Eigenvalues of symmetric non-normalized discrete trigonometric transforms.

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. • New analytic expressions for the eigenvalues are derived for DCT1, DCT5, and DST • Closed-form expressions of the trace square of all symmetric DTT matrices are derived. [ABSTRACT FROM AUTHOR]