A Comparison Between Different Discrete Ambiguity Domain Definitions in Stochastic Time-Frequency Analysis

The ambiguity domain plays a central role in estimating the time-varying spectrum and in estimating the covariance function of nonstationary random processes in continuous time. For processes in discrete time, there exist different definitions of the ambiguity domain, but it is well known that neither of these definitions perfectly resembles the usefulness of the continuous ambiguity domain. In this paper, we present some of the most frequently used definitions of the ambiguity domain in discrete time: the Claasen-Mecklenbrauker, the Jeong-Williams, and the Nuttall definitions. For the first time, we prove their equivalence within some necessary conditions and we present theorems that justify their usage.