Sequential algorithm for life threatening cardiac pathologies detection based on mean signal strength and EMD functions
 Emran M Abu Anas^{1},
 Soo Y Lee^{2} and
 Md K Hasan^{1, 2}Email author
https://doi.org/10.1186/1475925X943
© Anas et al; licensee BioMed Central Ltd. 2010
Received: 19 April 2010
Accepted: 4 September 2010
Published: 4 September 2010
Abstract
Background
Ventricular tachycardia (VT) and ventricular fibrillation (VF) are the most serious cardiac arrhythmias that require quick and accurate detection to save lives. Automated external defibrillators (AEDs) have been developed to recognize these severe cardiac arrhythmias using complex algorithms inside it and determine if an electric shock should in fact be delivered to reset the cardiac rhythm and restore spontaneous circulation. Improving AED safety and efficacy by devising new algorithms which can more accurately distinguish shockable from nonshockable rhythms is a requirement of the presentday because of their uses in public places.
Method
In this paper, we propose a sequential detection algorithm to separate these severe cardiac pathologies from other arrhythmias based on the mean absolute value of the signal, certain loworder intrinsic mode functions (IMFs) of the Empirical Mode Decomposition (EMD) analysis of the signal and a heart rate determination technique. First, we propose a direct waveform quantification based approach to separate VT plus VF from other arrhythmias. The quantification of the electrocardiographic waveforms is made by calculating the mean absolute value of the signal, called the mean signal strength. Then we use the IMFs, which have higher degree of similarity with the VF in comparison to VT, to separate VF from VTVF signals. At the last stage, a simple rate determination technique is used to calculate the heart rate of VT signals and the amplitude of the VF signals is measured to separate the coarse VF from VF. After these three stages of sequential detection procedure, we recognize the two components of shockable rhythms separately.
Results
The efficacy of the proposed algorithm has been verified and compared with other existing algorithms, e.g., HILB [1], PSR [2], SPEC [3], TCI [4], Count [5], using the MITBIH Arrhythmia Database, Creighton University Ventricular Tachyarrhythmia Database and MITBIH Malignant Ventricular Arrhythmia Database. Four quality parameters (e.g., sensitivity, specificity, positive predictivity, and accuracy) were calculated to ascertain the quality of the proposed and other comparing algorithms. Comparative results have been presented on the identification of VTVF, VF and shockable rhythms (VF + VT above 180 bpm).
Conclusions
The results show significantly improved performance of the proposed EMDbased novel method as compared to other reported techniques in detecting the life threatening cardiac arrhythmias from a set of large databases.
Background
Ventricular Fibrillation (VF) and Ventricular Tachycardia (VT) are lifethreatening cardiac arrhythmias generally observed in adults with coronary artery disease. In 1979, automatic external defibrillators (AEDs) were introduced to accurately analyze the cardiac rhythms and, if appropriate, advise/deliver a highenergy shock to those patients who suffer from coarse VF and VT of a rate above 180 bpm, combinedly known as the shockable rhythms [6]. Though a significant number of works have been published on this topic, the scope for development of more accurate and reliable techniques relaxing assumptions of certain previous works and incorporating features from diverse nature of the cardiographic signals is yet open. Based on separation capability, the algorithms available in the literature can be classified into categories such as, separating VF from VT [4, 7, 8], VF from normal sinus rhythm (NSR) [9], VF plus VT from nonVTVF [10], shockable rhythms from other ECG pathologies [5, 11, 12], VF from nonVF [1–4, 13–24]. Comprehensively, the last two categories [25] are the most realistic for fruitful hospital management of cardiac abnormalities.
