Adaptive Interference Cancellation of ECG Signals - MDPI

sensors Article

Adaptive Interference Cancellation of ECG Signals Aifeng Ren 1 , Zhenxing Du 1 , Juan Li 1 , Fangming Hu 1 , Xiaodong Yang 1, * and Haider Abbas 2,3,4 1 2 3 4

*

School of Electronic Engineering, Xidian University, Xi’an 710071, China; [email protected] (A.R.); [email protected] (Z.D.); [email protected] (J.L.); [email protected] (F.H.) King Saud University, Riyadh 11653, Saudi Arabia; [email protected] National University of Sciences and Technology (NUST), Islamabad 44000, Pakistan Department of Computer Sciences, Florida Institute of Technology (FIT), Melbourne, FL 32901, USA Correspondence: [email protected]; Tel.: +86-29-8820-2830

Academic Editors: Giancarlo Fortino, Hassan Ghasemzadeh, Wenfeng Li, Yin Zhang and Luca Benini Received: 11 March 2017; Accepted: 15 April 2017; Published: 25 April 2017

Abstract: As an important biological signal, electrocardiogram (ECG) signals provide a valuable basis for the clinical diagnosis and treatment of several diseases. However, its reference significance is based on the effective acquisition and correct recognition of ECG signals. In fact, this mV-level weak signal can be easily affected by various interferences caused by the power of magnetic field, patient respiratory motion or contraction, and so on from the sampling terminal to the receiving and display end. The overlapping interference affects the quality of ECG waveform, leading to the false detection and recognition of wave groups, and thus causing misdiagnosis or faulty treatment. Therefore, the elimination of the interference of the ECG signal and the subsequent wave group identification technology has been a hot research topic, and their study has important significance. Based on the above, this paper introduces two improved adaptive algorithms based on the classical least mean square (LMS) algorithm by introducing symbolic functions and block-processing concepts. Keywords: ECG signal; interference cancellation; LMS algorithm

1. Introduction As the most important organ in the human body, the heart is the power source of metabolism of various organs and tissues. The basic units of the heart are the cardiomyocytes, and the human electrocardiogram (ECG) signal is actually their electrical activity response [1]. When there is a certain way to stimulate a certain intensity through the myocardial cells, it will result in intracellular and extracellular ion flows, resulting in an action potential. ECG signals completely record this change process [2], and ECG waveform reflects the physiological conditions of various parts of the heart in medical diagnosis, and is a very valuable reference for treatment [3]. The amplitude of the ECG signal is in the range of 10 µV to 4 mV and it is very small and weak and therefore very sensitive to the effects of various disturbances [4]. One of the main sources of interference are loop factors and 50 Hz frequency interference caused by the electromagnetic field and the patient, baseline wander (BW) caused by the patient’s limb movement and breathing, and electromyogram (EMG) interference caused by skeletal muscle stimulation and contraction [5]. Power frequency interference [6], the most common ECG signal interference, is caused by the magnetic field distributed by the human body by the power supply, resulting in added 50 Hz sinusoidal and harmonic components in the pure ECG signals [7]. Figure 1 shows the time-domain and frequency-domain diagrams of the ECG signals with power-line interference (PLI).

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Figure1. 1.ECG ECGsignal signalwith withPLI. PLI. Figure Figure 1. ECG signal with PLI.

BW is is another another interference interference affected affected by by the the patient’s patient’s ECG ECG monitored monitored breathing, breathing, electrode electrode BW is another interference affected by the patient’s ECG monitored breathing, electrode BW movement, and other frequently occurring factors [8]; its shape is similar to a periodic sinusoidal movement, and and other other frequently frequently occurring occurring factors factors [8]; [8]; its its shape shape is is similar similar to to aa periodic periodic sinusoidal sinusoidal movement, signal, generally generally below below the the 11 Hz Hz low-frequency low-frequency signal, signal, resulting resulting in in aa baseline baseline signal signal instability instability drift, drift, signal, signal, generally below the 1 Hz low-frequency signal, resulting in a baseline signal instability drift, making the the ECG ECG waveform waveform show show aa slow slow change change [9]. [9]. The The time time and and frequency frequency domains domains of of the the ECG ECG making making the ECG waveform show a slow change [9]. The time and frequency domains of the ECG waveforms affected by BW are shown in Figure 2. waveforms affected affected by byBW BWare areshown shownin inFigure Figure2.2. waveforms

Figure2. 2.ECG ECGsignals signalsunder underBW BWinterference. interference. Figure Figure 2. ECG signals under BW interference.

