Power spectrum in the free metaplectic transformation domain: Theory and application

Abstract

The parameter estimation of chirp signals has emerged as a prominent topic in the signal processing domain. Although existing estimation methods can accurately determine signal parameters, they are often ineffective for chirp signals characterized by unseparable terms. This study introduces the concept of the free metaplectic power spectrum (FMPS) and free metaplectic correlation function (FMCF) for random processes, and derives the relationship between the FMPS for the input and output of free metaplectic transform domain filters. Additionally, the interrelationship between the FMCF and FMPS is explored. The simulation utilizes derived theories alongside a coarse-to-fine search strategy for parameter estimation. The results indicate that the FMPS method significantly outperforms traditional techniques in estimating parameters of chirp signals with unseparable terms, while it maintains estimation accuracy comparable to the conventional power spectrum methods for chirp signals devoid of unseparable terms. At the end of the paper, some potential applications of the proposed method in fields of radar and communications are described.