To separate VF from VT many efforts have been aimed at characterizing these abnormalities by means of diverse techniques such as the sequential hypothesis algorithm proposed by Thakor et al. [4], continuous wavelet transform [7], paired unipolar electrograms [8] etc. But only separating VF from VT is not useful for cardiac management. Because, in real life problems, other types of abnormalities are also present. A recent work is presented in [9] using the EMD technique to separate VF from NSR which shows almost 100% accuracy. But, when other types of pathology except the NSR and VF are present, poor accuracy is obtained. To separate VT plus VF from other arrhythmias, a time domain based complexity measure algorithm has been proposed in [10]. But it fails to show good performance due to its weakness in selecting a proper threshold value. Another approach has been reported in [5] to classify arrhythmias into two types: shockable and nonshockable signals. This work shows quite good accuracy but improvement area is still open. Various algorithms have been developed for classifying the abnormalities according to the last category. To separate VF from other arrhythmias, different methods were proposed based on different techniques of signal processing, such as the threshold crossing interval (TCI) algorithm [4], autocorrelation function (ACF) [13], probability density function method [14], VFfilter method [15], [16], [17], rate and irregularity analysis [18], [19], sequential hypothesis testing algorithm [20], [21], correlation waveform analysis [22], spectral analysis [3] and four fast template matching algorithms [23]. But these algorithms fail to show good performance when tested on a large database due to the some shortcomings in their reported algorithms. For example, the TCI method, based on a time domain technique, fails to detect the normal sinus rhythm (NSR) signal due to several factors, e.g., choice of 1s analysis window, improper threshold etc. [24]. An improved version of this algorithm called the threshold crossing sample count (TCSC) method has been reported in [24] by removing some of the drawbacks of the TCI method. But the TCSC algorithm does not consider the shape of the ECG signal, therefore, it fails to classify VT into the nonVF group. On the other hand, the ACF relies on the regularity in NSR and irregularity in VF rhythms [26]. But practically, in most cases, there is no strict regularity found in the NSR signal and, therefore, the detection accuracy of the NSR signal by this method severely falls. The spectral analysis method successfully detects the nonVF signal from ECG arrhythmias. But in the detection of VF, this method shows poor accuracy due to the false detection of the VF signal with low peak frequency in the spectrum [26]. On the other hand, the Hilbert transform (HILB) [1] and phase space reconstruction (PSR) [2] algorithms employing phase space plot of the ECG signal demonstrate improved performance of VF detection. Because the phase space plot is based on the histogram of a signal, it does not consider the shape of this signal. Thus, to separate VT from VF when other arrhythmias are also present, these two methods are not very suitable.
