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ECG signal denoising and feature extraction

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https://www.eduzhai.net American Journal of Biomedical Engineering 2016, 6(6): 180-201 DOI: 10.5923/j.ajbe.20160606.04 EKG Signals – De-noising and Features Extraction Saleh Alomari*, Mohammed Shujauddin, Vahid Emamian Department of Electrical Engineering, St. Mary’s University, Camino Santa Maria, San Antonio Texas, USA Abstract The need of effective method to obtain and analyse electrocardiogram (EKG) signal has inspired This research paper to designed an efficient algorithm that can handle any (EKG), remove the most dominant noises associated with it, and extract the important futures. EKG signal is an electrical signal represents the physical human’s heart activity. Nonetheless, this signal is affected by various noise including baseline wondering and power interference. These noises affect the signal to noise ratio (SNR) especially in P and T waves which have less amplitudes than R peaks. Removing these noises result in cleaner signal that can be conveniently processed to extract important features such as heart health condition. EKG features play the main role in diagnosing the heart rate, normality and abnormality of heart activities, and heart diseases. For a healthy person, one heart beat consists of P, QRS Complex, T, and in some signals U waves. In this paper, a robust and numerically sufficient algorithm is developed to de-nosing EKG signal and extract all major features. For de-nosing EKG signal, FIR Equiripple High pass filter is used. FIR Equiripple Low pass filter follows this filter to remove the power interference noises. Haar wavelet transform is used to accurately detect the R peaks. Haar wavelet is found to be better than other common methods that are used to detect R peaks. Haar wavelet shows high accuracy when it is applied on EKG signal to detect R peaks. In fact, it succeeded to detect all R peaks in hundreds of EKG signals (obtained from Physio net website). All other features are detected based on the R peaks by creating a set of windows which their lengths depend on the maximum normal wave durations and locations. These filters and algorithm have been implemented in Matlab. The algorithm has been applied on 108 EKG signals collected from physionet website and could detect all EKG signals’ heart rates successfully despite the fact that some signals were extremely distorted. Keywords EKG, ECG, Base line noise, Power interference noise, FIR Equiripple High pass filter, FIR Equiripple Low pass filter, Zero phase filter, Haar wavelet transform, QRS complex detection, P wave detection, T wave detection, Matlab 1. Introduction The EKG is a graphical record represents the cardiac physical activities which are created by re-polarization and depolarization of atria and ventricular of the heart [1]. Every heart beat consists of P, QRS Complex, T waves. Those waves are extremely important in analysis heart condition, if they are present, they must be within certain amplitude and duration limits. Exceeding these maximum limits or failing to reach these minimum limits indicate illness. Absence of any of these waves is a sign of certain type of heart diseases. Fig (1) shows the typical EKG signal. Feature extraction through accurate waves detection is significant to measure heart rate and find any suspicion of diseases related to arrhythmias such as Heart Rate Variation, Tachycardia, Bradycardia. These diseases can be diagnosed by observing the abnormalities on the heart beats [2]. Nonetheless, detecting EKG waves is not easy due to time-varying morphology of the investigated signal and occurrence of noises. This paper implements a robust and an effective algorithm that is used to detect R peaks and based on that extracts the most important features of EKG signal. * Corresponding author: engsalehalomari@gmail.com (Saleh Alomari) Published online at https://www.eduzhai.net Copyright © 2016 Scientific & Academic Publishing. All Rights Reserved Figure 1. Normal EKG signal American Journal of Biomedical Engineering 2016, 6(6): 180-201 181 2. Methodology EKG signal holds all major features that can be extracted to diagnose heart condition. Unfortunately, the EKG signal obtained from a patient is corrupted by a lot of noises. Therefore, it must be preprocessed before extracting any feature. The wondering baseline and power interference noises are the main noises that must be removed from the signal. Wondering baseline noise presents due to low frequency produced by