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\title{Detection of QRS Complexes in ECG Signals Based on Empirical Mode Decomposition}
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             \author[1]{Dr.  S.A.Taouli}

             \author[2]{  F.Bereksi-Reguig}

             \author[3]{Dr.  S.A.Taouli}

             \affil[1]{  Faculty of technology,University Aboubekr Belkaid telmcen}

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\date{\small \em Received: 19 October 2011 Accepted: 10 November 2011 Published: 21 November 2011}

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\begin{abstract}
        


Arrhythmia is one kind of diseases that gives rise to the death and possibly forms the immedicable danger. The most common cardiac arrhythmia is the ventricular premature beat. The main purpose of this study is to develop an efficient arrhythmia detection algorithm based on Empirical Mode Decomposition (EMD). This algorithm requires the following stages: band-pass Butterworth filters, Empirical Mode Decomposition, sum the first three Intrinsic Functions Mode (IMFs), and take its absolute value, retain the amplitudes, find the position of the maximum. The excellent performance of the algorithm is confirmed by a sensitivity of 99.82 % (204 false negatives) and a positive predictivity of 99.89% (114 false positives) against the MIT-BIH arrhythmia database.

\end{abstract}


\keywords{ECG signal, Empirical Mode Decomposition, QRS detection.}

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\let\tabcellsep& 	 	 		 
\section[{INTRODUCTION}]{INTRODUCTION}\par
he Electrocardiogram signal which represents the electric activity of the heart is characterized by a periodic behaviour or quasi periodical. It is typically composed of three called significant waves; P wave, QRS complex and T wave (see fig. \hyperref[fig_0]{1}). The detection of the R-peaks and consequently of the QRS complexes in an ECG signal provides information on the heart rate, the conduction velocity, the condition of tissues within the heart as well as various other abnormalities and, thus, it supplies evidence to support the diagnoses of cardiac diseases. For this reason, it has attracted considerable attention over the last three decades.\par
The algorithms in the relevant bibliography adapt a range of different approaches to yield a procedure leading to the identification of the waves under consideration. These approaches are mainly based on derivative-based techniques \hyperref[b0]{[1]}, \hyperref[b1]{[2]}, classical digital filtering \hyperref[b2]{[3]}- \hyperref[b4]{[5]}, adaptive filtering \hyperref[b16]{[6]}, \hyperref[b5]{[7]}, Tompkins method \hyperref[b6]{[8]},wavelets \hyperref[b7]{[9]}, Christov's algorithm \hyperref[b8]{[10]}, genetic algorithms \hyperref[b9]{[11]}, Hilbert Transform \hyperref[b10]{[12]} and zero-crossing-based identification techniques \hyperref[b11]{[13]}. The Empirical Mode Decomposition (EMD) is a new method designed by N. E. Huang for nonlinear and non-stationary signal analysis \hyperref[b12]{[14]}. The key part of this method is that any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMFs) that admits well behaved Hilbert transforms. This decomposition method is adaptive, and, therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to nonlinear and nonstationary processes.\par
The major advantage of the EMD is that the basis functions are derived from the signal itself. Hence, the analysis is adaptive, in contrast to the wavelet method where the basis functions are fixed. In this paper, a detection method based on the EMD approach is proposed. The EMD is based on the sequential extraction of energy associated with various intrinsic time scales of the signal starting from finer temporal scales (high frequency modes) to coarser ones (low frequency modes). The total sum of the IMFs matches the signal very well and therefore ensures completeness.\par