When the the ECG ECG signal signal is iscollected collected using using different differentmeasurement measurement modes, modes, the the signal signal strength strength is is When the ECG signal is collected using different measurement modes, the signal strength is When different. In the actual acquisition in front of the armpit the ECG signal is the most obvious, as the different. In In the the actual actual acquisition acquisition in of the the armpit armpit the the ECG ECG signal signal is is the the most most obvious, obvious, as as the the different. in front front of ECGsignal signalis isobtained obtainedwith withno nointerference, interference,as asshown shownin inFigure Figure3.3. 3. ECG signal is obtained with no interference, as shown in Figure ECG

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Figure 3. ECG signals with no interference.

Figure 3. ECG signals with no interference.

Based on the classical least mean square (LMS) algorithm [10], two improved adaptive Figure 3. ECG signals with no interference.

Based on theare classical leastnamely, mean square (LMS) algorithm [10], two improved adaptive algorithms proposed, the normalized LMS (NLMS) algorithm [11] based on algorithms symbol function and the normalized block-processing LMS (BLMS) algorithm based on symbol function [12]. the are proposed, namely, the normalized LMS (NLMS) algorithm [11] based on symbol function and Based on the classical least mean square (LMS) algorithm [10], two improved adaptive The symbolic functions [13] and the block-processing [14] concept are introduced and applied to the normalized block-processing LMS (BLMS) algorithm based on symbol function [12]. on The symbolic algorithms are proposed, namely, the normalized LMS (NLMS) algorithm [11] based symbol the elimination of two kinds of interference: ECG signal frequency interference and BW interference. functions [13]and andthe thenormalized block-processing [14] concept introduced and applied to thefunction the elimination function block-processing LMS are (BLMS) algorithm based on symbol [12]. Thesymbolic MIT-BIHfunctions ECG database and the real ECG data [14] collected byare a miniature ECG collector inthe the The [13] and the block-processing concept introduced and applied to of two kinds of interference: ECG signal frequency interference and BW interference. The MIT-BIH laboratory were used to validate the algorithm and analyze the results in detail. the elimination of two kinds interference: ECG frequency interference BW laboratory interference.were ECG database and the real ECGofdata collected bysignal a miniature ECG collectorand in the The MIT-BIH ECG database and the real ECG data collected by a miniature ECG collector in the used to algorithm analyze the results in detail. 2. validate Proposedthe Technique forand Adaptive Interference Cancellation laboratory were used to validate the algorithm and analyze the results in detail.

2. Proposed Technique for Adaptive Cancellation 2.1. Adaptive Noise Cancellation BasedInterference on LMS Algorithm

2. Proposed Technique for Adaptive Interference Cancellation TheNoise basicCancellation principle of Based the adaptive noise canceller is to use the noise source to output, then to 2.1. Adaptive on LMS Algorithm 2.1. Adaptive Noise Cancellation Based on LMS Algorithm digitally filter [15], to estimate the noise most accurately, and then to subtract the estimated noise The basic principle of thus the adaptive noise canceller is to useuseful the noise source tonoise. output, then to from the original input, achieving the separation of the signal fromto the Figure The basic principle of the adaptive noise canceller is topure use the noise source output, then to4 digitally filter [15], to estimate the noise most accurately, and then to subtract the estimated noise shows a block diagram of an adaptive noise canceller based on Wiener filtering [16], wherein thefrom digitally filter [15], to estimate the noise most accurately, and then to subtract the estimated noise main input signal is X(n), which consists of the useful signal s(n) and the background interference the original thus achieving the separation of the pure fromthe the noise. Figure 4 from theinput, original input, thus achieving the separation of the pureuseful useful signal signal from noise. Figure 4 signal (n), and these areadaptive not related. The reference input signal v1(n) must be the input signal showsshows a block diagram of two an adaptive noise canceller based on Wiener filtering [16], wherein av0block diagram of an noise canceller based on Wiener filtering [16], wherein the the associated with signal v0(n). main main input signal is the X(n), which consists ofofthe signals(n) s(n)and andthe the background interference input signal is interfering X(n), which consists theuseful useful signal background interference (n), and these related.The Thereference reference input must be the input signal signalsignal v0 (n),v0and these twotwo areare notnot related. inputsignal signalv1v(n) must be the input signal 1 (n) associated with the interfering signal v 0 (n). associated with the interfering signal v0 (n).