patient respiration. This low frequency ranges between 0.05 to 0.5 Hz [3]. Hence, High pass filter is capable to eliminate this noise from EKG signal. Nevertheless, there are enormous type of filters that can be applied. Choosing appropriate filter type is not easy task. Every filter has its own properties, advantages, and drawbacks. Choosing the right filter should be based on the signal that is processed and desired outcomes. For example, IIR filter type capable of removing the baseline noise from the signal. However, this type of filter introduces some distortion of the original signal since this type of filter has nonlinear phase response. Figure 2 shows the typical amplitude and phase response of IIR Butterworth filter. This distortion cannot be tolerated in EKG signal. Distortion means loss of some important information. Thus, FIR filter is proposed to be used. Equiripple highpass filter to remove wondering base line noise Zero phase filter Equiripple lowpass filter to remove the power line interference noise Zero phase filter Pure EKG signal Feature Extraction (a) (b) Figure 2. Amplitude (a) and phase respose (b) For IIR buterworth filter Haar wavelet transform 2nd detail coefficient Detecting R peaks Finding R peaks in original signal 182 Saleh Alomari et al.: EKG Signals – De-noising and Features Extraction 3. Filter Design Calculating heart rate beats per minute based on R peaks Detecting Q and S components of QRS Complex (first Q and last S are detected separately) calculating QRS Complex time duration for every single beat Detecting P waves (first P wave is detected separately) Detecting T waves (last T wave is detected separately) Detecting P onset and offset and calculating P time duration for every single beat Removing the wandering baseline noise needs a highly efficient filter that has short transition band. This noise corresponds to frequency ranges between 0.15 to 0.5 Hz. This sharp edges mathematically forms discontituaty that can not be implimented in practice. Designning effective filter depends mainly on finding filter with low order whose frequency response efficinetly approximate the desireded specification. Among all type of filters, the Equiripple FIR filter is superior of optimizing the transition width and ripple hight in both stop and pass bands. Equiriplle filter algorithm has been developed by parks and mcclellan. They derived a new algorithm from the general remez exchange algorithm. The parks and mcclellan filter works to minimizing chebychev error [4]. The parks mcclellan algoritnm considers wighted approximation error between designed and intended frequency response which is distributed evenly across passband and stopband minimizing the maximum error. The difference equation for FIR filter design in general is given as: y= (n) b0x(n) + b1x(n −1) + ...... + bM−1x(n − M +1) (1) M −1 ∑ = y(n) bk x(n − k) (2) k=0 bk is the filter coefficients, the output can be presented also as a form of input signal convolve with unit response as following: M −1 ∑ = y(n) h(k)x(n − k) (3) k=0 The FIR filter can be described by the system function as following equation: M −1 ∑ H(z) = h(k)z−1 (4) k=0 Detecting T onset and offset and calculating T time duration for every single beat 3.1. FIR Filter Designing To precisely describe Equiripple filter designing, the ripple magnitude that occurs in passband and stopband must be bounded by the following limits [5]: 1− δ1 ≤ Hr (ω) ≤ 1+ δ1 ω ≤ ωp (5) Figure 3. Flowchart for algorithm used in this paper −δ2 ≤ Hr (ω) ≤ δ2 ω > ωs (6) Hence, this paper used a very effective filter that has narrow transition width and optimum filter length that meet desired filter specification. After effectively removing all type of noises, the signal is ready to be processed for feature extraction. Haar wavelet transform is used for detecting the R peaks. Based on R peaks, all other features have been extracted using windows with different sizes for every wave. Figure 3 shows the flowchart for the algorithm that is used in this paper to de-noise EKG signal and extract the important features out of it. Where δ1 and δ2 are the ripples in passband and stopband respectively. There are 4 cases that result in a linear FIR filter. These cases can be handled by equiriple filter. Two of these cases are the symmetric unit sample response and the other two are the antisymmetric. In both cases, the filter order can be either even or odd. The following table summarize all cases: American Journal of Biomedical Engineering 2016, 6(6): 180-201 183 Table 1. Frequency response functions for linear phase FIR