In this paper, the EMD is used for ECG QRS complex detection. Therefore, the algorithm consists of several steps, namely, band-pass Butterworth filter, decomposition of the ECG signal into a collection of AM-FM components (called Intrinsic Mode Functions (IMF)), sum the first three Intrinsic Functions Mode (IMFs), and take its absolute value, retain the amplitudes, find the position of the maximum.\par
The proposed algorithm is evaluated by using the ECG MIT-BIH database  {\ref [15]} and is compared to other methods. As we will show later, very promising results are obtained. The number of extrema and the number of zero crossings must differ by at most 1. ii. 
\section[{II. EMPIRICAL MODE DECOMPOSITION}]{II. EMPIRICAL MODE DECOMPOSITION}\par
At any point the mean value of the envelope defined by maxima and the envelope defined by minima must be zero. 
\section[{a) Sifting Process}]{a) Sifting Process}\par
The basic principle of this method is to identify the intrinsic oscillatory modes by their characteristic time scales in the data empirically and then decompose the data.\par
A systematic way to extract the IMFS is called the Sifting Process and is described below:\par
1. Identify all the extrema (maxima and minima) of ( )   t x .( ) ( ) ( ) [ ] 2 max min t e t e t m + = . 4. Get an IMF candidate from ( ) ( ) ( ) t m t x t h ? = (extract the detail). 
\section[{Check the weather properties ( )}]{Check the weather properties ( )}t h i is an IMF. If ( ) t h i is not an IMF, repeat the procedure from step 1. If ( ) t h i is an IMF, then set ( ) ( ) t h t x r i ? = and then i i c t h = ) () ( ) ( ) ? = + = n i n i t r t c t x 1 (1)\par
In practice, after a certain number of iterations, the resulting signals do not carry significant physical information. To prevent this, we go for some boundary conditions. We can stop the sifting process by limiting the normalized standard deviation (SD).\par
The SD is defined as:( ) ( ) ( ) ( ) ( ) ? = ? ? ? = T t k k k t h t h t h SD 0 2 1 1 2 1 1 1 (2)\par
The SD is set between 0.2 and 0.3 for proper results \hyperref[b12]{[14]}. When the SD is smaller than a threshold, the first IMF component from the data, designated as ( ) ( )t h t c k 1 1 = (3) is obtained. Then ( ) t c 1 is separated from ( ) t x to obtain ( ) ( ) ( ) t r t c t x 1 1 = ? (4)\par
Since the residue, ( ) t r 1 still contains information of longer period components, it is treated as the new data and subjected to the same sifting process as described above. This procedure can be repeated on all the subsequent ( ) t r i , and the result is( ) ( ) ( ) N i t r t c t r i i i ,........, 1 , 1 = = ? ? (5)\par
where ( ) ( ) The sifting process was applied on an ECG signal to obtain the various IMFs. This has been represented in Fig. \hyperref[fig_5]{2} and Fig. \hyperref[fig_1]{3}. The EMD method is a powerful tool for analyzing ECG signal. It is very reliable as the base functions depend on the signal itself. EMD is very adaptive and avoids diffusion and leakage of signal.   We first apply a moving average filter of order 5 to the signal. This filter removes high frequency noise like interspersions and muscle noise. Then, drift suppression is applied to the resulting signal. This is done by a high pass filter with a cut off frequency of 1Hz. Finally, a low pass Butterworth filter with a limiting frequency of 30 Hz is applied to the signal in order to suppress needless high frequency information even more. Fig. \hyperref[fig_11]{5} illustrates respectively; noisy ECG signal (record 101) ( ) n s , and the resulting filtered ECG signal ( )t x t r = 0 and ( ) t c i is the ith IMF ofn s r . b) Decomposing ECG into IMFs\par
