Using constrained cubic spline instead of natural cubic spline to eliminate overshoot and undershoot in Hilbert Huang Transform

Hilbert-Huang Transform (HHT), proposed by N. E. Huang in 1998, is a novel algorithm for nonlinear and non-stationary signal processing. The key part of this method is decomposition the signal into finite number of Intrinsic Mode Functions (IMF) which will meet the requirements of Hilbert Transform. In this part, the algorithm uses natural cubic spline to connect all local maxima and local minima to produce upper and lower envelope of the signal. However natural cubic spline which may lead overshoot and undershoot at intermediate point. In this paper we propose to apply constrained cubic spline into first part of the HHT to eliminate overshoot in upper and lower envelope. We also propose an improvement on Improved Slope Base Method (ISBM) to limit swing at the end points. The experiments showed that our proposals get better result than original proposal and speed up Empirical Mode Decomposition (EMD) process.