Bivariate Empirical Mode Decomposition

Abstract

The Empirical Mode Decomposition (EMD) has been introduced quite recently to adaptively decompose nonstationary and/or nonlinear time series [1]. The method being initially limited to real-valued time series, we propose here an extension to bivariate (or complex-valued) time series which generalizes the rationale underlying the EMD to the bivariate framework. Where the EMD extracts zero-mean oscillating components, the proposed bivariate extension is designed to extract zero-mean rotating components. The method is illustrated on a real-world signal and properties of the output components are discussed. Free Matlab/C codes are available at http://perso.ens-lyon.fr/patrick.flandrin.

Comparative study of methods for solving the correspondence problem in EMD applications

“…In the case of DBSCAN, a higher threshold distance results in the assignment of all IMFs in one cluster, and a smaller value assigns better the high-index IMFs and excludes the other ones in the noise cluster. The physiologically most relevant IMFs (5)(6)(7)(8) for HRV data given their spectral components [4,13] are best assigned in the case of the reference-based approach and k-cardinality assignment with k = 10.…”

“…Currently several modified versions of EMD exist that either address disadvantages like the mixing problem, i.e. similar frequencies can appear in different IMFs, such as ensemble empirical mode decomposition (EEMD) [5] and complete ensemble empirical mode decomposition with adaptive noise (CEEMD) [6], or are multivariate extensions of EMD such as bivariate EMD [7], trivariate EMD and multivariate empirical mode decomposition (MEMD) [8] when multichannel (multi-trial) data are available. The advantage of the multivariate versions is that the number of IMFs is equal for all channels (trials) and the filter bank property is preserved [9].…”

Empirical Mode Decomposition for Advanced Speech Signal Processing

“…The main difference between bEMD and cEMD is that the latter uses the basic EMD to decompose complex signals, whereas bEMD adapts the rationale underlying the EMD to a bivariate framework [28,29]. In bEMD two variables are decomposed simultaneously based on their rotating properties.…”

“…In bEMD two variables are decomposed simultaneously based on their rotating properties. The algorithm of bEMD, as proposed in [28], is as follows: …”

Extraction of the JEM Component in the Observation Range of Weakly Present JEM Based on Complex EMD

“…그러나 여기서는 JEM이 미약하게 관측되는 범위에서 JEM 성분의 최대 진폭이 body 성분의 진폭에 비해 -15 dB 이상 작은 상황을 가정한다. 이에 본 논문에서는 복소 신호의 경험적인 모드분리법(Complex Empirical Mode Decomposition: CEMD) [5] 을 통해 레 이더 수신 신호를 여러 고유 모드 함수(Intrinsic Mode Function: IMF)로 분리하는 한편, 복소 신호의 이심률(eccentricity) 개념 [6] 을 [6] . [7] 복소 평면의 중심축에 대해 원형의 회전 형태를 유지함을 알 수 있다.…”