Identifiability and Aliasing in Polynomial-Phase Signals

Abstract

Polynomial-phase signals have numerous applications including radar, sonar, geophysics, and radio communication. Many techniques for estimating the parameters of polynomial-phase signals have been described in the literature. Despite the significant interest, aliasing of polynomial-phase parameters has not been fully clarified. We address the problem of identifiability and aliasing in polynomial-phase signals. We fully describe the region in which aliasing does not occur for polynomial-phase signals of any order. We call this the identifiable region. We find that this region is the Voronoi region of a lattice generated by the coefficients of a set of polynomials known as the integer-valued polynomials. We show how aliasing can be resolved by solving the nearest lattice point problem. We discuss some of the consequences of these results on a popular estimator for polynomial-phase signals that is based on the discrete polynomial phase transform (DPPT). It is shown that the range of parameters suitable for the DPPT estimator is very small compared to the identifiable region.