In this paper, we propose a sequential detection algorithm based on the mean absolute strength and certain loworder intrinsic mode functions (IMFs) of the EMD analysis of the signal along with a simple rate determination technique. In our proposed algorithm, we not only separate VF but also VT from other arrhythmias. VT plus VF (VTVF) is separated from other arrhythmias in the first stage using an index called the mean absolute value (MAV). Then we decompose the VTVF signal into IMFs using the EMD technique to discriminate VF from VT. EMD was introduced in [27] for processing signals from nonlinear and nonstationary processes. Here, we apply the EMD technique to biomedical signals and particularly for ECG analysis. Next, a simple rate determination algorithm is utilized to classify VT according to the heart rate and to separate coarse VF from fine VF, amplitude of the VF signals are measured. Finally, this sequential ECG arrhythmias classification approach is interpreted as three different detection schemes, such as, VTVF from nonVTVF; VF from nonVF; shockable from nonshockable rhythms. While proposing an algorithm for detecting the shockable rhythms special care must be taken to make the specificity high. It will then ensure the false alarm generation probability of the AEDs low. But an algorithm with high specificity generally results in low sensitivity. To mitigate this contradictory requirement, detection of the shockable rhythms using a sequential algorithm is found to be more effective. At last, in the 'Results' Section, we compare our algorithm with different wellknown algorithms available in the literature.
Methods
ECG signals
We use the MITBIH Arrhythmia Database (MITDB) [28], Creighton University Ventricular Tachyarrhythmia Database (CUDB) [29] and MITBIH Malignant Ventricular Arrhythmia Database (VFDB) [30] to evaluate our algorithm. The MITDB contains 48 files, 2 channels per file, each channel 1805 seconds long. The CUDB contains 35 files, 1 channel per file, each channel 508 seconds long. The VFDB contains 22 files, 2 channel per file, each channel 2100 seconds long. In our analysis, we choose episodes of 8s long from the whole MITBIH arrhythmia and CU databases. We perform a continuous analysis by taking the data in steps of 1 sec. Thus, the total number of 8s episodes collected from the MITDB and CUDB are (18057) × 48 × 2 = 172608 and (5087) × 35 = 17535, respectively. Since, the VFDB includes ECG recordings of subjects who have experienced episodes of sustained VT and VF, we use this database for VF and VT episodes. By taking the ECG signal in steps of 1 sec we choose 4000 episodes of VF and 4000 episodes of VT from this database. Therefore, a total of 172608 + 17535 + 4000 + 4000 = 198143 episodes are used to compare our algorithm with other algorithms. Amongst these 198143 episodes, we have noticed some episodes which are annoted as the noise signals. Since, in this work we have no interest in these noise signals, we have omitted these noise episodes. Also, analysis of the distinct mode asystole signal is not presented here. Therefore, this type of ECG signal is not included into our complete dataset.
 1.
Normal beat
 2.
Left bundle branch block beat (LBBB)
 3.
Right bundle branch block beat (RBBB)
 4.
Atrial premature beat (APC)
 5.
Aberrated atrial premature beat
 6.
Nodal (junctional) premature beat
 7.
Supraventricular premature or ectopic beat
 8.
Premature ventricular contraction (PVC) beat
 9.
Fusion of ventricular and normal beat
 10.
Atrial escape beat
 11.
Nodal (junctional) escape beat
 12.
Paced beat
 13.
Fusion of paced and normal beat
 14.
Unclassifiable beat
 15.
Blocked APC
 16.
Ventricular tachycardia
 17.
Ventricular fibrillation
 1.
(1805  7) × 23 × 2 = 82708 episodes from MITDB (file no. 100109, 111119, 121124).
 2.
2000 episodes of VF and 2000 episodes of VT from VFDB.
 1.
(1805  7) × 25 × 2 = 89900 episodes from MITDB (file no. 200203, 205, 207210, 212215, 217, 219223, 228, 230234).
 2.
2000 episodes of VF and 2000 episodes of VT from VFDB.
Classification of the ECG signals according to the AHA recommendations
 1.
Shockable rhythms

