Paper deals with mathematical modelling of impulse waveforms and impulse switching functions used in electrical engineering. Using z-transformation the impulse switching functions can be obtained for any discrete time instant as impulse sequences of exciting functions. Applying such an impulse sequence to electrical circuit the response of state variables can be investigated using inverse z-transformation. Theoretical derived wave-forms are verified by LT-Spice circuit simulator and compared to those of simulation worked-out results.