Electronic Structure Theory (EST) describes the behavior of electrons in matter and is used to predict material properties. Conventionally, this involves forming a Hamiltonian and solving the Schrödinger equation through discrete computation. Here, a new perspective to EST is provided by treating a perfectly crystalline material as a Linear Translation Invariant (LTI) system. The validity of this LTI-EST formalism is demonstrated by determining band structures for a one-dimensional chain of atoms, including the phenomenon of band structure folding in super cells. The proposed formalism allows for analytical traceability of band structure folding and offers computational advantage by bypassing the O(N) eigenvalue calculations. The spike-based computing nature of the proposed LTI-EST formalism is highlighted; thereby implying potential for material simulations solely in the spiking domain.