'coarse VF': any VF signal with an amplitude of > 200 μV.

'VThi': rapid ventricular tachycardia with a rate of > 180 bpm.
 2.
Nonshockable rhythms

'NSR': normal sinus rhythm.

'N': other arrhythmia, including supraventricular tachycardia, sinus bradycardia, LBBB, RBBB, APC and PVC beats.

'Asyst': asystole; ECG signal with a peaktopeak amplitude of < 100 μV, lasting more than 4 s.
 3.
Intermediate rhythms

'VTlo': slow ventricular tachycardia with a rate of < 180 bpm.

'fine VF': any VF signal with an amplitude in the range 100  200 μV.
It is clear from this classification that VT is divided into two categories according to heart rate; 'VThi' and 'VTlo'. This VT classification considers border heart rate as 180 bpm. It is, however, not strict. It may be in the range 150  180 bpm. AEDs only advise/deliver shock to shockable rhythms, and intermediate rhythms are treated in a different way called antitachycardia pacing.
Detection of VTVF from other arrhythmias
Here, n stands for the number of samples within the chosen length. In case of NSR, the main representative of the nonVTVF group, the duration of the QRS complex is small as compared to one ECG period as illustrated in Figure 1(a). It is also observed from this figure that the NSR signal level is low for most of the time in an ECG cycle. Therefore, the absolute signal level of the QRS complexes dominates in the summation of MAV calculation (eqn. (1)). A low MAV is thus obtained for such episodes. In case of VT, we see that the QRS complex is much wider than that of NSR, and the ECG signal hardly goes through the baseline as is the case for VF. Therefore, the MAV of VT and VF for a fixed duration window is comparatively larger than that for the NSR.
Observation of other nonVTVF ECG waveforms such as Premature Ventricular Contraction (PVC), Premature Atrial Contraction (PAC), Supraventricular Tachycardia (SVT) etc. reveals that these abnormalities also have low MAV compared to VT and VF. For example, PVC arrhythmia has small MAV because a PVC beat contains only wide QRS complex and no P waves or T waves are associated with this abnormal beat [31]. Thus, we can use MAV as the performance index to discriminate the VTVF from other arrhythmias.
In ECG analysis, it is important that we choose the episode length or decision frame appropriately. Decision frame should be taken in such a way that is neither too short to make a false alarm nor too long to cause severe cardiac arrest. Decreasing the episode length from its optimum value results in a low accuracy but quick detection. On the contrary, increasing the episode length improves the accuracy up to a certain level but requires longer detection time.
 1.
Choose a segment of ECG signal of L _{ e } second duration. This segmented ECG signal of L _{ e } second duration should be stored for the second stage.
 2.
The segment of the ECG signal is preprocessed using the wellknown filtering process as used in [32], which is carried out in a MATLAB routine, called filtering.m [33]. The filtering algorithm works in four successive steps.

First, the mean value is subtracted from the signal.

Second, a moving average filter is applied in order to remove the power line noise.

Third, a drift suppression is carried out by a high pass filter with a cutoff frequency of 1 Hz.

In the last step, a low pass Butterworth filter with a cutoff frequency of 30 Hz is applied in order to suppress the high frequency noise like interspersions and muscle noise.
 3.
Then, choose a smaller segment x(n) from the ECG signal of L _{ e } second duration in such a way that the length of the segment is 2s. If the sampling frequency of the ECG signal is F _{ s } samples/s, then the total sample within this segment (N) is 2F _{ s } . For example, the sampling frequency of the ECG signal of the MITDB is 360 smaples/sec. Thus the length of the smaller segment N is 2 × 360 = 720 samples.
 4.
Next, divide the smaller segment x(n) by the maximum absolute value found in that segment.
 5.
Calculate the MAV using (1).
 6.
Shift the window by 1s successively for other segments of 2s within the L _{ e } second ECG episode and go through step (4) to (5).
 7.Make decision on every L _{ e } second ECG episode (L _{ e } ≥ 2) by averaging the L _{ e }  1 consecutive values of MAV obtained from the L _{ e }  1 consecutive 2s segments with 1s step. The average value, MAV _{ a } for an L _{ e } second episode is calculated as$MA{V}_{a}=\frac{1}{{L}_{e}1}{\displaystyle \sum _{i=1}^{{L}_{e}1}M}A{V}_{i}$(2)
where MAV _{ i } is the value of MAV in the ith 2s stage.
Separation of VF from VTVF
Now that we have separated VTVF from other arrhythmias. In this stage, we separate VF from VT. Before we explain our motivation for using the EMD technique, we briefly describe what EMD is.
EMD Preliminaries
EMD is a signal decomposing method which is fully datadriven and does not require any a priori basis function [27, 34]. The aim of the EMD is to decompose the signal into a sum of intrinsic mode functions (IMFs). An IMF is a function that satisfies two conditions: (1) in the whole data set, the number of extrema and the number of zero crossings must either be equal or differ at most by one; and (2) at any point, the mean value of the envelop defined by the local maxima and the envelop defined by the local minima is zero. An IMF represents the oscillatory mode embedded in the data as a counterpart to the simple harmonic function used in Fourier analysis [35].
The results of the decomposition are q  intrinsic modes and a residue. The lower order IMFs capture the fast oscillation modes while the higher order IMFs typically represent the slow oscillation modes present in the underlying signal [27, 37]. An example illustrating the Empirical Mode Decomposition is given in the 'Appendix' section.
To exploit the property of unique relationship between the ECG signal and the sum of its first two IMFs that exists in case of the VF only, sum of the first two IMFs from the ECG signal is subtracted and the MAV of the difference signal is calculated. Since, the dynamic range of the ECG signal varies from database to database, we normalize this MAV with respect to the original ECG signal. In case of a VF episode, the normalized MAV or NMAV of the difference signal is very small than that of a VT episode. Here, we choose a 2s analysis window as in the previous case. But in this case, the performance index (NMAV ) is less sensitive to the analysis window length.
 1.
First, choose a segment x(n) of duration 2s and N samples from the previously saved ECG signal of L _{ e } second duration.
 2.
At this stage, the ECG signal is preprocessed in three successive steps.

