Standard Empirical Mode Decomposition Research Articles

End-effects mitigation in empirical mode decomposition using a new correlation-based expansion model

The real-time analysis of time-varying data has become extremely significant in mechanical systems. The Hilbert–Huang transform (HHT) is a recent development in signal processing based on time–frequency distribution for analyzing complex signals. The HHT permits instantaneous attributes to be used to study signals that display complex behavior and stochastically vary with time. This transform combines empirical mode decomposition (EMD) and Hilbert transform (HT). The EMD converts a signal of time into various intrinsic mode functions (IMF), which are subsequently used by the HT to insert into the same time–frequency space. However, the restriction of the end-effect is an important problem when employing the EMD method. End-effect causes several issues such as changing the shapes of envelopes, deviating IMF, computational instabilities at the signal borders, and modal aliasing. To mitigate the end-effects, this study presents a correlation-based expansion model at both ends of the signal. Motivated by end-effects mitigation, data outside of the signal boundaries are predicted based on the similarity of the signal’s start and end segments with the signal's inner segment. Correlation techniques are a reliable method to find signal pattern similarities. Seven simulated signals are used to verify the method's performance. The seven signals include six monovarietal signals with various amplitude modulation-frequency modulation behaviors and a one-channel functional near-infrared spectroscopy (fNIRS) signal. The comparison results of the proposed technique with standard EMD and EMD coupled with other expansion methods show that the end-effect in the EMD method by correlation expansion can effectively reduce.

Ground Roll Attenuation of Multicomponent Seismic Data with the Noise-Assisted Multivariate Empirical Mode Decomposition (NA-MEMD) Method

Multicomponent seismic exploration provides more wavefield information for imaging complex subsurface structures and predicting reservoirs. Ground roll is strongly coherent noise in land multicomponent seismic data and exhibits similar features, which are strong energy, low frequency, low velocity and dispersion, in each component. Ground roll attenuation is an important step in seismic data processing. In this study, we utilized multivariate empirical mode decomposition to multicomponent seismic data for attenuating ground roll. By adding extra components containing independent white noise, noise-assisted multivariate empirical mode decomposition is adopted to overcome the mode-mixing effect in standard empirical mode decomposition. This method provides a more robust analysis than the standard empirical mode decomposition EMD method performed separately for each component. Multicomponent seismic data are decomposed into different intrinsic mode functions in frequency scale. According to different frequency scales of seismic reflection wave and ground roll, intrinsic mode functions with low frequency are eliminated to suppress ground roll, and the remaining are reconstructed for seismic reflection waves. Synthetic and field data tests show that the proposed approach performs better than the traditional attenuation method.

Component-scaled signal reconstruction for enhanced noise filtration

This research introduces a procedure for signal denoising based on linear combinations of intrinsic mode functions (IMFs) extracted using empirical mode decomposition (EMD). The method, termed component-scaled signal reconstruction, employs the standard EMD algorithm, with no enhancements to decompose the signal into a set of IMFs. The problem of mode mixing is leveraged for noise removal by constructing an optimal linear combination of the potentially mixed IMFs. The optimal linear combination is determined using an optimization routine with an objective function that maximizes and minimizes the information and noise, respectively, in the denoised signal. The method is demonstrated by applying it to a computer-generated voice sample and the displacement response of a cantilever beam with local stiffness nonlinearity. In the first application, the noise is introduced into the sample manually by adding a Gaussian white-noise signal to the signal. In the second application, the response of the entire beam is filmed using two 1-megapixel cameras, and the three-dimensional displacement field is extracted using digital image correlation. The noise in this application arises entirely from the images captured. The proposed method is compared to existing EMD, ensemble EMD, and LMD based denoising approaches and is found to perform better.

FPGA-Based Design for Online Computation of Multivariate Empirical Mode Decomposition

Multivariate or multichannel data have become ubiquitous in many modern scientific and engineering applications, e.g., biomedical engineering, owing to recent advances in sensor and computing technology. Processing these data sets is challenging owing to their large size and multidimensional nature, thus requiring specialized algorithms and efficient hardware designs for online and real time processing. In this paper, we address this issue by proposing a fully FPGA based hardware architecture of a popular multi-scale and multivariate signal processing algorithm, termed as multivariate empirical mode decomposition (MEMD). MEMD is a data-driven method that extends the functionality of standard empirical mode decomposition (EMD) algorithm to multichannel or multivariate data sets. Since its inception in 2010, the algorithm has found wide spread applications spanning different engineering related fields. Yet, no parallel FPGA based hardware design of the algorithm is available for its online and real time processing. Our proposed architecture for MEMD uses fixed-point operations and employs cubic spline interpolation (CSI) within the sifting process. Finally, examples of decomposition of multivariate synthetic and real-world biological signals are provided.

