Compact Empirical Mode Decomposition: an Algorithm to Reduce Mode Mixing, End Effect, and Detrend Uncertainty

A compact empirical mode decomposition (CEMD) is presented to reduce mode mixing, end effect, and detrend uncertainty in analysis of time series (with N data points). This new approach consists of two parts: (a) highest-frequency sampling (HFS) to generate pseudo extrema for effective identification of upper and lower envelopes, and (b) a set of 2N algebraic equations for determining the maximum (minimum) envelope at each decomposition step. Among the 2N algebraic equations, 2(N − 2) equations are derived on the base of the compact difference concepts using the Hermitan polynomials with the values and first derivatives at the (N − 2) non-end points. At each end point, zero third derivative and determination of the first derivative from several (odd number) nearest original and pseudo extrema provide two extra algebraic equations for the value and first derivative at that end point. With this well-posed mathematical system, one can reduce the mode mixing, end effect, and detrend uncertainty drastically, and separate scales naturally without any a priori subjective criterion selection.