Figure 4. Block diagram of adaptive noise cancellation.

Because the reference signal v1(n) is correlated with the interference portion v0(n) in the main Figure 4. Block diagram of adaptive noise cancellation. input, the filter will remove this correlation at its output. This is achieved by generating an estimate Figure 4. Block diagram of adaptive noise cancellation. of the interference in the main input from thewith noise ofinterference the referenceportion channel andinsubtracting Because the reference signal v1(n)signal is correlated the v0(n) the main the estimated interference value from the main input to obtain the final output of the as an input, the filter will remove this correlation at its output. This is achieved by generatingsystem an estimate Because the reference signal v1In (n)summary, is correlated with the interference portion adaptive v0 (n) in the main estimate of the wanted signal. the specific steps for implementing noise of the interference in the main input signal from the noise of the reference channel and subtracting input, cancellation the filter will remove this correlation at its output. This is achieved by generating an estimate of on LMSvalue can be summarized follows: the estimatedbased interference from the main as input to obtain the final output of the system as an

the interference main signal. input signal from the of the reference channel and subtracting estimate of in thethe wanted In summary, thenoise specific steps for implementing adaptive noise the estimated interference value from the main input to obtain the final output of the system as an estimate cancellation based on LMS can be summarized as follows: of the wanted signal. In summary, the specific steps for implementing adaptive noise cancellation based on LMS can be summarized as follows:

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The initial value is set to start the default weight coefficient vector. Calculate the output signal of the adaptive FIR filter, wherein the order is L − 1: L −1

∑ Wi v1 (n − i),

vˆ (n) =

(1)

i =0

3.

Estimate the error of the current time n: e(n) = x (n) − vˆ (n) ≈ sˆ(n),

4.

Use the steepest descent LMS algorithm to adjust the weight vector of the filter continuously: Wi+1 (n + 1) = Wi (n) + 2µe(n) X (n − i ) 0 ≤ i ≤ L − 1,

5.

(2)

(3)

Verify whether the standard deviation of the standard error has been satisfied. If it is, immediately stop iteration; otherwise, continue to the following operation.

2.2. NLMS Algorithm Based on Symbol Function The NLMS algorithm is a kind of adaptive algorithm that is extended and improved based on LMS algorithm. The improvement of the algorithm is to use the variable step method, thus reducing the time required for full convergence, which corresponds to the weight coefficient update formula: W ( n + 1) = W ( n ) +

µ e ( n ) X ( n ), p + X T (n) X (n)

(4)

Therefore, the variable step size can be expressed as: µe (n) =

µ p+

X T (n) X (n)

,

(5)

Here, the step size is a fixed factor that controls the speed of convergence of the algorithm. The parameter p prevents the denominator from being too small. When the step size parameter is too large, the p value is generally a small positive number [17]. One of the major drawbacks of the adaptive algorithm extended by the basic LMS algorithm is that the excess mean square error is too large to cause distortion of the filtered signal. Thus, Muhammad proposed an error NLMS (ENLMS) algorithm with a variable step size proportional to the square of the error signal in the adaptive algorithm for removing the ECG signal power frequency interference. The corresponding iterative adjustment formula of the algorithm is as follows: W ( n + 1) = W ( n ) +

µ e ( n ) X ( n ), p + e T (n)e(n)

(6)

Therefore, in the LMS algorithm, the variable step size is expressed as: µe (n) =

µ , p + e T (n)e(n)

(7)

The parameters µ and p have the same meanings as above. Compared to the NLMS algorithm, ENLMS in the step-length selection is no longer dependent on the input signal; thus, for the convergence rate and steady-state error, ENLMS should perform better. However, according to the formula of the variable step size, the ENLMS algorithm needs additional computation to obtain the variable step size compared to the traditional LMS algorithm. Therefore, to further reduce the amount of computation without affecting the quality of the filtered signal, a sign function is introduced in the weight coefficient updating Equation (9).

