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The authors have been engaged in experimental and modeling investigations of the electrical turn-on behavior of high-pressure gas discharge switching. Emphasis has been on characterizing the first few nanoseconds of switch turn-on for a range of operational conditions (i.e., gas type, gas pressure, gap length, drive circuit impedance, etc.). This paper describes the modeling, signal processing, and systems analysis aspects of the investigations, which were driven by interest in pursuing the extent to which limited experimental data could be usefully augmented with available computer modeling tools and techniques. A high-fidelity 3-D model of the experimental apparatus was developed and simulations performed using a full 3-D time-domain Maxwell solver. This provided detailed electrical characterization of the experimental system that allowed for the development of transfer functions enabling the estimation of time-varying discharge gap voltage and current waveforms based on experimental D-dot probe measurements taken some distance away from the discharge gap. The steps of this process are outlined, example results shown, conclusions presented, and directions for future work suggested.