First, the mean value is subtracted from the signal.

Second, a drift suppression is carried out by a highpass filter with a cutoff frequency of 1 Hz.

In the last step, a lowpass Butterworth filter with a cutoff frequency of 20 Hz and order 12 is applied to suppress the high frequency information.
 3.Apply EMD on x(n) and determine$im{f}_{12}(n)=im{f}_{1}(n)+im{f}_{2}(n)$
 4.Then, calculate the difference between the original signal and sum of its first two IMFs,$e(n)=x(n)im{f}_{12}(n)$
 5.The normalized MAV of e(n) used as the index for discriminating VF from VT is calculated as$NMAV=\frac{{\scriptscriptstyle \frac{1}{N}}{\displaystyle \sum _{n=0}^{N1}\lefte\left(n\right)\right}}{{\scriptscriptstyle \frac{1}{N}}{\displaystyle \sum _{n=0}^{N=1}\leftx\left(n\right)\right}}$
 6.
Shift the window by 1s successively for other segments of 2s within the L _{ e } second ECG episode and go through step (ii) to (iv).
 7.Make decision on every L _{ e } second ECG episode (L _{ e } ≥ 2) by averaging L _{ e }  1 consecutive values of NMAV obtained from L _{ e }  1 consecutive 2s data segments with 1s step. The average value NMAV _{ a } for an L _{ e } second episode is calculated as$NMA{V}_{a}=\frac{1}{{L}_{e}1}{\displaystyle \sum _{i=1}^{{L}_{e}1}N}MA{V}_{i}$(8)
where NMAV _{ i } is the value of NMAV in the ith 2s stage.
Classification of VT and VF according to the AHA recommendations
 1.
First, choose a segment x(n) of duration L _{ e } second and N samples from the previously saved ECG signal and then perform preprocessing as stated in Section.
 2.Calculate the first derivative (x _{ d } (n)) of x(n).${x}_{d}(n)=x(n)x(n1)$
 3.Keep only the positive part of x _{ d } (n).${x}_{dp}(n)=\{\begin{array}{cc}\begin{array}{r}\hfill {x}_{d}(n)\\ \hfill 0\end{array}& \begin{array}{l}if{x}_{d}(n)\ge 0\hfill \\ ;otherwise\hfill \end{array}\end{array}$
 4.Apply the moving average filter on x _{ dp } (n) and find x _{ dpf } (n).${x}_{dpf}(n)={\displaystyle \sum _{k=0}^{k=\alpha}x}(nk)$
 5.Determine the maximum value (C) and the corresponding peak index (I) of x _{ dpf } (n) and calculate the threshold value (T _{ h } ) from C.$\begin{array}{lll}C\hfill & =\hfill & \mathrm{max}\{{x}_{dpf}(n)\}\hfill \\ {T}_{h}\hfill & =\hfill & C\times \beta \hfill \end{array}$
 6.Store the peak index (I) and mask x _{ dpf } (n) around this position.${x}_{dpf}(I\gamma :I+\gamma )=0$
 7.
Now, calculate again the maximum value (C) of x _{ dpf } (n) and go through step (vi) until C goes below the T _{ h } .
 8.Determine the total number of peaks (N _{ p } ) those are above T _{ h } and calculate H _{ R } .${H}_{R}=\frac{{N}_{p}\times 60}{{L}_{e}}bpm$
If the heart rate of the VT signal is greater than 180 bpm, then this VT is called the shockable VT. As the decision of shockable or intermediate VT is dependent on the heart rate of the episode, hence, we calculate the total number of QRS beats in a episode. Now, to check the efficiency of the heart rate determination algorithm, two episodes selected are shown in Figs. 8(e)(f). At first, the total number of QRS beats in these episodes are determined from the annotation. Then, the proposed derivative based heart rate determination algorithm is used to calculate the total number of QRS beats and it is found to be 15 beats for Figure 8(e) and 17 beats for Figure 8(f). In both cases, the total number of QRS complexes obtained by using our algorithm are the same as determined from the annotation. Thus, this heart rate determination method, though simple, may be used to calculate the heart rate of an ECG episode. However, in more complicated cases any standard heart rate determination algorithm reported in the literature [38, 39] may be adopted to classify the VT. On the other hand, the amplitude of the VF signal is determined by taking the maximum value of the absolute VF signal within a episode. If the amplitude is greater than 200 μV, than this VF is called the coarse VF.
Quality Parameters
For 'VF' and 'shockable rhythm' detection, the definition of these four quality parameters contain 'VF' and 'shockable rhythm' in place of 'VTVF', respectively. While calculating these four quality parameters to judge the effectiveness of an algorithm, in case of any unsatisfactory results obtained, the values of the respective thresholds were adjusted in order to obtain the best possible results.
Results and Discussion
 1.
VTVF and nonVTVF
 2.
VF and nonVF (nonVTVF+VT)
 3.
shockable (VF+VT above 180 bpm) and nonshockable (nonVTVF+VT below 180 bpm)
Since the annotated files do not contain enough lowamplitude signals (fine VF), therefore, this type of signal is not addressed in this identification scheme and the VF signals in the shockable rhythms are actually coarse VF. Now, this section is divided into three subsections and each subsection presents the results of each identification scheme.
Detection of VTVF from other arrhythmias
Quality parameters of VTVF detection.
Algorithm  Quality Parameters for VTVF detection  

