Office under grant DAAL03-86-K-0171, and DARPA grant AFOSR-89-0506

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. John von Neumann, The Computer and the Brain, Yale University Press, New Haven, 1958.

    MATH  Google Scholar 

  2. John von Neumann, Theory of Self-Reproducing Automata, University of Illinois Press, Urbana, IL, 1966.

    Google Scholar 

  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.

    Article  MATH  MathSciNet  Google Scholar 

  4. Norbert Wiener, Extrapolation, Interpolation and Smoothing of Stationary Time Series, MIT Press, Cambridge, MA and John Wiley, New York, 1949.

    MATH  Google Scholar 

  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).

    MathSciNet  Google Scholar 

  6. D. O. Hebb, The Organization of Behavior, John Wiley, New York, 1949.

    Google Scholar 

  7. R. M. Gray and A. Gresho, Adaptive Quantization, John Wiley, New York, 1991.

    Google Scholar 

  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. G. B. Clayton, Data Converters, John Wiley, New York, 1992.

    Google Scholar 

  10. E. A. Guillemin, Passive Network Synthesis, John Wiley, New York, 1965.

    Google Scholar 

  11. B. Widrow and Stearns, Adaptive Signal Processing, Prentice-Hall, Englewood Cliffs, New Jersey, 1985.

    MATH  Google Scholar 

  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. 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.)

    Article  MATH  MathSciNet  Google Scholar 

  14. R. W. Brockett, “Least Squares Matching Problems,” Linear Algebra and Its Applications, Vols. 122/123/124, pp. 761–777, 1989.

    Article  MathSciNet  Google Scholar 

  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. 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. 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. 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. Misha Mahowald and Rodney Douglas, “A Silicon Neuron”, Nature, Vol. 354, pp. 515–518, Dec. 1991.

    Article  Google Scholar 

  20. Carver Mead, Analog VLSI and Neural Systems, Addison-Wesley, Reading, MA, 1989.

    MATH  Google Scholar 

  21. A.L. Hodgkin and A.F. Huxley, Propagation of Pulses, J. of Physiology, (London), Vol. 117, pp. 500–544, 1952.

    Google Scholar 

  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 

Download references

Author information

Authors and Affiliations

Authors

Editor information

A. Bensoussan J. -P. Verjus

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Brockett, R.W. (1992). Analog and digital computing. In: Bensoussan, A., Verjus, J.P. (eds) Future Tendencies in Computer Science, Control and Applied Mathematics. INRIA 1992. Lecture Notes in Computer Science, vol 653. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56320-2_65

Download citation

  • DOI: https://doi.org/10.1007/3-540-56320-2_65

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56320-4

  • Online ISBN: 978-3-540-47520-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics