Electrical & Computer Engineering Technical Reports

Document Type

Technical Report

Publication Date

Spring 2-27-2023

Abstract

Commuting matrix methods furnish a full basis of orthog- onal eigenvectors for the discrete Fourier transform or its centered version needed for computing the discrete fractional Fourier transform and multicomponent chirp signal analysis. However, these approaches suffer from ill-conditioning issues at higher matrix sizes, and require a computationally expensive eigenvalue decomposition.

In this paper, ill-conditioning issues associated with the QMFD approach developed previously by the authors are addressed via diagonal modification. Further symmetries of the eigenvectors are used to reduce the size of the underlying eigenvalue problem. These modifications are then incorporated into the real-arithmetic implementation of the QMFD approach that is shown to be significantly superior to the conventional implementation and the corresponding MSE of the chirp parameter estimates are shown to approach their Cramer Rao lower bounds.

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