In this paper, we investigate the excitation of a capacitively coupled plasma using a non-sinusoidal voltage waveform whose amplitude- and slope-asymmetry varies continuously with a period which is a multiple of the fundamental RF period. We call this period the ?beating? period. Through particle-in-cell (PIC) simulations, we show that such waveforms cause oscillation of the self-bias at this beating frequency, corresponding to the charging and discharging of the external capacitor. The amplitude of this self-bias oscillation depends on the beating period, the value of the external capacitor, and the ion flux to the electrodes. This self-bias oscillation causes temporal modulation of the ion flux distribution function (IFDF), albeit at a constant ion flux and constant mean ion energy, and allows the energy width of the IFDF (averaged over the beating period) to be varied in a controlled fashion.