Parkinsonian Tremor Signal Decomposition: Segregating Effects of Deep Brain Stimulation and Medication.

Analysis of tremor signal is a crucial part in the study of Parkinsonian subject, specially to understand effectiveness of treatment and progression of disease. Aim of this paper is to segregate the effects of Deep Brain Stimulation (DBS) and medicinal components from Parkinson's disease (PD) tremor signal. Tremor signal has multiple effects embedded in a single channel and identifying the hidden components from it is a challenging process. Conventional methods like Empirical Mode Decomposition (EMD) and Ensemble EMD (EEMD) serve the purpose, however, these methods fail with increase in noise in the signal. We propose the usage of Variational Mode Decomposition (VMD) to identify the underlying hidden components in the tremor signal. It decomposes the tremor signal into different source components, which can be identified as medicinal or DBS components. Results show that VMD is more efficient in disintegrating the medicine and DBS component from the single channel tremor signal, compared to standard EMD and EEMD techniques. This study can help in better understanding of PD tremor suppression mechanism.

Augmented EMD for complex‐valued univariate signals

In this study, the authors propose an efficient extension of the standard empirical mode decomposition (EMD) for complex-valued univariate signal decomposition. The key idea of the extension is to convert a complex-valued univariate signal into a longer real-valued signal by augmenting the real part with the flipped imaginary part, and then to decompose it into intrinsic mode functions (IMFs) using the EMD once only. The bivariate IMFs are then retrieved from the obtained IMFs. Their empirical results on synthetic data show that the proposed method significantly outperforms the traditional bivariate EMD (BEMD) method in terms of computational efficiency while producing a comparable extraction error. Moreover, the proposed method shows better micro-Doppler signature analysis performance on physically measured continuous-wave radar data than that of the BEMD.

Radar Signal Emitter Recognition Based on Combined Ensemble Empirical Mode Decomposition and the Generalized S-Transform

Present radar signal emitter recognition approaches suffer from a dependency on prior information. Moreover, modern emitter recognition must meet the challenges associated with low probability of intercept technology and other obscuration methodologies based on complex signal modulation and must simultaneously provide a relatively strong ability for extracting weak signals under low SNR values. Therefore, the present article proposes an emitter recognition approach that combines ensemble empirical mode decomposition (EEMD) with the generalized S-transform (GST) for promoting enhanced recognition ability for radar signals with complex modulation under low signal-to-noise ratios in the absence of prior information. The results of Monte Carlo simulations conducted using various mixed signals with additive Gaussian white noise are reported. The results verify that EEMD suppresses the occurrence of mode mixing commonly observed using standard empirical mode decomposition. In addition, EEMD is shown to extract meaningful signal features even under low SNR values, which demonstrates its ability to suppress noise. Finally, EEMD-GST is demonstrated to provide an obviously better time-frequency focusing property than that of either the standard S-transform or the short-time Fourier transform.

Frequency mode identification using modified masking signal‐based empirical mode decomposition

A modified masking empirical mode decomposition (EMD) for effectively improving the mode separation capability of standard EMD while analysing power system signals with closely spaced modes of frequency is proposed here. A multi-frequency test signal resembling the dynamic power system signal and the actual data recorded by wide area measurement systems (WAMS) from Northern Grid, India, on 1 June 2010 due to generation loss are analysed by both the existing method and the proposed method. Various components of modal frequency extracted by masking signal base EMD are compared with extracted components by the proposed modified masking EMD. Further, the time–frequency representation of extracted modes by Hilbert spectral analysis is implemented to know mode behaviour with time reference. Simulation results prove that the EMD with proposed modification is capable of separating various modes of frequencies present in the WAMS signal.

