A New Tool for Nonstationary and Nonlinear Signals: The Hilbert-Huang Transform in Biomedical Applications

Time-frequency techniques constitutes a major improvement in signal analysis, namely at the field of biomedical signals in which the interdisciplinary nature of the proposed questions implies the development of new strategies to answer to specific problems. Timefrequency analysis using Wavelets, Wigner-Ville transform and more recently the HilbertHuang Transform (HHT) constitutes the core of these tools with applications in biomedical signals in last years. The non-linearity and non-stationarity nature of these signals puts HHT as a powerful tool to process signals with those properties, avoiding artefacts related to the use of linear and stationary assumptions. Classical spectral analysis using Fourier Transform still the most commonly used method when one wants to measure the global power-frequency distribution (power spectrum) of a given signal. In all areas of knowledge, Fourier-based analysis of time-series data faces constraining limitations. In biomedical signals, the critical constraining factors are the shortness of total data span, the non-stationarity of the data and the nonlinearity of the underlying physiological process. Methods using Short Time Fourier Transform (STFT) are able to extract the spectral information by defining short time windows and locally computing the Fourier transform, thereby coping with non-stationary phenomena. The frequency resolution is inversely proportional to the window length, and changes in time resolution (window length) compromise the frequency resolution. Even with optimized joint time-frequency localization, the trade-off between time and frequency resolution is unavoidable. In spite of these limitations, classical Fourier spectral analysis is still widely used to process biomedical data, for lack of alternatives. The uncritical use of Fourier spectral analysis and the careless adoption of the stationary and linear assumptions may give misleading results. Wavelet theory developed in the 90’s of last century was a significant contribution to tackle the problem of non-stationarity in time-series analysis. In common with Fourier-based analysis such as STFT, wavelet analysis yields a time-frequency representation, the main difference being that the decomposition is not based on sinusoidal functions, but rather