Abstract
The empirical mode decomposition (EMD) was recently proposed as a new time-frequency analysis tool for nonstationary and nonlinear signals. Although the EMD is able to find the intrinsic modes of a signal and is completely self-adaptive, it does not have any implication on reconstruction optimality. In some situations, when a specified optimality is desired for signal reconstruction, a more flexible scheme is required. We propose a modified method for signal reconstruction based on the EMD that enhances the capability of the EMD to meet a specified optimality criterion. The proposed reconstruction algorithm gives the best estimate of a given signal in the minimum mean square error sense. Two different formulations are proposed. The first formulation utilizes a linear weighting for the intrinsic mode functions (IMF). The second algorithm adopts a bidirectional weighting, namely, it not only uses weighting for IMF modes, but also exploits the correlations between samples in a specific window and carries out filtering of these samples. These two new EMD reconstruction methods enhance the capability of the traditional EMD reconstruction and are well suited for optimal signal recovery. Examples are given to show the applications of the proposed optimal EMD algorithms to simulated and real signals.
Highlights
The empirical mode decomposition (EMD) is proposed by Huang et al as a new signal decomposition method for nonlinear and nonstationary signals [1]
The EMD decomposes a signal into a collection of oscillatory modes, called intrinsic mode functions (IMF), which represent fast to slow oscillations in the signal
A direct approach is using linear weighting of IMFs. This leads to our first proposed optimal signal reconstruction algorithm based on EMD (OSR-EMD)
Summary
The empirical mode decomposition (EMD) is proposed by Huang et al as a new signal decomposition method for nonlinear and nonstationary signals [1]. When the EMD is used for denoising a signal, partial reconstruction based on the IMF energy eliminates noise components [15]. Such partial reconstruction utilizes a binary IMF decision, that is, either discarding or keeping IMFs in the partial summation. Stated more formally, the problem addressed here is the following: given a signal, how best to reconstruct the signal by the IMFs. EURASIP Journal on Advances in Signal Processing obtained from a signal that bears some relationship to the given signal. A direct approach is using linear weighting of IMFs. A direct approach is using linear weighting of IMFs This leads to our first proposed optimal signal reconstruction algorithm based on EMD (OSR-EMD). When the SD is smaller than a threshold, the first IMF c1(n) is obtained, which is written as
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