The primary EMD is applied on ( ) t x and the IMFs are obtained to locate the fiducial points in the ECG signal. The EMD of ( ) t x (equation 1) is given by \hyperref[b12]{[14]}, where ( ) t c i is the ith IMF and ( ) t r n is the residue.\par
The IMFs are obtained by applying EMD on the filtered ECG signal ( ) t x . These IMFs and the ECG signal are then used to determine the fiducial points of the ECG signal. 
\section[{c) R Peak Detection}]{c) R Peak Detection}\par
Since the R wave is the sharpest component in the ECG signal, it is captured by the lower order IMFs which also contain high frequency noise. Past analysis using the EMD of clean and noisy ECG indicates that the QRS complex is associated with oscillatory patterns typically presented in the first three IMFs \hyperref[b13]{[16]}.\par
In our analysis, we have also found similar results. We denote the sum of first three IMFs as fine to coarse three, ( )t c f 3 2 given by ( ) ( ) ? = = 3 1 3 2 i i t c t c f (6)\par
The oscillations associated with QRS complex in  (ii) Retain the amplitudes of ( ) t a larger than a threshold, T, where T is statistically selected to be half of the maximum value of ( ) t a and make others zero. This eliminates the noise. Find the position of the maximum of a segment of time duration R t starting from the first non zero value of ( ) t a (Fig. \hyperref[fig_13]{7}). This is the first R-peak position. Similarly, find all other R-peak positions until the end of ( )n c f 3 2 RR Peak detection ( ) t imf 2 ( ) t imf 3 ( ) t imf 1 ( ) t xt a is reached.\par
According to the width of QRS complex which is normally 100 ms with variation of ± 20 ms [6], we select R t to be about 200 ms. We have considered the absolute value of ( )t c f 3 2\par
since R-wave, and thus ( )t c f 3 2\par
, give a negative peak in some ECG leads.\par
After finding the R-peak position, 0 t , we can find whether the peak is positive or negative from the value of ( )    IV.0 3 2 t c f . If 
\section[{RESULTS AND DISCUSSION}]{RESULTS AND DISCUSSION}\par
The algorithm was tested against a standard ECG database, i.e. the MIT-BIH Arrhythmia Database. The database consists of 48 half-hour ECG recordings and contains approximately 109,000 manually annotated signal labels. ECG recordings are two channel, however for the purpose of QRS complex detection only the first channel was used (usually the MLII lead). Database signals are sampled at the frequency of 360 Hz with 11-bit resolution spanning signal voltages within ±5 mV range.\par
QRS complex detection statistic measures were computed by the use of the software from the Physionet Toolkit provided with the database. The two most essential parameters we used for describing the overall performance of the QRS complex detector are: sensitivity Se and positive predictivity +P.\par
The sensitivity and positive predictivity of the detection algorithms are computed by Detection of QRS Complexes in ECG Signals Based on Empirical Mode Decomposition Therefore, the R-peak detection comprises the following steps which are also illustrated in Fig. \hyperref[fig_13]{7} for a series of ECG beats.   where TP is the number of true positives, FN the number of false negatives, and FP the number of false positives \hyperref[b14]{[17]}. The sensitivity reports the percentage of true QRS complexes that were correctly detected. The positive predictivity reports the percentage of detected QRS complexes which were in reality true QRS complexes.\par
