Eigenvalues of symmetric non-normalized discrete trigonometric transforms, By Taher Yazdanpanah

Research

Title	Eigenvalues of symmetric non-normalized discrete trigonometric transforms
Type	Article
Keywords	Discrete trigonometric transforms, Discrete cosine transforms, Discrete sine transforms, eigenvalues
Journal	SIGNAL PROCESSING
DOI	https://doi.org/10.1016/j.sigpro.2023.109379
Researchers	Ali Bagheri-Bardi (First researcher) , Milos Dakovic (Second researcher) , Taher Yazdanpanah (Third researcher) , Ljubiša Stanković (Fourth researcher)

Abstract

A comprehensive approach to the spectrum characterization (derivation of eigenvalues and the corresponding multiplicities) for non-normalized, symmetric discrete trigonometric transforms (DTT) is presented in the paper. Eight types of the DTT are analyzed. New explicit analytic expressions for the eigenvalues, together with their multiplicities, for the cases of three DTT (DCT(1), DCT(5), and DST(8)), are the main contribution of this paper. Moreover, the presented theory is supplemented by new, original derivations for the closed-form expressions of the square and the trace of all symmetric DTT matrices including existing results and the new ones.