2003 | Patrick Flandrin, Fellow, IEEE, Gabriel Rilling and Paulo Gonçalvès
This paper presents an analysis of Empirical Mode Decomposition (EMD) as a filter bank for fractional Gaussian noise (fGn). EMD is a method for adaptively decomposing nonstationary signals into intrinsic mode functions (IMFs), which are zero-mean amplitude and frequency modulated components. The study shows that EMD behaves like a dyadic filter bank, similar to wavelet decompositions, when applied to fGn. The decomposition of fGn into IMFs results in a set of filters that can be interpreted as band-pass filters, with the first IMF acting as a high-pass filter and subsequent IMFs as overlapping band-pass filters. The number of zero-crossings in each IMF decreases exponentially with mode index, indicating a dyadic structure. The power spectra of the IMFs can be renormalized to collapse onto a single curve, supporting the claim that EMD acts as a dyadic filter bank of constant-Q band-pass filters for fGn. The Hurst exponent H can be estimated from the variance progression across IMFs, with linear dependence observed for H ≥ 1/2. The results suggest that EMD can be used to analyze self-similar processes, and that its behavior is consistent with a dyadic filter bank structure. The study highlights the adaptability of EMD in decomposing broadband noise and provides insights into its theoretical underpinnings. The findings support the use of EMD as a powerful tool for analyzing nonstationary and self-similar signals.This paper presents an analysis of Empirical Mode Decomposition (EMD) as a filter bank for fractional Gaussian noise (fGn). EMD is a method for adaptively decomposing nonstationary signals into intrinsic mode functions (IMFs), which are zero-mean amplitude and frequency modulated components. The study shows that EMD behaves like a dyadic filter bank, similar to wavelet decompositions, when applied to fGn. The decomposition of fGn into IMFs results in a set of filters that can be interpreted as band-pass filters, with the first IMF acting as a high-pass filter and subsequent IMFs as overlapping band-pass filters. The number of zero-crossings in each IMF decreases exponentially with mode index, indicating a dyadic structure. The power spectra of the IMFs can be renormalized to collapse onto a single curve, supporting the claim that EMD acts as a dyadic filter bank of constant-Q band-pass filters for fGn. The Hurst exponent H can be estimated from the variance progression across IMFs, with linear dependence observed for H ≥ 1/2. The results suggest that EMD can be used to analyze self-similar processes, and that its behavior is consistent with a dyadic filter bank structure. The study highlights the adaptability of EMD in decomposing broadband noise and provides insights into its theoretical underpinnings. The findings support the use of EMD as a powerful tool for analyzing nonstationary and self-similar signals.