Application of the Hilbert Transform to Measure the Nonlinearity in the Driven Dust Acoustic Wave

This paper presents an analysis of the application of the time-resolved Hilbert transform to simulated measurements of the wave structure in the dust acoustic wave. It is shown that the observation of structures in the dominant frequency modes that have been made in experimental measurements of the driven dust acoustic wave is due to the nonlinearity in the wave mode and that the time-resolved Hilbert transform can be used to measure the nonlinearity in the driven wave mode. This was tested on experimental data and excellent agreement was observed.