An empirical signal separation algorithm for multicomponent signals based on linear time-frequency analysis

Abstract The empirical mode decomposition (EMD) is a powerful tool for non-stationary signal analysis. It has been used successfully for non-stationary signals separation and time-frequency representation. Linear time-frequency analysis (TFA) is another powerful tool for non-stationary signal. Linear TFAs, e.g. short-time Fourier transform (STFT) and wavelet transform (WT), depend linearly upon the signal analysis. In the current paper, we utilize the advantages of EMD and linear TFA to propose a new signal reconstruction method, called the empirical signal separation algorithm. First we represent the signal with STFT or WT. After that, by using an EMD-like procedure, we extract the components in the time-frequency (TF) plane one by one, adaptively and automatically. With the iterations carried out in the sifting process, the proposed method can separate non-stationary multicomponent signals with fast varying frequency components which EMD may not be able to separate. The experiments results demonstrate the efficiency of the proposed method compared to standard EMD, ensemble EMD and synchrosqueezing transform.

Localization of Active Brain Sources From EEG Signals Using Empirical Mode Decomposition: A Comparative Study.

The localization of active brain sources from Electroencephalogram (EEG) is a useful method in clinical applications, such as the study of localized epilepsy, evoked-related-potentials, and attention deficit/hyperactivity disorder. The distributed-source model is a common method to estimate neural activity in the brain. The location and amplitude of each active source are estimated by solving the inverse problem by regularization or using Bayesian methods with spatio-temporal constraints. Frequency and spatio-temporal constraints improve the quality of the reconstructed neural activity. However, separation into frequency bands is beneficial when the relevant information is in specific sub-bands. We improved frequency-band identification and preserved good temporal resolution using EEG pre-processing techniques with good frequency band separation and temporal resolution properties. The identified frequency bands were included as constraints in the solution of the inverse problem by decomposing the EEG signals into frequency bands through various methods that offer good frequency and temporal resolution, such as empirical mode decomposition (EMD) and wavelet transform (WT). We present a comparative analysis of the accuracy of brain-source reconstruction using these techniques. The accuracy of the spatial reconstruction was assessed using the Wasserstein metric for real and simulated signals. We approached the mode-mixing problem, inherent to EMD, by exploring three variants of EMD: masking EMD, Ensemble-EMD (EEMD), and multivariate EMD (MEMD). The results of the spatio-temporal brain source reconstruction using these techniques show that masking EMD and MEMD can largely mitigate the mode-mixing problem and achieve a good spatio-temporal reconstruction of the active sources. Masking EMD and EEMD achieved better reconstruction than standard EMD, Multiple Sparse Priors, or wavelet packet decomposition when EMD was used as a pre-processing tool for the spatial reconstruction (averaged over time) of the brain sources. The spatial resolution obtained using all three EMD variants was substantially better than the use of EMD alone, as the mode-mixing problem was mitigated, particularly with masking EMD and EEMD. These findings encourage further exploration into the use of EMD-based pre-processing, the mode-mixing problem, and its impact on the accuracy of brain source activity reconstruction.

An Efficient ECG Denoising Technique Based on Non-local Means Estimation and Modified Empirical Mode Decomposition

Noninvasive nature of Electrocardiogram (ECG) signal makes it widely accepted for cardiac diagnosis. During the process of data acquisition, ECG signal is generally corrupted by a number of noises. Further, during ambulatory monitoring and wireless recording, ECG signal gets corrupted by additive white Gaussian noise. Without affecting the morphological structure, denoising of ECG signal is essential for proper diagnosis. This paper presents an ECG denoising method based on an effective combination of non-local means (NLM) estimation and empirical mode decomposition (EMD). Earlier works have shown that the patch-based NLM approach is insufficient for denoising the under-averaged region near high-amplitude QRS complex. To address this issue, the denoised signal obtained by NLM is decomposed into intrinsic mode functions (IMFs) using EMD in this work. Next, thresholding of the IMFs is done using the instantaneous half period criterion and the soft-thresholding to obtain the final denoised output. Furthermore, the modified empirical mode decomposition (M-EMD) is used in the place of standard EMD to reduce the computational cost. Performance of the proposed method is tested on a number of ECG signals from the MIT-BIH database. The experimental results presented in this paper show that the aforementioned shortcoming of the NLM method is addressed to a large extent. Moreover, the proposed approach provides improved performance when compared to different state-of-the-art ECG denoising methods.

Extraction of Plant-wide Oscillations using Fast Multivariate Empirical Mode Decomposition

This paper proposes a novel time-frequency method for plant-wide oscillation analysis based on the multivariate extension of standard empirical mode decomposition (EMD). The raised fast multivariate empirical mode decomposition (FMEMD) is generalized from EMD by solving an overdetermined system of linear equations. Due to its capability to analyze multiple channels data, FMEMD is especially suitable for characterizing plant-wide control loop oscillations. Unlike traditional methods, both the regularity of oscillations (in frequency domain) and evolution of local characteristics (in time scale) can be well captured via FMEMD. Validity of the raised approach is demonstrated on simulations as well as an industrial case.

