In this section, we derive the theoretical framework required for using the DCT. Specifically, the analytical DCTs for the generalized Warburg element , ZARC element , Havriliak-Negami (HN) element, which generalizes the ZARC , and a circuit consisting of the series combination of a ZARC element and a generalized Warburg element are derived. These formulae are key for calculating parameters using the DCT. The analytical DCTs for the newly developed YARC element and the de Levie model are also presented. Importantly, similarities and differences between the DRT and DCT are highlighted.