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The symbolic function sgn(x) is defined as follows:    1:x>0 sgn(n) = 0:x=0   −1 : x < 0

  

,

(8)

 

An NLMS algorithm based on the symbolic function is obtained. Therefore, the final weight coefficient iterative adjustment formula is as follows: W (n + 1) = W (n) + µe (n)sgn{ X (n)}{e(n)}.

(9)

2.3. Normalized BLMS Algorithm Based on Symbol Function From the NLMS algorithm based on symbol function proposed in the previous section, the concept of block processing can be introduced to further reduce the computational complexity of the algorithm. The basic idea of the widely used BLMS algorithm [11] is that, unlike the basic LMS algorithm, the filter coefficients are recalculated and updated for each sample value. The block-processing algorithm is implemented in each block region, that is, every k points to a weight coefficient update [18]. Therefore, the filter weight vector iterative adjustment formula of the block-processing algorithm is as follows: k −1

W (n + 1) = W (n) + µ ∑ X (nk + i )e(nk + i ),

(10)

i =0

Then, the time-averaged gradient vector is: k −1

φ(n) = µ ∑ X (nk + i )e(nk + i ),

(11)

i =0

The filter coefficient vector based on the BLMS algorithm is adjusted once per k sampling points, and the coefficient update is based on the average gradient vector of the k sampling points. It can be deduced that the BLMS algorithm also converges to the Wiener solution, but this does not mean that it will achieve the final result sooner than the LMS. The block processing is introduced into the NLMS algorithm based on symbol function proposed in the previous section, that is, the input signal is processed in blocks (10), and then the absolute value of the error signal in each block region of length L is selected. The value is used to obtain the variable step size. Thus, the weight coefficient updating formula becomes: W ( n + 1) = W ( n ) +

µ sgn{ X (n)}sgn{e(n)}, e2Li

(12)

Then, we obtain the weight coefficient update formula of the normalized BLMS algorithm based on symbol function, which is further simplified, where e Li = max |ek |, k ∈ Zi0 , Zi0 = {iL, iL + 1, . . . , iL + L − 1}, i ∈ Z, and if e Li = 0, Equation (12) becomes: W ( n + 1) = W ( n ).

(13)

3. Implementation 3.1. Adaptive Interference Cancellation to Remove Power Frequency Interference In the following, we use the MIT-BIH public library’s record file and the data collected by the minicollector to compare and validate the ECG signal’s interference elimination performance. First of all, for the pure ECG signal from the MIT-BIH public library, artificially joining the same sampling rate of 50 Hz power frequency interference will add interference after the signal as the main

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filter input, the reference input, and select interference with the same frequency cosine [14]. Figure 5 shows the pure ECG of Sensors 2017, 17, 942 signal and the waveform after superimposed PLI. Figure 6 shows the spectrum 6 of 15 ECG with PLI. is942 clear that there is a strong 50 Hz noise. Sensors 2017,It17, 6 of 15 Sensors 2017, 17, 942

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Figure 5. MIT-BIH ECG waveform before and after PLI. Figure 5. MIT-BIH ECG waveform before and afterPLI. PLI. Figure 5. MIT-BIH ECG waveform before and after Figure 5. MIT-BIH ECG waveform before and after PLI.

Figure 6. Spectrum of MIT-BIH ECG by PLI. Figure 6.6.Spectrum ofof MIT-BIH ECG by Figure MIT-BIH ECG by PLI. 6. Spectrum of MIT-BIH ECG byPLI. PLI. Figure 7 shows theFigure output of Spectrum adaptive interference cancellation. Figure 8 shows the convergence of the statistical mean square error of the three adaptive interference cancellation Figure 77 shows shows the the output cancellation. Figure 8 shows the the Figure output ofof adaptive adaptiveinterference interference cancellation. Figure 8 shows algorithms. Figure 7 shows the of adaptive interference cancellation. Figure 8 shows the convergence convergence theoutput statistical mean three adaptive interference cancellation convergence ofof the statistical mean square squareerror errorofofthethe three adaptive interference cancellation of thealgorithms. statistical algorithms.mean square error of the three adaptive interference cancellation algorithms.