SEPARATION OF TWIN FETAL ECG FROM MATERNAL ECG USING EMPIRICAL MODE DECOMPOSITION TECHNIQUES

In this study, by using a combination of standard Empirical Mode Decomposition (EMD), Ensembling Empirical Mode Decomposition (EEMD), Completing Empirical Mode Decomposition (CEMD) and Principal Component Analysis (PCA), a new method was introduced to separate twin fetal heart rate (FHR) from maternal ECG. The data which were the results of modeling fetal and maternal ECG which be longed to 10 mothers with a sampling frequency of 250[Formula: see text]Hz. In this method, first R-wave of maternal ECG was determined, and then maternal QRS is removed. Further, to clarify these changes and increase resistance to environmental noises, PCA was used. In the next step, all FHRs related to twin fetuses were extracted from signals. Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) was used for denoising. By using the proposed method for noise with an amplitude of over 10 dB, the FHR of the first and second (if any) fetuses were separated from maternal ECG with an accuracy of 93.3% and 91.1% respectively. The goal was to improve signal processing dimensions of fetal ECG and provides deeper insight about this issue using EEMD technique. It was tested on a twin fetus with the results suggesting its effectiveness even with increased number of fetuses with slight modifications.

Implementation of Empirical Mode Decomposition Based Algorithm for Shunt Active Filter

In this paper, an online empirical mode decomposition (EMD) based algorithm is proposed for the control of a shunt active filter (AF). Standard EMD algorithm has worked on the principle of time-scale difference between the upper maximum values and lower minimum values of a signal, and for a long time it has been considered good for offline analysis of signals. This paper deals with the real-time application of EMD for the control of AF under balanced and unbalanced loads. Linear interpolators are employed for construction of upper and lower envelopes to avoid computation complexity. Moreover, customized iterative computations for extraction of intrinsic mode functions maintain the efficiency of algorithm. The algorithm extracts the fundamental component of load current and helps in estimating reference currents. Simulations are performed on MATLAB/Simulink platforms. Simulation results are verified with experimental results of a developed prototype of shunt AF.

A simple method inspired by empirical mode decomposition for denoising seismic data

We developed a new and simple method for denoising seismic data, which was inspired by data-driven empirical mode decomposition (EMD) algorithms. The method, which can be applied either as a trace-by-trace process or in the [Formula: see text] domain, replaces the use of the cubic interpolation scheme, which is required to calculate the mean envelopes of the signal and the residues, by window averaging. The resulting strategy is not viewed as an EMD per se, but a user-friendly version of EMD-based algorithms that permits us to attain, in a fraction of the time, the same level of noise cancellation as standard EMD implementations. Furthermore, the proposed method requires less user intervention and easily processes millions of traces in minutes rather than in hours as required by conventional EMD-based techniques on a standard PC. We compared the performance of the new method against standard EMD methods in terms of computational cost and signal preservation and applied them to denoise synthetic and field (microseismic and poststack) data containing random, erratic, and coherent noise. The corresponding [Formula: see text] EMDs implementations for lateral continuity enhancement were analyzed and compared against the classical [Formula: see text] deconvolution to test the method.

A better decomposition of speech obtained using modified Empirical Mode Decomposition

The objective of this work is to obtain meaningful time domain components, or Intrinsic Mode Functions (IMFs), of the speech signal, using Empirical Mode Decomposition (EMD), with reduced mode mixing, and in a time-efficient manner. This work focuses on two aspects – firstly, extracting IMFs of the speech signal which can better reflect its higher frequency spectrum; and secondly, to get a better representation and distribution of the vocal tract resonances of the speech signal in its IMFs, compared to that obtained from standard EMD. To this effect, modifications are proposed to the EMD algorithm for processing speech signals, based on the critical nature of the interpolation points (IPs) used for cubic spline interpolation in EMD. The effect of using different sets of IPs, other than the extrema of the residue – as used in standard EMD – is analyzed. It is found that having more IPs is beneficial only upto a certain limit, after which the characteristic dyadic filterbank nature of EMD breaks down. For certain sets of IPs, these modified EMD processes perform better than EMD, giving better frequency separability between the IMFs, and an enhanced representation of the higher frequency content of the signal. A detailed study of the distribution of the formants, in the IMFs of the speech signal, is done using Linear Prediction (LP) analysis of the IMFs. It is found that the IMFs of the EMD variants have a far better distribution of the formants structure within them, with reduced overlapping amongst their filter spectrums, compared to that of standard EMD. Henceforth, when subjected to the task of formants estimation of voiced speech, using LP analysis, the IMFs of the modified EMD processes cumulatively exhibit a superior performance than that of standard EMD, or the speech signal itself, under both clean and noisy conditions.

