The Empirical Mode Decomposition (EMD) has been introduced quite recently to adaptively decompose nonstationary and/or nonlinear time series [1]. The method being initially limited to real-valued time series, we propose here an extension to bivariate (or complex-valued) time series which generalizes the rationale underlying the EMD to the bivariate framework. Where the EMD extracts zero-mean oscillating components, the proposed bivariate extension is designed to extract zero-mean rotating components. The method is illustrated on a real-world signal and properties of the output components are discussed. Free Matlab/C codes are available at http://perso.ens-lyon.fr/patrick.flandrin.

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In an Oceanography article published 13 years ago, three of us identified salinity measurement from satellites as the next ocean remote-sensing challenge. We argued that this represented the next "zeroth order" contribution to oceanography (Lagerloef et al., 1995) because salinity variations form part of the interaction between ocean circulation and the global water cycle, which in turn affects the ocean's capacity to store and transport heat and regulate Earth's climate. Now, we are pleased to report that a new satellite program scheduled for launch in the near future will provide data to reveal how the ocean responds to the combined effects of evaporation, precipitation, ice melt, and river runoff on seasonal and interannual time scales. These measurements can be used, for example, to close the marine hydrologic budget, constrain coupled climate models, monitor mode water formation, investigate the upper-ocean response to precipitation variability in the tropical convergence zones, and provide early detection of low-salinity intrusions in the subpolar Atlantic and Southern oceans. Sea-surface salinity (SSS) and sea-surface temperature (SST) determine sea-surface density, which controls the formation of water masses and regulates three-dimensional ocean circulation.

The influence of higher-order wavelet properties on the analytic wavelet transform behavior is investigated, and wavelet functions offering advantageous performance are identified. This is accomplished through detailed investigation of the generalized Morse wavelets, a two-parameter family of exactly analytic continuous wavelets. The degree of time/frequency localization, the existence of a mapping between scale and frequency, and the bias involved in estimating properties of modulated oscillatory signals, are proposed as important considerations. Wavelet behavior is found to be strongly impacted by the degree of asymmetry of the wavelet in both the frequency and the time domain, as quantified by the third central moments. A particular subset of the generalized Morse wavelets, recognized as deriving from an inhomogeneous Airy function, emerge as having particularly desirable properties. These "Airy wavelets" substantially outperform the only approximately analytic Morlet wavelets for high time localization. Special cases of the generalized Morse wavelets are examined, revealing a broad range of behaviors which can be matched to the characteristics of a signal.Comment: 15 pages, 6 Postscript figure

The generalized Morse wavelets are shown to constitute a superfamily that essentially encompasses all other commonly used analytic wavelets, subsuming eight apparently distinct types of analysis filters into a single common form. This superfamily of analytic wavelets provides a framework for systematically investigating wavelet suitability for various applications. In addition to a parameter controlling the time-domain duration or Fourier-domain bandwidth, the wavelet {\em shape} with fixed bandwidth may be modified by varying a second parameter, called $\gamma$. For integer values of $\gamma$, the most symmetric, most nearly Gaussian, and generally most time-frequency concentrated member of the superfamily is found to occur for $\gamma=3$. These wavelets, known as "Airy wavelets," capture the essential idea of popular Morlet wavelet, while avoiding its deficiencies. They may be recommended as an ideal starting point for general purpose use