The correlations between local plasma oscillations and the discharge current or cathode potential variations are studied in a high-voltage Hall-effect thruster (HET). A set of electric probes is used to collect the signals. The probes are located in the exhaust region of the thruster, beyond its outer circumference. Measurements are performed for various probe positions and bias potentials, within a wide range of thruster operating conditions. The non-stationary signals are subsequently expanded into finite sets of intrinsic modes with the use of the Empirical Mode Decomposition (EMD) method. The Hilbert-Huang power spectra indicate characteristic bands in the low frequency (LF, tens of kHz), medium frequency (MF) and high frequency (HF, tens of MHz) range. However, the regular HF emission that has been observed in our previous low-voltage characterization of a PPS-100 thruster, is only observable in some particular operating conditions. When the supply voltage is low (e.g. 400 V), the known electrostatic drift wave propagating along the thruster azimuth is unambiguously identified in the probe signals. For higher voltages, HF spectra are usually broadband and do not highlight well the defined peaks. HF emission becomes very irregular or even seemingly random. On the other hand, when regular waves appear (intermittently or in series of bursts), frequencies in the ss 5-100 MHz band can be observed. The oscillations within the MF band that were previously weak in the PPS-100 thruster, appear now to dominate the discharge current spectrum when the thruster operates at the highest voltages. Intense oscillations in the MF range are identified with the use of positively biased probes and by examination of the cathode potential and discharge current variations. The correlations of all the mentioned signals are clear in this frequency band. Correlating the oscillations in the HF band with the MF discharge current wave, one can deduce that HF oscillations are periodically triggered by MF waves at high voltage, while at lower voltage they are triggered by the LF breathing mode, as previously observed in the case of the PPS-100 thruster.