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\title{Removal of Power Line Interference from Electrocardiograph (ECG) Using Proposed Adaptive Filter Algorithm}
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\begin{document}

             \author[1]{Duong Trong  Luong}

             \author[2]{Nguyen Duc  Thuan}

             \author[3]{Dang Huy  Hoang}

             \affil[1]{  Hanoi University of science and Technology}

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\date{\small \em Received: 14 December 2014 Accepted: 1 January 2015 Published: 15 January 2015}

\maketitle


\begin{abstract}
        


ECG signals in measurements are contaminated by noises including power line interference. In recent years, adaptive filters with different approaches have been investigated to remove power line interference in ECG.In this paper, an adaptive filter is proposed to cancel power line interference in ECG signals. The proposed algorithm is experimented with MIT-BIH ECG signals data base. The algorithm?s results are compared with the results of other adaptive filter algorithms using Least Mean Square (LMS), Normalized Least Mean Square (NLMS) by Signal to Noise (SNR). Theses works are performed by LabVIEW software.

\end{abstract}


\keywords{ECG signal processing; adaptive filters, power line interference, least mean square.}

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\let\tabcellsep& 	 	 		 \par
Introduction lectrocardiography (ECG) plays an important role in monitoring and diagnosing cardiovascular diseases. The frequency bandwidth for therapy of the ECG signal is from 0.05Hz to 100Hz, and the highest peak is about 1mV \hyperref[b0]{[1]}.During recording of ECG signals, the ECG signals get contaminated such as power supply harmonic 50Hzor power line interference (Most country including Viet Nam use 50Hz electric system)with the amplitude approaches 50\% the highest peak of the ECG signal, artifacts caused by losing the direct contact between electrodes and the skin, or by EMG-this artifact's amplitude is 10\% of the highest peak's amplitude of the ECG signal, or by respiratory with noise's amplitude is 15\% of the highest peak of the ECG signal at 0.3 Hz frequency \hyperref[b1]{[2]}.In the listed noises, the power line noise affects P wave and Q wave of the ECG signal. That causes errors in arrhythmia and myocardial infarctiondiagnosis \hyperref[b3]{[3]}.In recent years, a few adaptive filters with different approaches are investigated to remove the power line noise 50 Hz in the ECG signal such asdesign of an adaptive filter with a dynamic structure for ECG signal processing \hyperref[b3]{[3]}, adaptive filtering in ECG denoising: a comparative study \hyperref[b4]{[4]}, denoising ECG signals using adaptive filter algorithm \hyperref[b5]{[5]}, denoising ECG signals with adaptive filtering algorithm \& patch based method \hyperref[b6]{[6]}, investigation of adaptive filtering for noise cancellation in ECG signals \hyperref[b7]{[7]}, designing and implementation of algorithms on Matlab for Adaptive noise cancellation from ECG signal \hyperref[b8]{[8]}, performance comparison of adaptive filter algorithms for ECG signal Enhancement \hyperref[b9]{[9]}, performance evaluation of different adaptive filters for ECG signal processing \hyperref[b10]{[10]}.Most of the researches use Least Mean Square (LMS) and Normalize Least Mean Square algorithm (NLMS). These algorithms enable to change filter coefficients with given order; the algorithms are quite reliable and effective with small convergent time. However, in case of the power line noise's amplitude equals to 40-50\% amplitude of the highest (QRS peak) of the ECG signal, these algorithms give not effective results, and the filtered signal still contains noise. To overcome this problem, the authors propose an adaptive filter algorithm based on Fast Fourier Transform (FFT). This algorithm is experimented with ECG database such as number of record 117 and aVL lead of patient279/s0532 from ECG database MIT-BIH  {\ref [11]}. The results of this algorithm are compared with that of LMS, NLMS by SNR criterion. The process and experiments are performed by LabVIEW software. 
\section[{II.}]{II.} 
\section[{Methodology}]{Methodology}\par
The aim of adaptive filter based on Fast Fourier Transform (FFT) is detecting the power line noise frequency, and determining threshold of this noise's magnitude. Fourier transform:If x(n) is a discrete signal satisfying the condition (1), ? |??(??)| < ? +? ??=?? (1) So Fourier transform equation for x(n) is given formula (2) (\textbf{2})\par
where i is the imaging part, i 2 = -1 According to the material \hyperref[b11]{[12]}, B.Widrow has shown that the adaptive filter transfer function is descripted as (3)(3)\par
where ? is the step size of the adaptive filter; K is the magnitude of power line noise; ? 0 is the angular frequency. In this study, ifS(n) is ECG signal contaminated power supply harmonic 50 Hz, soS(n) is expressed in the equation (  {\ref 4}).\par
Year 2015 
\section[{Global Journal of C omp uter S cience and T echnology}]{Global Journal of C omp uter S cience and T echnology}\par
Volume XV Issue II Version I ( )C S(n) = X(n) + N(n) (4)\par
Where X(n) is the clean ECG signal, N(n) is the power supply harmonic 50 Hz. Based on the equations (  {\ref 1}) and ( \hyperref[formula_0]{2}), (4) equation can be displayed in another form \hyperref[b5]{(5)}. 
\section[{S(?) = X(?) +N(?)}]{S(?) = X(?) +N(?)}\par
(5)\par
The magnitude-frequency spectrum of X(?),N(?) and S(?) is shown as figure \hyperref[fig_0]{1}, figure \hyperref[fig_1]{2},and figure \hyperref[fig_2]{3} corresponsive.   Step 1: Importing input signal S(n)\par
