Ambiguity Functions and Group Representations

Abstract

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) Find all ambiguity functions;

• (2) Develop a theory for sampling ambiguity functions;

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