Figure 7. Output of the three adaptive interference cancellation algorithms. Figure 7. Output of the three adaptive interference cancellation algorithms.

Figure 7. Output of the three adaptive interference cancellation algorithms. Figure 7. Output of the three adaptive interference cancellation algorithms.

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Figure8.8.Mean Meansquare squareerror errorconvergence convergenceofofthe thethree threeadaptive adaptiveinterference interferencecancellation cancellationalgorithms. algorithms. Figure Figure Figure 8. 8. Mean Mean square square error errorconvergence convergenceof ofthe thethree threeadaptive adaptiveinterference interferencecancellation cancellationalgorithms. algorithms.

Basedon onthe thealgorithms algorithmsofofECG ECGdata dataacquisition acquisitionininthe theMIT-BIH MIT-BIHpublic publiclibrary, library,the theECG ECGdata dataofof Based Basedon onthe thealgorithms algorithmsofofECG ECGdata dataacquisition acquisitionininthe theMIT-BIH MIT-BIHpublic public library, ECG data Based library, thethe ECG data of of a classmatewere wereprocessed processedusing usingaamini-ECG mini-ECGcollector. collector.Figure Figure99shows showsthe theoriginal originalECG ECGwaveforms waveforms aaclassmate a classmate were processed using a mini-ECGcollector. collector.Figure Figure9 9shows showsthe theoriginal originalECG ECGwaveforms waveforms classmate were processed using a mini-ECG andthe thewaveforms waveformsafter afteradding addingPLI. PLI.Figure Figure10 10isisits itsspectrum. spectrum. and andthe thewaveforms waveformsafter afteradding addingPLI. PLI.Figure Figure10 10isisits itsspectrum. spectrum. and

Figure9.9.Before Beforeand andafter afterthe theimpact impactofofPLI PLIby bythe theECG ECGwaveform. waveform. Figure Figure 9. Before and after the impact of PLI by the ECG waveform.

Figure10. 10.Influence InfluenceofofPLI PLIon onthe theECG. ECG. Figure Figure 10. Influence of PLI on the ECG.

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Figure 11 11 shows shows the the output output of of adaptive adaptive interference interference cancellation. cancellation. Figure Figure 12 12 shows shows the the average average Figure Figure 11 shows the output of adaptive interference cancellation. Figure 12 shows the average mean square error convergence curve for 100 simulation simulations of the three adaptive meansquare square error convergence 100 simulation simulations the three adaptive mean error convergence curvecurve for 100for simulation simulations of the threeofadaptive interference interference cancellation algorithms. interferencealgorithms. cancellation algorithms. cancellation

Figure 11. Output of the three adaptive interference cancellation algorithms. Figure Figure11. 11.Output Outputof ofthe thethree threeadaptive adaptiveinterference interferencecancellation cancellationalgorithms. algorithms.

Figure 12. Convergence of mean square error of the three adaptive interference cancellation Figure of mean squaresquare error oferror the three adaptive cancellation algorithms. Figure12.12.Convergence Convergence of mean of the three interference adaptive interference cancellation algorithms. algorithms.

3.2. Adaptive Interference Cancellation Removes BW 3.2. Adaptive Adaptive Interference Interference Cancellation Cancellation Removes Removes BW BW 3.2. First of all, for the pure ECG waveform sampled from the MIT-BIH common library, the baseline First of of all, all, in forthe the pure ECG ECG waveform sampled from the the MIT-BIH commonon library, the drift interference common library with thesampled same sampling rateMIT-BIH is superimposed the pure First for the pure waveform from common library, the baseline drift interference in the common library with the same sampling rate is superimposed on ECG waveform, and then the signal is used as thethe main input and therate reference input is used baseline drift interference in mixed the common library with same sampling is superimposed on the pure ECG waveform, waveform, and then the the mixed signal is is used used as the the correlation main input input and and the the reference reference input as the artificial input of the baseline drift interference. Thus, between the reference the pure ECG and then mixed signal as the main input is used as the artificial input of the baseline drift interference. Thus, the correlation between the input andasthe signal of in the main input is 1,interference. and interference is most effective. is used theinterfering artificial input baseline drift Thus,cancellation the correlation between the reference input and andpure the interfering interfering signaland in the the main input is is 1, 1, and and interference cancellation is most most Figure 13 shows the ECG waveform themain waveform after adding the baseline drift. Figure 14 reference input the signal in input interference cancellation is effective. Figure 13 shows the pure ECG waveform and the waveform after adding the baseline drift. iseffective. the spectrum waveform after adding the baseline It can be seen that the Figureof13the shows the pure ECG waveform and thedrift. waveform after adding the baseline baseline drift drift. Figure 14 14 is ismostly the spectrum spectrum of the the waveform after adding adding the baseline drift. It can can be be seen seen that that the the interference concentrates onwaveform the low-frequency bandthe near the zerodrift. frequency. Figure the of after baseline It baseline drift drift interference interference mostly mostly concentrates concentrates on on the the low-frequency low-frequency band band near near the the zero zero frequency. frequency. baseline