Step 2: Transforming FFT S(n) (for detecting the magnitude and frequency of the 50Hz power supply )\par
Step 3: Determining the frequency and magnitude of the power line interference: Choosing the frequency bandwidth is from 30Hz to 70Hz; setting the threshold of noise's FFT magnitude is 15(based on experiments with FFT of the contaminated ECG signal)\par
Step 4: Initializing for loop, starting from i: =0\par
Step 5: Checking condition: the magnitude of the power line noise in FFT is less than 15 or not? If true:\par
Step 6: Displaying the filtered signal and ending the processing. 
\section[{If false:}]{If false:}\par
Step 7: Realizing the transfer function (3)\par
Step 8: Calculating the output signal:y(n) = H(n). S(n)\par
Step 9: Transforming FFT y(n) (for checking whether or not existing noise in the frequency bandwidth from 30Hz to 70 Hz?)\par
Step 10: Increasing the iteration: i: = i++and returning to the step 5.\par
To experiment and test these above steps and LMS, NLMS adaptive filter algorithms, the authors used adaptive filter toolkit available in Lab VIEW. The results of the proposed algorithm are compared with that of LMS and NLMS algorithms by Signal to Noise (SNR). This criterion is followed by equation \hyperref[b6]{(6)}.SNR = 20log 10 ? RMS (y (n ) ) RMS (X (n ) ? y (n ) ) ? (\textbf{6})\par
where RMS(y (n) ) is the Root Mean Square of the filtered ECG signal; RMS(x (n) ) is the Root Mean Square of the original ECG signal.\par
III. 
\section[{Results and Discussion}]{Results and Discussion}\par
The authors have tested the proposed algorithm by using a few standard ECG database records such as record mitdb117 and a VL lead of record patient 279/s 0532 from ECG database MIT-BIH added with the power supply harmonic 50 Hz having variable magnitude is from 0.4mV to 0.5mV. This signal is generated by using LabVIEW. Figure \hyperref[fig_3]{4a} is the ECG signal of the record mitdb117, and this signal is added with the power line noise 50Hz (shown in Fig. \hyperref[fig_3]{4b}). Figure \hyperref[fig_3]{4c, 4d and 4e} display the results of filtering the power line interference with 0.4 mV magnitude using the proposed adaptive filter, LMS and NLMS corresponding adaptive filters. Intuitively, the filtered ECG signal using the proposed algorithm has nearly no appearance of noise and has the morphology similar to the original ECG signal. To prove the efficiency of the proposed algorithm in filtering the power line noise in ECG signal compared with LMS, and NLMS algorithms, the authors continue experimenting these algorithms with ECG data base of aVL lead of recordpatient279/s0532.The results are shown in figures 5c, 5d and 5e.These results indicate that the better efficiency of the proposed adaptive filter algorithm compared with the others. Figure \hyperref[fig_4]{5c} shows the effectiveness. To affirm the efficiency of the proposed algorithm with LMS, NLMS algorithms, the authors used SNR criterion SNR calculated by equation ( \hyperref[formula_5]{6}). Table \hyperref[tab_0]{1} show the comparison among three methods filtering the power line noise with 0.4 mV magnitude, and the noise is added directly to the ECG signal in the record mitdb117.The SNR value of the proposed algorithm is higher than that of LMS and NLMS algorithms when the step size?=0.02; ?= 0.03 and?=0.04. However, in case that ?=0.01 the SNR value of the proposed algorithm is just smaller 0.079 than that of NLMS.  
\section[{Conclusion}]{Conclusion}\par
The proposed adaptive filter algorithm for removing the power line interference in ECG signal based on Fast Fourier Transform (FFT) has been investigated with applications in the steps of the algorithm. That detects the power line frequency, and sets the threshold for the noise magnitude in FFT has high efficiency. In addition, that uses many for loops in the proposed algorithm support to filter the power line noise more carefully. The appearance of the noise is insignificant in the filtered ECG signal. Three algorithms are proceeded at the same time: adaptive filter LMS, NLMS (with different step sizes),and the proposed algorithm to remove the power supply harmonic 50 Hz (with 0.4 mV magnitude) added to the ECG signal of the record mitdb117,aVL lead of the record patient 279/s0532. The experimental results show that the proposed adaptive filter algorithm produces good ECG signal with little noise, similar to the original ECG signal displayed in figure \hyperref[fig_3]{4} and figure \hyperref[fig_4]{5}. Furthermore, to demonstrate the efficiency of the algorithm, the authors have compared the proposed algorithm with LMS and NLMS adaptive filter algorithms by SNR criterion. From the results in table 1 and table 2, the proposed adaptive filter algorithm for removing the power line noise 50 Hz with 0.4 mV magnitude has higher efficiency. That is asserted by SNR value in the table \hyperref[tab_1]{1 and table 2.} \begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-2.png}
\caption{\label{fig_0}Figure 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2}\includegraphics[]{image-3.png}
\caption{\label{fig_1}Figure 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3}\includegraphics[]{image-4.png}
\caption{\label{fig_2}Figure 3 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{4}\includegraphics[]{image-5.png}
\caption{\label{fig_3}RemovalCFigure 4 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{5}\includegraphics[]{image-6.png}
\caption{\label{fig_4}Figure 5 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1} \par 
\begin{longtable}{P{0.85\textwidth}}
Year 2015\end{longtable} \par
 
