Bounds on the volume and height distributions of the ambiguity function

Abstract

Augmenting Woodward's total-volume invariance, new information on ambiguity-function behavior is obtained and illustrated by example. The results are of two types, the first dealing with the time4requency volume distribution and providing lower bounds to local volume, and upper bounds to attainable "clear area"; these follow from Parseval's theorem as applied to Siebert's self-transform property. The second category of necessary conditions consists of a set of upper bounds on the norms of the ambiguity function, which places restrictions on the height distribution of the ambiguity surface. As a corollary, it is demonstrated that not all nonnegative functions that are serf-transformable can be ambiguity functions.