B-spline Based Empirical Mode Decomposition

This paper discusses some mat hematical issues related to empirical mode decomposition (EMD). A B-spline EMD algorithm is introduced and developed for the convenience of mathematical studies. The numerical analysis using both simulated and practical signals and application examples from vibration analysis indicate that the B-spline algorithm has a comparable performance to that of the original EMD algorithm. It is also demonstrated that for white noise, the B-spline algorithm acts as a dyadic filter bank. Our mathematical results on EMD include Euler splines as intrinsic mode functions, the Hilbert transform of B-splines, and the necessary and sufficient conditions which ensure the validity of the Bedrosian identity of the Hilbert transform of product functions.