The noise spectrum of the magnetoresistivity in the breakdown of the Integral Quantum Hall Effect (IQHE) at high currents is studied in wide high-quality GaAs/AlGaAs heterostructures on thei=2 Hall plateau, in particular for values of current and/or magnetic field at which pronounced steps and striking temporal patterns showing switching between different levels are observed. The noise spectra obtained from data which display switching are compared with the spectra obtained in the absence of switching. By an analysis based on time series simulation, Lorentzian noise components are separated and found to have similar characteristics in both types of data.