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Figure and after BW. Figure13. 13.MIT-BIH MIT-BIHECG ECGwaveform waveformbefore beforeand andafter afterBW. BW. Figure 13. MIT-BIH ECG waveform before

Figure BW. Figure14. 14.MIT-BIH MIT-BIHECG ECGbefore beforeand andafter afterBW. BW. Figure 14. MIT-BIH ECG before and after

Figure Figure1515shows showsthe theoutput outputofofadaptive adaptiveinterference interferencecancellation. cancellation.Figure Figure1616shows showsthe the Figure 15 shows the output of adaptive interference cancellation. Figure 16 shows the convergence convergence convergencecurve curveofofthe thestatistical statisticalmean meansquare squareerror errorofofthe thethree threeadaptive adaptiveinterference interferencecancellation cancellation curve of the statistical mean square error of the three adaptive interference cancellation algorithms. algorithms. algorithms.

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Figure15. 15.Output OutputMIT-BIH MIT-BIHsignal signalafter afteradaptive adaptiveinterference interferencecancellation. cancellation. Figure Figure 15. Output MIT-BIH signal after adaptive interference cancellation.

Figure16. 16.Mean Meansquare squareerror errorconvergence convergenceofof ofthe thethree threeadaptive adaptiveinterference interferencecancellation cancellationalgorithms algorithms Figure 16. Mean square error convergence the three adaptive interference cancellation algorithms Figure for MIT-BIH signals. for forMIT-BIH MIT-BIHsignals. signals.

Afterverifying verifyingthe thewaveforms waveformsof ofthe thecentral centralbank bankof ofthe thepublic publiclibrary, library,the theECG ECGwaveforms waveformsof of After After verifying the waveforms of the central bank of the public library, the ECG waveforms of a certain classmate are collected for processing using a minicollector. Figure 17 shows the actual certainclassmate classmate are arecollected collectedfor forprocessing processingusing usingaaminicollector. minicollector. Figure Figure 17 17 shows shows the theactual actual aacertain measurement of the signal obtained. Figure18 shows the spectrum. measurementof ofthe thesignal signalobtained. obtained.Figure Figure18 shows the the spectrum. spectrum. measurement 18 shows

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Figure ECG interference BW. Figure17. 17. ECGwaveforms waveformsbefore beforeand andafter after interferencewith with BW. Figure 17. ECG waveforms before and after interference with BW.

Figure 18. ECG ECG spectrum disturbed by BW. Figure18. spectrum disturbed BW. Figure18. ECG spectrum disturbedby by BW.

Figure shows ofofadaptive interference cancellation. 2020 shows Figure19 shows theoutput output adaptive interference cancellation. Figurethe showsthe the Figure 1919shows thethe output of adaptive interference cancellation. Figure 20 Figure shows convergence convergence curve square error ofofthe adaptive interference cancellation convergence curveofofthe thestatistical statistical mean square error thethree three adaptive interference cancellation curve of the statistical mean square mean error of the three adaptive interference cancellation algorithms. algorithms. algorithms.

