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During recent years, higher order statistics (HOS) have found a wide applicability in many diverse fields, e.g. biomedicine, harmonic retrieval and adaptive filtering. In power spectrum estimation, the signal under consideration is processed in such a way that the distribution of power among its frequency is estimated and phase relations between the frequency components are suppressed. Higher order statistics and their associated Fourier transforms reveal not only amplitude information about a signal, but also phase information. If a non‐Gaussian signal is received along with additive Gaussian noise, a transformation to higher order cumulant domain eliminates the noise. These are some methods for estimation of signal components, based on HOS. In the paper we apply the MUSIC method both for the correlation and the fourth order cumulant, to investigate the state of asynchronous running of synchronous machines and the fault operation of inverter‐fed induction motors. When the investigated signal is distorted by a coloured noise, more exact results can be achieved by applying cumulants.