The location and motion of Saturn’s equatorial current sheet is the result of an interplay between a quasi-static deformation that varies in radial distance and local time, impulsive perturbations that produce large-scale displacements, quasi-periodic perturbations near the planetary rotation period, and wave-like structures on shorter timescales. This study focuses on the latter, aperiodic wave pulses with periods from 1-30 minutes, that are unrelated to the quasi-periodic ‘flapping’ with a period near that of Saturn’s rotation. Cassini magnetometer data were surveyed for these aperiodic structures and then fitted to a simple model in order to estimate the properties of the waves.The model consists of a modified Harris current sheet model deformed by a Gaussian pulse wave function. This then allows for the extraction of wave parameters and current sheet properties. In particular we show an increase in current sheet scale height with radial distance from Saturn, an increase in the wave amplitude with radial distance, and the resolution of propagation directions using the wave vector fitted by the model. The dominant propagation direction is found to be radially outwards from Saturn.