The Application of Wavelet-Kalman Hybrid Filter in EMD Edge Problem

Empirical mode decomposition is one of effective new methods to process signals disturbed by noise, which has been attracted extensively attention and applied successfully in many engineering fields. Usually, cubic spline interpolation operation is used to fit the upper and lower envelopes of given signals in the traditional EMD approach. However, the ill behavior often appears on the edges of the signals, which influences the quality of signal processing. Aiming at the above case, by use of the random walk property of a time series composed by the wavelet coefficients of lots of periodic signals, the paper applies the hybrid filter which consists of wavelet transform and Kalman filter to extending two edges of signal by forwards forecasting or backwards smoothing, and create these new upper and lower envelopes to overcome shortcoming arose from foregone methods. Computer simulation validates the effectiveness of the new technique presented in the letter