Abstract: Due to the envelope fitting problem exists in the process of empirical mode decomposition， an improved algorithm was proposed which could eliminate the undershoot phenomenon exactly. Firstly， in this improved algorithm， the cubic spline interpolation was used to determine the regions of undershoot which generated during the execution of envelope fitting. Secondly， the envelope intervals of undershoot regions were compensated by the monotone piecewise cubic polynomial interpolation. The original signal could be wrapped tightly by this modified envelope， which did not affect the characteristics of signal itself， and could keep the smoothness of previous envelope as well as possible. The simulation results showed that the undershoot phenomenon caused by cubic spline interpolation could be effectively eliminated and the envelope could be obtained better by this algorithm. In addition， the accuracy of empirical mode decomposition could be further improved.

Key words: Hilbert-Huang transform, empirical mode decomposition, undershoot phenomenon, envelope fitting, monotone piecewise cubic polynomial interpolation