Sensitivity (%)  Specificity (%)  Pos. Pred. (%)  Accuracy (%)  
MAV  93.69  99.39  89.46  99.07 
CPLX [10]  48.95  79.48  11.82  77.86 
Detection of VF from other arrhythmias
Quality parameters of different VF detection algorithms for L _{ e }= 8s.
Algorithm  Quality Parameters for VF detection  

Sensitivity (%)  Specificity (%)  Pos. Pred. (%)  Accuracy (%)  
TCI  94.64  65.08  8.46  66.05 
SPEC  41.42  99.57  76.67  97.65 
HILB  71.76  98.87  68.41  97.98 
PSR  63.69  99.05  69.57  97.88 
TCSC  80.19  98.53  65.66  97.96 
MAV & EMD  86.49  99.32  81.27  98.90 
Performance comparison of different algorithms for a fixed specificity and for L _{ e }= 8s.
Algorithm  Sensitivity if Specificity =  

99%  98%  96%  
TCI  0.33  0.73  5.73 
SPEC  65.2  69.35  74.93 
HILB  65.32  84.79  91.58 
PSR  62.17  77.53  92.40 
TCSC  65.07  84.23  93.94 
MAV & EMD  89.32  94.76  95.61 
Detection of shockable rhythms from other arrhythmias
Modifications in the threshold values proposed in [5] (C 1 = Count 1, C 2 = Count 2, C 3 =Count 3).
Condition No.  for L _{ e }= 10s  for L _{ e }= 8s 

