Periodically driven quantum systems defined in continuous time, also known as Floquet systems, share intriguing similarities with static/undriven lattice field theories defined in discrete time. E.g. in the former, periodic driving leads to Brillouin zone in quasi-energy space which is reminiscent of frequency Brillouin zones in the latter. These similarities lead to a natural question, {\it{is there a concrete correspondence between the two systems?}}
In this work I address this question and demonstrate that there indeed exists a concrete mathematical correspondence between a certain $1+1$ dimensional non-interacting Floquet system and a $1+1$ dimensional lattice Dirac fermion defined on naively discretized time lattice. I also comment on the possibility of extending this type of correspondence to higher dimensional theories.