Non-overshooting and non-undershooting cubic spline interpolation for empirical mode decomposition

To suppress the overshoots and undershoots in the envelope fitting for empirical mode decomposition (EMD), an alternative cubic spline interpolation method without overshooting and undershooting is proposed. On the basis of the derived slope constraints of knots of a non-overshooting and non-undershooting cubic inter-polant, together with "not-a-knot" conditions the cubic spline interpolants are constructed by replacing the requirement for equal second order derivatives at every knot with Brodlie's derivative formula. Analysis and simulation experiments show that this approach can effectively avoid generating new extrema, shifting or exaggerating the existing ones in a signal, and thus significantly improve the decomposition performance of EMD.