Understanding Instantaneous frequency detection: A discussion of Hilbert-Huang Transform versus Wavelet Transform

Abstract

Nonlinear and/or nonstationary properties have been observed in measurements coming from microgrids in modern power systems and biological systems. Generally, signals from these two domains are analyzed separately although they may share many features and can benefit from the use of the same methodology. This paper explores the use of Hilbert-Huang transform (HHT) and Wavelet transform (WT) for instantaneous frequency detection in these two different domains, in the search for a new adaptive algorithm that can be used to analyze signals from these domains without the need to make many a-priory adjustments. Two signals are selected for the investigation: a synthetic signal containing a time varying component and a real EEG signal obtained from The Ecole Polytechnique Federale de Lausanne. The two signals are analyzed with HHT and a discrete WT (DWT). When interpreting the results obtained with the synthetic signal, it is clear that the HHT reproduces the true components, while the DWT does not, making a meaningful interpretation of the modes more challenging. The results obtained when applying HHT to the EEG signal shows 5 modes of oscillations that appear to be well behaved Intrinsic Mode Functions (IMFs), while the results with DWT are harder to interpret in terms of modes. The DWT requires a higher level of decomposition to get closer to the results of the HHT, however multi-frequency bands may be useful depending on the application. The reconstruction of the signal from the approximation and detail coefficients shows a good behavior and this is one application for DWT especially for removing the unwanted noise of a signal.