The discrete polynomial transform (DPT), its properties and applications

The discrete polynomial transform (DPT) is a new tool for analyzing constant-amplitude continuous-phase signals. It is based on modeling the signal phase by a polynomial function of time. The main properties of the DPT are its ability to identify the degree of the phase polynomial and to estimate its coefficients. The transform is robust to deviations from the ideal signal model, such as slowly varying amplitude, additive noise, and nonpolynomial phase. Its effect on polynomial-phase signals is shown. Its main mathematical properties are listed and proofs are provided for some. It is shown how to use those properties to derive estimation and classification algorithms for continuous-phase signals. Some recent results on the statistical accuracy of these algorithms are stated. Applications of the DPT to certain radar and communication problems are discussed