Multivariate empirical mode decomposition and application to multichannel filtering

TLDR: A novel EMD approach, which allows for a straightforward decomposition of mono- and multivariate signals without any change in the core of the algorithm, is proposed, and Qualitative results illustrate the good behavior of the proposed algorithm whatever the signal dimension is.

About: This article is published in Signal Processing.The article was published on 2011-12-01 and is currently open access. It has received 75 citations till now. The article focuses on the topics: Filter bank & Filter (signal processing).

Figures

Figure 2: X-EMD bivariate decomposition of the signal s21.

Figure 4: X-EMD filter bank structure: i) top (first and second lines): number of oscillation extrema, Next, with boxplots as a function of the index of IMFs for uncorrelated white noises of dimensions : D = 1, D = 2 and D = 3,D = 4, D = 5 andD = 6, ii) bottom (third and fourth lines): averaged number of oscillation extrema, Next (cross) as a function of the index of IMFs in log2 coordinates and the associated linear regression model (continuous line).

Figure 5: Influence of channel correlation on the filter bank structure: fitting errors vs. ρ values (left), and slope vs. ρ values (right).

Figure 1: X-EMD monovariate decomposition of the signal s12. Dashed line: real IMF / plain line: estimated IMF.

Table 2: Comparative study of X-EMD versus Huang (1D), Rilling (2D), Rehman (2D) and 2T-EMD (1D, 2D and 3D) reference methods.

Figure 6: Application of X-EMD to multichannel sleep recording.

Frequently asked questions

Q1. What have the authors contributed in "Multivariate empirical mode decomposition and application to multichannel filtering" ?

In this paper, a novel EMD approach called X-EMD ( eXtended-EMD ) is proposed, which allows for a straightforward decomposition of monoand multivariate signals without any change in the core of the algorithm. Moreover, a comparative study of X-EMD with classical monoand multivariate methods is presented and shows its competitiveness. Besides, the authors show that X-EMD extends the filter bank properties enjoyed by monovariate EMD to the case of multivariate EMD. Finally, a practical application on multi-channel sleep recording is presented. 

Q2. What are the future works in "Multivariate empirical mode decomposition and application to multichannel filtering" ?

More simulated and real data decompositions will be performed in future works. 

Q3. What is the purpose of the proposed X-EMD method?

The proposed X-EMD method aims at providing a unique tool able to process mono- and multivariate signals without any modification. 

Q4. Why can't a function be rewritten as s?

Due to the continuity of the inner product, it is noteworthy that function αs can be rewritten as:∀t ∈ R, αs(t) = 〈lim h→0 Ts(t− h), lim h→0 Ts(t+ h)〉 

Q5. What is the main limitation of the approach?

A restricted scope of application mainly due to the use of the first derivative in the algorithm remains the most important limitation of their approach. 

Q6. What is the main idea of the 2T-EMD algorithm?

More pre-cisely, 2T-EMD algorithm is based on two main steps: i) identification of all elementary oscillations and ii) computation of the barycenters of each associated elementary oscillations and interpolation between all these barycenters to obtain the signal mean trend. 

Q7. What are the two methods of multivariate EMD?

As far as the cases of multivariate signals are concerned, two methods, namely 2T-EMD algorithm [19, 20] and Rehman’s method [18], are considered. 

Q8. What is the linear regression quality of the IMFs?

The linear regression quality shows how Next exponentially decreases with the number of IMFs, and suggests a filter bank structure whatever the considered dimension is.