Paper deals with mathematical modelling of impulse waveforms and impulse switching functions used in electrical engineering. Impulse rectangular waveforms are created by periodical trigonometric functions with modulo π, so, the waveforms are discontinuous and strongly non-harmonic ones. Impulse switching functions are investigated using direct-and inverse z-transformation. The results make it possible to present those functions as infinite series expressed in pure numerical-, exponential-or trigonometric forms. Theoretical derived waveforms are compared with simulation worked-out results.