Skip to main content
Log in

Optimal filter design subject to output sidelobe constraints: Computational algorithm and numerical results

  • Contributed Papers
  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

An algorithm is presented for the design of optimal detection filters in radar and communications systems, subject to inequality constraints on the maximum output sidelobe levels. This problem was reduced in an earlier paper (Ref. 1) to an unconstrained one in the dual space of regular Borel measures, with a nondifferentiable cost functional. Here, the dual problem is solved via steepest descent, using the directional Gateaux differential. The algorithm is shown to be convergent, and numerical results are presented.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Fortmann, T. E., andAthans, M.,Optimal Filter Design Subject to Output Sidelobe Constraints: Theoretical Considerations, Journal of Optimization Theory and Applications, Vol. 14, No. 2, 1974.

  2. Van Trees, H. L.,Detection, Estimation, and Modulation Theory, Part I, John Wiley and Sons, New York, New York, 1968.

    Google Scholar 

  3. Cook, C. E., andBernfeld, M.,Radar Signals, Academic Press, New York, New York, 1967.

    Google Scholar 

  4. Luenberger, D. G.,Optimization by Vector Space Methods, John Wiley and Sons, New York, New York, 1969.

    Google Scholar 

  5. Evans, R. J.,On the Design of Optimal Sidelobe Reduction Filters, University of Newcastle, Australia, M.E. Thesis, 1973.

  6. Dunford, N., andSchwartz, J.,Linear Operators, Part I, John Wiley and Sons (Interscience Publishers), New York, New York, 1958.

    Google Scholar 

  7. Rudin, W.,Real and Complex Analysis, McGraw-Hill Book Company, New York, New York, 1966.

    Google Scholar 

  8. Kantorovich, L. V., andAkilov, G. P.,Functional Analysis in Normed Spaces, Pergamon Press, Oxford, England, 1964.

    Google Scholar 

  9. Luenberger, D. G.,Control Problems with Kinks, IEEE Transactions on Automatic Control, Vol. AC-15, No. 5, 1970.

  10. Bertsekas, D. P., andMitter, S. K.,A Descent Numerical Method for Optimization Problems with Nondifferentiable Cost Functionals, SIAM Journal on Control, Vol. 11, No. 4, 1973.

  11. Fortmann, T. E.,Optimal Design of Filters and Signals Subject to Sidelobe Constraints, Massachusetts Institute of Technology, Report No. ESL-R-400, 1969.

  12. Pierre, D. A.,Optimization Theory with Applications, John Wiley and Sons, New York, New York, 1969.

    Google Scholar 

  13. Evans, R. J., andFortmann, T. E.,Near-Optimal Resolution of Rectangular Pulses in Noise (to appear).

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by Y. C. Ho

This research was supported by the Australian Research Grants Committee.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fortmann, T.E., Evans, R.J. Optimal filter design subject to output sidelobe constraints: Computational algorithm and numerical results. J Optim Theory Appl 14, 271–290 (1974). https://doi.org/10.1007/BF00932611

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00932611

Key Words

Navigation