1  C 1 < 250, C 2 > 950 and C 1 × C 2/C 3 < 210  C 1 < 200, C 2 > 760 and C 1 × C 2/C 3 < 168 
2  250 ≤ C 1 < 400, C 2 < 600 and C 1 × C 2/C 3 < 210  200 ≤ C 1 < 320, C 2 < 480 and C 1 × C 2/C 3 < 168 
3  C 1 ≥ 250 &C 2 > 950  C 1 ≥ 200 &C 2 > 760 
4  C 2 ≥ 1100  C 2 ≥ 880 
Quality parameters for the detection of shockable rhythms using L _{ e }= 8s.
Algorithm  Quality parameters for the detection of shockable rhythms  

Sensitivity (%)  Specificity (%)  Pos. Pred. (%)  Accuracy (%)  
MAV & EMD  91.09  99.42  90.71  99.21 
Count [5]  88.90  99.29  85.99  98.93 
Conclusions
A novel method for the identification of life threatening cardiac abnormalities from other arrhythmias has been presented. Performing sequential signal processing, we have detected these cardiac abnormalities with good accuracy. It has been shown that the proposed algorithm based on the MAV parameter and EMD technique can detect the VT plus VF signals correctly from other arrhythmias, and the accuracy level remains higher than that of other reported techniques. The effectiveness of the proposed technique has been demonstrated using standard databases over a vast range of both normal and abnormal ECG records. The MAV index successfully separates the VTVF arrhythmias from different types of abnormalities. And the other parameter NMAV which is calculated using the IMFs of the EMD technique can successfully separate VF from VTVF. Finally, a fast and simple heart rate determination technique is used to separate the high rate VT. Consistent results have been obtained by applying our algorithm on different wellknown databases namely, MITBIH database, CU database and MITBIH Malignant Ventricular Arrhythmia database. Determination of the threshold parameters from the training dataset and then their successful application on the test dataset proves that the proposed parameters are universal. Some signal episodes were very difficult for classification even by expert cardiologists. Accuracy of our proposed technique slightly falls due to these confusing episodes. The algorithm presented here has strong potential to be applied in clinical applications for accurate detection of life threatening cardiac arrhythmias.
Appendix
 1.
Determine the upper envelop e _{ u } (n) and the lower envelop e _{ l } (n). These two envelopes are shown in Figure 11(a) along with the original signal x(n).
 2.
Determine the mean of the envelope, i.e., m _{1}(n) = [e _{ u } (n) + e _{ l } (n)]/2. The variation of m _{1}(n) is displayed in Figure 11(a).
 3.
Extract the first component h _{1}(n) using eqn. (3).
 4.
Ideally, h _{1}(n) should be the first IMF. But, it is observed from Figure 11(b) that the h _{1}(n) does not satisfy the conditions of an IMF.
 5.
Now, treat h _{1}(n) as x(n) in step (1). Determine the two envelopes from h _{1}(n) and the mean of these two envelopes (Figure 11(b)). After subtraction of the mean from the h _{1}(n) a new signal h _{1(2)}(n) is obtained. Now, check the conditions of an IMF and also calculate the value of SD from eqn. (4), where h _{1(1)}=h _{1}(n).
 6.
Continue the process until h _{1(k1)}satisfies the conditions of the IMFs. When the conditions are satisfied, the first IMF is found as shown in Figure 11(c). Now, the first IMF is subtracted from the initial signal x(n).
 7.
The second IMF (Figure 11(d)) is extracted following the steps (1) to (6) except that the subtracted signal is used instead of x(n). No further decomposition is performed here as we need two IMFs for our analysis. The residue of the EMD is shown in Figure 11(e).
Declarations
Acknowledgements
This work was supported in part by the National Research Foundation (NRF) of Korea funded by the Korean government (MEST) (No: 20090078310).
Authors’ Affiliations
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