Table     The average sensitivity of the algorithm is 99.82\% and its positive predictivity is 99.89 \%. The EMD method is found to have a good sensitivity and predictivity. Moreover this method is much more evolved than others. It is because the fast oscillatory QRS complex is highly detectable in the lower order IMFs irrespective of other characteristic wave amplitude. 
\section[{Algritms}]{Algritms}\par
P (\%) Se (\%)\par
Proposed Algorithm 99.89 99.82 Kohler \hyperref[b11]{[13]} 88.70 99.57 Pan \hyperref[b6]{[8]} 99.07 98.55 Zheng \hyperref[b7]{[9]} 98.07 94.18 Christov's \hyperref[b8]{[10]} 99.65 99.74 Martineze \hyperref[b15]{[18]} 99.86 99.80 Madeiro  {\ref [19]} 98.96 98.47\par
Table \hyperref[tab_1]{.}2 : Comparison of the performance.\par
Comparing the sensitivity and predictivity of the different methods in Table \hyperref[tab_1]{.} 2 we find that EMD is a better choice for R peak detection.\par
V. 
\section[{CONCLUSION}]{CONCLUSION}\par
We have developed a new algorithm based on the EMD for the automatic detection of QRS complex. The algorithm is evaluated for all of records obtained from the MIT-BIH. The proposed algorithm exhibits better performance than the threshold based technique and achieves high sensitivity Se=99.82 \% and predictivity P=99.89 \% for the QRS complex detection. The EMD method works not only for lead II but also for other leads. Only three lower order IMFs are needed to completely identify the QRS complex in the ECG signal.\begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-2.png}
\caption{\label{fig_0}Fig. 1 :}\end{figure}
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\noindent\textbf{3}\includegraphics[]{image-3.png}
\caption{\label{fig_1}3 .}\end{figure}
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\noindent\textbf{}\includegraphics[]{image-4.png}
\caption{\label{fig_2}.}\end{figure}
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\noindent\textbf{}\includegraphics[]{image-5.png}
\caption{\label{fig_3}(}\end{figure}
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\noindent\textbf{}\includegraphics[]{image-6.png}
\caption{\label{fig_4}}\end{figure}
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\noindent\textbf{2}\includegraphics[]{image-7.png}
\caption{\label{fig_5}Fig. 2 :}\end{figure}
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\noindent\textbf{3}\includegraphics[]{image-8.png}
\caption{\label{fig_6}Fig. 3 :}\end{figure}
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\noindent\textbf{4}\includegraphics[]{image-9.png}
\caption{\label{fig_7}Fig. 4 :}\end{figure}
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\noindent\textbf{3}\includegraphics[]{image-10.png}
\caption{\label{fig_8}3 2.}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2011}\includegraphics[]{image-11.png}
\caption{\label{fig_9}Wander © 2011}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{5}\includegraphics[]{image-12.png}
\caption{\label{fig_11}Fig. 5 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{6}\includegraphics[]{image-13.png}
\caption{\label{fig_12}Fig. 6 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{7}\includegraphics[]{image-14.png}
\caption{\label{fig_13}Fig. 7 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-15.png}
\caption{\label{fig_14}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{8}\includegraphics[]{image-16.png}
\caption{\label{fig_15}Fig. 8 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{9}\includegraphics[]{image-17.png}
\caption{\label{fig_16}Fig. 9 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{10}\includegraphics[]{image-18.png}
\caption{\label{fig_17}Fig. 10 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{11}\includegraphics[]{image-19.png}
\caption{\label{fig_18}Fig. 11 :}\end{figure}
  \begin{figure}[htbp]
\noindent\textbf{.} \par 
\begin{longtable}{P{0.85\textwidth}}
(a)\\
(b)\end{longtable} \par
 
