Ambiguity Functions and Group Representations

  • L. Auslander
  • R. Tolimieri
Part of the Mathematical Sciences Research Institute Publications book series (MSRI, volume 6)


P.M. Woodward popularized the concept of ambiguity functions in his book ↑Wo←. Ambiguity functions did not yield to the standard theory of Abelian harmonic analysis and though studied by numerical methods their theory has not advanced much since the fundamental work of C. Wilcox ↑Wo←. In recent years, the Wigner transform, a close relative of the ambiguity function, has gained a lot of attention in engineering circles that are concerned with speech and its synthesis and non-intrusive methods for determining fluid flow in the human body. There seem to be three major theoretical problems that are of great interest in this subject:
  1. (1)

    Find all ambiguity functions;

  2. (2)

    Develop a theory for sampling ambiguity functions;

  3. (3)

    Complete Woodward’s program of giving an information theoretic model that includes the ambiguity function.



Heisenberg Group Dual Group Ambiguity Function Positive Definite Function Maximal Abelian Subgroup 
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    L. Auslander and R. Tolimieri, “Radar ambiguity functions and group theory,” SIAM J. Math, Anal., 16(1985) 577–601.MathSciNetMATHGoogle Scholar
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    C.H. Wilcox, “The synthesis problem for radar ambiguity functions,” MRC Technical Report 157 (1960), Mathematics Research Center, U.S. Army, University of Wisconsin.Google Scholar
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    P.M. Woodward, “Probability and Information Theory, with applications to Radar,” Pergamon Press, 1953.MATHGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1987

Authors and Affiliations

  • L. Auslander
  • R. Tolimieri

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