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This paper presents an integrated approach to taking a frequency-domain simulation problem into the discrete time domain, based on z transforms. The ideas are illustrated with free space, the Drude pole, and perfectly matched layer (PML) conversion examples, for both leapfrog time stepping and simultaneous time stepping. Numerical results for various perfectly matched layer methods are given. We then present a two-dimensional scattering example in which the conversion from frequency to discrete time is carried out. Numerical results are presented and compared with results from a Method-of-Moments formulation.