[en] The effect of a weakly coupled periodic lattice in terms of achieving emittance exchange between the transverse and longitudinal directions is investigated using the generalized Courant-Snyder theory for coupled lattices. Recently, the concept and technique of transverse-longitudinal emittance coupling have been proposed for applications in the Linac Coherent Light Source and other free-electron lasers to reduce the transverse emittance of the electron beam. Such techniques can also be applied to the driver beams for the heavy ion fusion and beam-driven high energy density physics, where the transverse emittance budget is typically tighter than the longitudinal emittance. The proposed methods consist of one or several coupling components which completely swap the emittances of one of the transverse directions and the longitudinal direction at the exit of the coupling components. The complete emittance exchange is realized in one pass through the coupling components. In the present study, we investigate the effect of a weakly coupled periodic lattice in terms of achieving emittance exchange between the transverse and longitudinal directions. A weak coupling component is introduced at every focusing lattice, and we would like to determine if such a lattice can realize the function of emittance exchange.