Unilateral contact between mating components is typically modeled with the Signorini condition modified by impact laws. While impact laws are widely used in time marching solution procedures, their adoption in frequency-time weighted residual methods, such as the Harmonic Balance Method, is limited by the continuity of the classical basis functions (e.g., Fourier, Polynomials, and Hat functions) used in the formulation. The proposed method addresses this problem for modeling periodic impact events. It relies on a discontinuous-Galerkin approach, where the governing dynamics are modeled with consecutive pre-, and post-impact subdomains upon which the contact quantities are approximated and projected upon. The approach introduces the time(s) of impact and contact force(s) as additional unknowns that are reconciled with an impact law and condition for contact closure. Periodicity can be satisfied by the basis functions or with additional equations. The unilateral formulation of the proposed method for a representative contact body is presented and compared to a time-domain approach. The results show that the method delivers highly accurate low-order approximations without Gibbs phenomenon. Additional advantages include rapid parameterization of previously intractable impulsive forced responses. The formulation naturally extends to other nonlinearities i.e., friction and multiple contact events by considering the equations in a per-impact framework.