An alternative analytical definition to the mean envelope for empirical mode decomposition

This paper presents a novel approach that gives an alternative analytical definition to the mean envelope in the sifting procedure using B-spline functions for the Empirical Mode Decomposition (EMD) algorithm. The basic concept lines mainly on the idea that B-spline functions form a basis for the space of splines and have refined-point representations by knot insertion. This newly-developed definition is essentially equivalent to the classical one, but gives a more explicit formulation on this issue. For purpose of studying the mathematical foundation of the EMD methodology, the proposed definition may afford an opportunity in this direction.