  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 analyzed DTT
matrices.
