Turning Tangent Empirical Mode Decomposition: A Framework for Mono- and Multivariate Signals

Abstract

A novel Empirical Mode Decomposition (EMD) algorithm, called 2T-EMD, for both mono- and multivariate signals is proposed in this paper. It differs from the other approaches by its computational lightness and its algorithmic simplicity. The method is essentially based on a redefinition of the signal mean envelope, computed thanks to new characteristic points, which offers the possibility to decompose multivariate signals without any projection. The scope of application of the novel algorithm is specified, and a comparison of the 2T-EMD technique with classical methods is performed on various simulated mono- and multivariate signals. The monovariate behaviour of the proposed method on noisy signals is then validated by decomposing a fractional Gaussian noise and an application to real life EEG data is finally presented.

Application of Multivariate Empirical Mode Decomposition and Sample Entropy in EEG Signals via Artificial Neural Networks for Interpreting Depth of Anesthesia

“…Nowadays, there are many types of EMD and each one has merits and demerits in processing the signal. For example, eXtended-EMD (X-EMD) [29] can produce better results than MEMD and Turning Tangent EMD (2T-EMD) [30] in dealing with multivariate signal denoising. However, in 2011 Rehman et al also proposed N-A EMD.…”

Removal of muscle artifact from EEG data: comparison between stochastic (ICA and CCA) and deterministic (EMD and wavelet-based) approaches

“…We also show in [35] that, in practice, a robust computation of the mean trend is obtained by averaging two envelopes: a first envelope interpolates the even indexed barycenters, and a second envelope interpolates the odd indexed barycenters. Compared to other approaches the 2T-EMD algorithm is simpler, has a lighter computational cost, and enables both mono and multivariate decompositions without any change in the core of the algorithm.…”

“…At each instant m, the jth sifting iteration consists: (i) in computing the mean envelope, M s nk;j m ½ À Á , of the residual signal, and (ii) in extracting the detail s nk;jþ1 m ½ ¼ s nk;j m ½ À M s nk;j m ½ À Á from the residue. This process is repeated until the stopping criteria is reached (Cauchy-like criterion used in [35]). Several EMD methods have been proposed in the literature [30,32,34,35], depending on the way the mean envelope M s nk;j m ½ À Á ;8m 2 N is calculated.…”

“…This process is repeated until the stopping criteria is reached (Cauchy-like criterion used in [35]). Several EMD methods have been proposed in the literature [30,32,34,35], depending on the way the mean envelope M s nk;j m ½ À Á ;8m 2 N is calculated. In the following, we will use the 2T-EMD method recently proposed by our team [35].…”

“…ð Þ is redefined as the signal which interpolates the barycenters of particular oscillations, called elementary oscillations (see [35] for more details). We also show in [35] that, in practice, a robust computation of the mean trend is obtained by averaging two envelopes: a first envelope interpolates the even indexed barycenters, and a second envelope interpolates the odd indexed barycenters.…”