\caption{\label{tab_1}Table . 1}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{P{0.0026153846153846153\textwidth}P{0.0008717948717948718\textwidth}P{0.0008717948717948718\textwidth}P{0.0008717948717948718\textwidth}P{0.0017435897435897436\textwidth}P{0.008717948717948718\textwidth}P{0.006102564102564103\textwidth}P{0.005230769230769231\textwidth}P{0.15866666666666668\textwidth}P{0.17435897435897435\textwidth}P{0.011333333333333334\textwidth}P{0.03835897435897436\textwidth}P{0.02441025641025641\textwidth}P{0.1421025641025641\textwidth}P{0.18569230769230768\textwidth}P{0.08805128205128204\textwidth}}
\multicolumn{2}{l}{Se}\tabcellsep \multicolumn{2}{l}{=}\tabcellsep \multicolumn{2}{l}{TP}\tabcellsep FN TP +\tabcellsep (7)\tabcellsep \multicolumn{2}{l}{Record Total No. (No. of beats)}\tabcellsep FP\tabcellsep \tabcellsep FN\tabcellsep Se\tabcellsep P\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 100\tabcellsep 2273\tabcellsep \tabcellsep 0\tabcellsep \tabcellsep 0\tabcellsep 100\tabcellsep 100\\
+\tabcellsep \multicolumn{2}{l}{P}\tabcellsep \multicolumn{2}{l}{=}\tabcellsep \multicolumn{2}{l}{FP TP TP +}\tabcellsep (8)\tabcellsep 101 102 103\tabcellsep 1865 2187 2084\tabcellsep 0 0\tabcellsep 0\tabcellsep 0 1\tabcellsep 0\tabcellsep 100 99.95 100\tabcellsep 100 100 100\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 104\tabcellsep 2230\tabcellsep \tabcellsep 2\tabcellsep \tabcellsep 1\tabcellsep 99.96\tabcellsep 99.91\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 105\tabcellsep 2572\tabcellsep \tabcellsep 0\tabcellsep \tabcellsep 3\tabcellsep 99.88\tabcellsep 99.61\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 106\tabcellsep 2027\tabcellsep \tabcellsep 5\tabcellsep \tabcellsep 2\tabcellsep 99.90 99.75\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 107\tabcellsep 2137\tabcellsep \tabcellsep 0\tabcellsep \tabcellsep 0\tabcellsep 100\tabcellsep 100\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 108\tabcellsep 1763\tabcellsep 7\tabcellsep \tabcellsep \multicolumn{2}{l}{14 99.21 99.60}\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 109\tabcellsep 2532\tabcellsep \tabcellsep 0\tabcellsep \tabcellsep 2\tabcellsep 99.92\tabcellsep 100\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 111\tabcellsep 2124\tabcellsep \tabcellsep 0\tabcellsep \tabcellsep 1\tabcellsep 99.95\tabcellsep 100\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 112\tabcellsep 2539\tabcellsep \tabcellsep 0\tabcellsep \tabcellsep 0\tabcellsep 100\tabcellsep 100\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 113\tabcellsep 1795\tabcellsep \tabcellsep 0\tabcellsep \tabcellsep 0\tabcellsep 100\tabcellsep 100\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 114\tabcellsep 1879\tabcellsep \tabcellsep 0\tabcellsep \tabcellsep 0\tabcellsep 100\tabcellsep 100\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 115\tabcellsep 1953\tabcellsep \tabcellsep 0\tabcellsep \tabcellsep 0\tabcellsep 100\tabcellsep 100\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 116\tabcellsep 2412\tabcellsep \tabcellsep 0\tabcellsep \tabcellsep 14 99.42\tabcellsep 100\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 117\tabcellsep 1535\tabcellsep \tabcellsep 1\tabcellsep \tabcellsep 0\tabcellsep 100\tabcellsep 99.93\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 118\tabcellsep 2275\tabcellsep \tabcellsep 0\tabcellsep \tabcellsep 0\tabcellsep 100\tabcellsep 100\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 119\tabcellsep 1987\tabcellsep \tabcellsep 0\tabcellsep \tabcellsep 0\tabcellsep 100\tabcellsep 100\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 121\tabcellsep 1863\tabcellsep \tabcellsep 0\tabcellsep \tabcellsep 1\tabcellsep 99.95\tabcellsep 100\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 122\tabcellsep 2476\tabcellsep \tabcellsep 2\tabcellsep \tabcellsep 0\tabcellsep 100\tabcellsep 99.92\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 123\tabcellsep 1518\tabcellsep \tabcellsep 0\tabcellsep \tabcellsep 0\tabcellsep 100\tabcellsep 100\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 124\tabcellsep 1619\tabcellsep \tabcellsep 0\tabcellsep \tabcellsep 1\tabcellsep 99.94\tabcellsep 100\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 200\tabcellsep 2601\tabcellsep \tabcellsep 2\tabcellsep \tabcellsep 10 99.62 99.92\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 201\tabcellsep 1963\tabcellsep \tabcellsep 0\tabcellsep \tabcellsep 15 99.24\tabcellsep 100\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 202\tabcellsep 2136\tabcellsep \tabcellsep 1\tabcellsep \tabcellsep 2\tabcellsep 99.91 99.95\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 203\tabcellsep 2982\tabcellsep \tabcellsep 2\tabcellsep \tabcellsep 29 99.03 99.93\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 205\tabcellsep 2656\tabcellsep \tabcellsep 0\tabcellsep \tabcellsep 7\tabcellsep 99.74\tabcellsep 100\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 207\tabcellsep 1862\tabcellsep \tabcellsep 14\tabcellsep \tabcellsep 26 98.60 99.24\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 208\tabcellsep 2956\tabcellsep 0\tabcellsep \tabcellsep \tabcellsep 10 99.66\tabcellsep 100\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 209\tabcellsep 3004\tabcellsep \tabcellsep 8\tabcellsep \tabcellsep 1\tabcellsep 99.97 99.73\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 210\tabcellsep 2647\tabcellsep \tabcellsep 4\tabcellsep \tabcellsep 15 99.4\tabcellsep 99.85\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 212\tabcellsep 2748\tabcellsep \tabcellsep 1\tabcellsep \tabcellsep 0\tabcellsep 100\tabcellsep 99.96\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 213\tabcellsep 3251\tabcellsep 2\tabcellsep \tabcellsep \tabcellsep 3\tabcellsep 99.91 99.94\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 214\tabcellsep 2262\tabcellsep \tabcellsep 4\tabcellsep \tabcellsep 3\tabcellsep 99.87 99.82\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 215\tabcellsep 3363\tabcellsep \tabcellsep 6\tabcellsep \tabcellsep 1\tabcellsep 99.9\tabcellsep 99.82\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 217\tabcellsep 2208\tabcellsep \tabcellsep 1\tabcellsep \tabcellsep 1\tabcellsep 99.95\tabcellsep 99.95\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 219\tabcellsep 2154\tabcellsep \tabcellsep 3\tabcellsep \tabcellsep 10 99.54\tabcellsep 99.86\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 220\tabcellsep 2048\tabcellsep \tabcellsep 2\tabcellsep \tabcellsep 0\tabcellsep 100\tabcellsep 99.90\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 221\tabcellsep 2427\tabcellsep \tabcellsep 15\tabcellsep \tabcellsep 1\tabcellsep 99.96\tabcellsep 99.39\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 222\tabcellsep 2484\tabcellsep \tabcellsep 0\tabcellsep \tabcellsep 5 99.80\tabcellsep 100\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 223\tabcellsep 2605\tabcellsep \tabcellsep 1\tabcellsep \tabcellsep 11 99.58\tabcellsep 99.96\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 228\tabcellsep 2053\tabcellsep \multicolumn{2}{l}{14}\tabcellsep \tabcellsep 2 99.90\tabcellsep 99.32\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 230\tabcellsep 2256\tabcellsep \tabcellsep 2\tabcellsep \tabcellsep 5 99.78\tabcellsep 99.91\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 231\tabcellsep 1886\tabcellsep \tabcellsep 0\tabcellsep \tabcellsep 0\tabcellsep 100\tabcellsep 100\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 232\tabcellsep 1780\tabcellsep \tabcellsep 5\tabcellsep \tabcellsep 1 99.94\tabcellsep 99.72\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 233\tabcellsep 3079\tabcellsep \tabcellsep 0\tabcellsep \tabcellsep 1 99.97\tabcellsep 100\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 234\tabcellsep 2753\tabcellsep \tabcellsep 0\tabcellsep \tabcellsep 5 99.82\tabcellsep 100\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep Total\tabcellsep 109809\tabcellsep 114\tabcellsep \tabcellsep \multicolumn{2}{l}{204 99.82}\tabcellsep 99.89\end{longtable} \par
 
\caption{\label{tab_2}}\end{figure}
 			\footnote{© 2011 Global Journals Inc. (US) Global Journal of Computer Science and Technology Volume XI Issue XX Version I 11} 			\footnote{December} 			\footnote{© 2011 Global Journals Inc. (US) Global Journal of Computer Science and Technology Volume XI Issue XX Version I 12} 			\footnote{© 2011 Global Journals Inc. (US) Global Journal of Computer Science and Technology Volume XI Issue XX Version I 15} 			\footnote{© 2011 Global Journals Inc. (US)} 			\footnote{December} 			\footnote{© 2011 Global Journals Inc. (US) Global Journal of Computer Science and Technology Volume XI Issue XX Version I} 			\footnote{DecemberEngineering \& Physics 29, pp.26-37, 2007.   } 		 		\backmatter  			  				\begin{bibitemlist}{1}
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