The long-term trends on the electricity markets: Comparison of empirical mode and wavelet decompositions

This paper proposes an improved approach to electricity prices trend-cyclical component filtering, which is based on the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN). A combined criterion for determining the modes to be included into the trend component is introduced. The performance of the proposed approach is compared with the ordinary empirical mode decomposition (EMD), as well as with the method of wavelet-decomposition well-known in the energy economics literature. We test it on four day-ahead electricity markets: the Europe-Ural and the Siberia price zones of the Russian ATS exchange, the PJM exchange of the USA and the APX exchange of the United Kingdom. Our results show that the proposed approach based on CEEMDAN and the combined criterion outperforms the standard EMD on all the four electricity markets, and on two of the studied markets (PJM, APX) it outperforms the wavelet-smoothing, while on the other two (ATS Europe-Ural and Siberia) it performs at least not worse than the wavelet-smoothing. At the same time, the proposed approach does not require a prior choice of the smoothing parameter, as in the case of the wavelet-decomposition, and demonstrates a certain degree of versatility on the studied markets.

A Multivariate Empirical Mode DecompositionBased Approach to Pansharpening

We propose a novel class of schemes for the pansharpening of multispectral (MS) images using a multivariate empirical mode decomposition (MEMD) algorithm. MEMD is an extension of the empirical mode decomposition (EMD) algorithm, which enables the decomposition of multivariate data into its intrinsic oscillatory scales. The ability of MEMD to process multichannel data directly by performing data-driven, local, and multiscale analysis makes it a perfect match for pansharpening applications, a task for which standard univariate EMD is ill-equipped due to the nonuniqueness, mode-mixing, and mode-misalignment issues. We show that MEMD overcomes the limitations of standard EMD and yields improved spatial and spectral performance in the context of pansharpening of MS images. The potential of the proposed schemes is further demonstrated through comparative analysis against a number of standard pansharpening algorithms on both simulated Pleiades and real-world IKONOS data sets.

Output-Only Modal Analysis Based on Improved Empirical Mode Decomposition Method

The output-only modal analysis for bridge structures based on improved empirical mode decomposition (EMD) is investigated in this study. First, a bandwidth restricted EMD is proposed for decomposing nonstationary output measurements with close frequency components. The advantage of bandwidth restricted EMD to standard EMD is illustrated by a numerical simulation. Next, the modal parameters are extracted from intrinsic mode function obtained from the improved EMD by both random decrement technique and stochastic subspace identification. Finally, output-only modal analysis of a railway bridge is presented. The study demonstrates the mode mixing issues of standard EMD can be restrained by introducing bandwidth restricted signal. Further, with the improved EMD method, band-pass filter is no longer needed for separating the closely spaced frequency components. The modal parameters extracted based on the improved EMD method show good agreement with those extracted by conventional modal identification algorithms.

EMD VIA MEMD: MULTIVARIATE NOISE-AIDED COMPUTATION OF STANDARD EMD

A noise-assisted approach in conjunction with multivariate empirical mode decomposition (MEMD) algorithm is proposed for the computation of empirical mode decomposition (EMD), in order to produce localized frequency estimates at the accuracy level of instantaneous frequency. Despite many advantages of EMD, such as its data driven nature, a compact decomposition, and its inherent ability to process nonstationary data, it only caters for signals with a sufficient number of local extrema. In addition, EMD is prone to mode-mixing and is designed for univariate data. We show that the noise-assisted MEMD (NA-MEMD) approach, which utilizes the dyadic filter bank property of MEMD, provides a solution to the above problems when used to calculate standard EMD. The method is also shown to alleviate the effects of noise interference in univariate noise-assisted EMD algorithms which directly add noise to the data. The efficacy of the proposed method, in terms of improved frequency localization and reduced mode-mixing, is demonstrated via simulations on electroencephalogram (EEG) data sets, over two paradigms in brain-computer interface (BCI).