\caption{\label{tab_0}Table 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2} \par 
\begin{longtable}{P{0.5911764705882353\textwidth}P{0.07352941176470587\textwidth}P{0.18529411764705883\textwidth}}
Algorithm\tabcellsep Step size\tabcellsep SNR\\
LMS\tabcellsep \tabcellsep 2.709\\
NLMS\tabcellsep 0.01\tabcellsep 2.744\\
Proposed\tabcellsep \tabcellsep 2.877\\
LMS\tabcellsep \tabcellsep 2.697\\
NLMS\tabcellsep 0.02\tabcellsep 2.671\\
Proposed\tabcellsep \tabcellsep 2.877\\
LMS\tabcellsep \tabcellsep 2.737\\
NLMS\tabcellsep 0.03\tabcellsep 2.678\\
Proposed\tabcellsep \tabcellsep 2.877\\
LMS\tabcellsep \tabcellsep 2.788\\
NLMS\tabcellsep 0.04\tabcellsep 2.704\\
Proposed\tabcellsep \tabcellsep 2.877\\
\multicolumn{3}{l}{From the table 2, the SNR value of the proposed}\\
\multicolumn{3}{l}{algorithm is higher than that of LMS, NLMS algorithms}\\
\multicolumn{2}{l}{with step size ?=0.01 ÷0.04 .}\tabcellsep \\
IV.\tabcellsep \tabcellsep \end{longtable} \par
 
\caption{\label{tab_1}Table 2 :}\end{figure}
 			\footnote{© 2015 Global Journals Inc. (US)} 			\footnote{© 2015 Global Journals Inc. (US) 1} 		 		\backmatter  			  				\begin{bibitemlist}{1}
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\end{document}