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Figure 19. Adaptive interference cancellation after the output signal. Figure19. 19.Adaptive Adaptiveinterference interferencecancellation cancellationafter afterthe theoutput outputsignal. signal. Figure

Figure 20.Mean Mean squareerror errorconvergence convergenceof ofthe thethree three adaptive adaptive interference interference cancellation algorithms. Figure cancellationalgorithms. algorithms. Figure 20. 20. Mean square square error convergence of the three adaptive interference cancellation

4. Conclusions and Analysis 4.4.Conclusions Conclusionsand andAnalysis Analysis The basicLMS LMS algorithm,the the NLMSalgorithm algorithm basedononsymbol symbol function,and and thenormalized normalized The Thebasic basic LMSalgorithm, algorithm, theNLMS NLMS algorithmbased based on symbolfunction, function, andthe the normalized BLMS algorithm based on symbol function are shown in Table 1 for comparison of the BLMS based on symbol function are shown Table 1in forTable comparison the computational BLMSalgorithm algorithm based on symbol function are inshown 1 for ofcomparison of the computational complexity per L sample points. complexity per Lcomplexity sample points. computational per L sample points.

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Table 1. Comparison of complexity of three kinds of adaptive algorithms. Algorithm Name

Times of Multiply-Add Operation

Times of Division

Basic LM Salgorithm NLMS algorithm based on symbol function Normalized BLMS algorithm based on symbol function

L+1 1 1

0 1 1

As shown in Tables 2 and 3, these three algorithms can effectively filter out the PLI and obtain the pure ECG waveform at the output. The improved NLMS algorithm and its block-processing algorithm based on symbol function are compared to the LMS algorithm get a higher signal-to-noise ratio (SNR) value. Table 2. SNR changes of MIT-BIH ECG with PLI before and after denoising. Algorithm Name

Before Filtering SNR (dB)

After Filtering SNR (dB)

SNRI (dB)

Basic LMS algorithm NLMS algorithm based on symbol function Normalized BLMS algorithm based on symbol function

−13.5234 −13.5234 −13.5234

19.6638 23.3935 23.4859

33.1872 36.9168 37.0093

Table 3. Changes of SNR before and after denoising of ECG signals from the minicollector with PLI. Algorithm Name

BeforeFiltering SNR(dB)

AfterFiltering SNB(dB)

SNRI (dB)


−12.600 −12.600 −12.600

7.4272 10.973 10.672

20.027 23.572 23.271

Table 4 shows the variation of SNR before and after the interference cancellation. It can be seen that the interference cancellation of the three algorithms improves the SNR by 12.5809, 15.8217, and 15.8337 dB, respectively, when the initial SNR is −3.2003 dB. Table 4. SNR changes of MIT-BIH ECG signals before and after filtering with BW interference. Algorithm Name


AfterFiltering SNR (dB)

SNRI (dB)


−3.2003 −3.2003 −3.2003

9.3806 12.6214 12.6334

12.5809 15.8217 15.8337

Table 5 shows the change of SNR before and after the interference cancellation. It can be seen that, under the strong baseline drift interference with the initial SNR of −2.7754 dB, the three adaptive interference cancellation algorithms increase the signal SNR by 13.9228, 16.6120, and 16.6158 dB, respectively. In summary, the improved symbol-based NLMS algorithm and its block-processing algorithm both improve the SNR both for the central database of the public library and for the analysis of signals from the mini-ECG. Its convergence is reached earlier and eliminating the signal noise interference is better with frequency variation. The improved symbol-based NLMS algorithm has achieved a higher enhancement.

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Table 5. SNR changes before and after denoising of ECG signals from the minicollector with BW interference. Algorithm Name


After Filtering SNR (dB)

SNRI (dB)


−2.7754 −2.7754 −2.7754

11.1474 13.8366 13.8404

13.9228 16.6120 16.6158

Acknowledgments: The work is supported in part by the National Natural Science Foundation of China (No. 61671349), in part by the Project Funded by China Postdoctoral Science Foundation, and in part by the Postdoctoral Research Projects Funded in Shaanxi Province. The authors also would like to extend their sincere appreciation to the Deanship of Scientific Research at King Saud University for its funding of this research through the Research Group Project No. RG-1435-048. Author Contributions: Aifeng Ren, Zhenxing Du, Juan Li and Fangming Hu wrote the paper, Xiaodong Yang and Haider Abbas contributed the ideas. Conflicts of Interest: The authors declare no conflict of interest.

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