In this paper an algorithm based on the ensemble empirical mode decomposition (EEMD) is presented. The key idea on the EEMD relies on averaging the modes obtained by EMD applied to several realizations of Gaussian white noise added to the original signal. The resulting decomposition solves the EMD mode mixing problem, however it introduces new ones. In the method here proposed, a particular noise is added at each stage of the decomposition and a unique residue is computed to obtain each mode. The resulting decomposition is complete, with a numerically negligible error. Two examples are presented: a discrete Dirac delta function and an electrocardiogram signal. The results show that, compared with EEMD, the new method here presented also provides a better spectral separation of the modes and a lesser number of sifting iterations is needed, reducing the computational cost.

The current understanding of hydroclimatic processes is largely based on time series analysis of observations such as river discharge. Although records of these variables are often nonlinear and nonstationary, they have been commonly analyzed by classical methods designed for linear and/or stationary data. This study investigates the possibility of analyzing hydroclimatic time series using a novel data‐driven method named Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN), which is suitable for nonlinear and nonstationary signals. CEEMDAN is here applied to a monthly mean discharge record (1904–2010) of the Paraná River (South America). The results obtained in this way are interpreted by comparing them with CEEMDAN decompositions of other records such as climate index time series. It is found that Paraná flow modes consist of (i) annual and intraannual oscillations reflecting the rainfall seasonality of different Paraná Basin sectors, and (ii) interannual to interdecadal changes linked to climate cycles like El Niño/Southern Oscillation, the North Atlantic Oscillation, and the Interdecadal Pacific Oscillation. A nonlinear trend of Paraná discharge is found and reveals a monotonic increase that could be attributed to global warming and anthropogenic land‐cover changes. The spectral separation of modes obtained using CEEMDAN is cleaner than that achieved by the Ensemble Empirical Mode Decomposition technique. This makes it easier to interpret CEEMDAN results. Hence, CEEMDAN is proposed as a powerful method for extracting physically meaningful information from hydroclimatic data.

Detection of desaturations on the pulse oximetry signal is of great importance for the diagnosis of sleep apneas. Using the counting of desaturations, an index can be built to help in the diagnosis of severe cases of obstructive sleep apnea-hypopnea syndrome. It is important to have automatic detection methods that allows the screening for this syndrome, reducing the need of the expensive polysomnography based studies. In this paper a novel recognition method based on the empirical mode decomposition of the pulse oximetry signal is proposed. The desaturations produce a very specific wave pattern that is extracted in the modes of the decomposition. Using this information, a detector based on properly selected thresholds and a set of simple rules is built. The oxygen desaturation index constructed from these detections produces a detector for obstructive sleep apnea-hypopnea syndrome with high sensitivity (0.838) and specificity (0.855) and yields better results than standard desaturation detection approaches.