filters Filter type Q(ω) P(ω) h(n) = h(M-1-n) M odd 1 Case (1) (M −1) / 2 ∑ a(k) cos(ωk) k=0 h(n) = h(M-1-n) M even Case (2) cos ω 2 (M / 2) −1 ∑ b (k) cos(ωk) k=0 h(n) = - h(M-1-n) M odd Case (3) sin ω (M −3) / 2 ∑ c (k) cos(ωk) k=0 Input filter parameter Initial guess of M+2 Extremal frequency Calculate the optimum α on extremal set h(n) = - h(M-1-n) M even Case (4) sin ω 2 (M / 2) −1 ∑ d (k) cos(ωk) k=0 The frequency response H(ω) can be expressed as: H(ω) = Q(ω) P(ω) (7) Where 1 Q(ω) = scionsωω2  sin ω 2 P(ω) = α (k) cos(ωk) This is a common form of equiriple filter where the length of filter (L) and coefficient α(k) changes based on which linear phase case is presented. Thus, Parks and McClellan algorithm can be implemented by finding symmetric or antisymmetric which minimizes the maximum weighted Chebyshev error as follow: = E(ω) min[maxω∈B (W(ω)(H(ω) − D(w)] (8) Where H(ω) is the actual frequency response, D(ω) is the desired frequency response, W(ω) is the weighted Chebyshev error, and B ranges between [0, π]. Plugging in the equivalent form of H(ω) and manipulating the previous equation results in the final form of the weighted error function: = E(ω) min[maxω∈B (W(ω)(P(ω) − D(w)] (9) Where W(ω) = W(ω)Q(ω) D(ω) = D(ω) Q(ω) M ∑ P(ω) = α(k) cos(ωk) k=0 Interpolate through M+1 Points to obtain P(ω) Calculate error by E(ω) And find where is local maxima More than M+2 extrema Retain M+2 largest maxima No Change Check where extremal point changed Best approximation Figure 4. Flowchart for algorithm used by Parks McClellan Alteration theorem: B is the subset of interval [0, π] which consists of frequencies of desired filter in both passband and stopband. B can be described by the following equation: ( ) B = B − endpoint where Q(ω) = 0 (10) 184 Saleh Alomari et al.: EKG Signals – De-noising and Features Extraction Thus, there are in B at least M+2 extremal points ω1, ……, ωL+2, such that: E(ωi )= c(−1)i[E(ω)] (11) where i = 1, 2, ……..., M+2. |E(ω)| reaches its maximum point at minimum of M+2 points. The error function changes its sign between two successive extremal frequencies from which this theorem takes its name “alteration theorem”. As a result, the weighted error function shows an equiripple manner. Figure 4 describes the Parks McClellan algorithm to design equiripple filter [5]. 3.2. Equiripple Highpass Filter Used to Remove Baseline Noise Baseline noise typically corrupts EKG signal due to patient’s respiration, motion of patient’s body, and electrodes. This noise could mask some important features. Therefore, it is extremely important to remove this noise. Equiripple highpass filter is capable of removing this noise completely without affecting the other important features of the signal. Equiripple highpass filter allows the main components of EKG signal to pass on such as P, QRS complex, and T waves as well as PR segment, PR interval, ST segment and QT interval. All mentioned intervals and segments correspond to certain frequencies. Hence, maintaining important frequencies are crucial. Based on American health association, the smallest component frequency is 0.05 Hz. Nonetheless, in practical, the baseline noise has frequency extend to the value of 1Hz. This means there is some feature that is distorted due to using highpass filter [6]. Nevertheless, the ST segment is not the area of interest in this paper. In fact, among the advantages that Equiripple filter has is the narrow band width that can be built and this feature can be maintained. However, building narrow transition band width that would maintain the ST segment using Equiripple requires filter with high order exceeds 5000. This order prevents us from using the zero phase filter built in as a function in Matlab to eliminate the time delay introduced by high pass filter which is crucial to preserve important feature. As a matter of fact, Matlab does not recognize zero or negative indices value that might be introduced due to time delay. This built-in function (filtfilt) requires the signal length to be more than three times of filter order. The Equiripple highpass filter used has a filter order of 2746, cutoff prequency at 1 Hz, stop frequency at 2 Hz, and stop attenuation of 80 dB. Figure 5,6,7 shows the original EKG signal, FFT of the signal, and EKG after removing baseline nose from the signal. It is so obvious that the baseline noise is completely removed while all features are preserved. After this stage, the DC offset due to baseline noise is successfully and completely removed. Figure 5. Row EKG Signal Figure 6. FFT for the EKG Signal Figure 7. EKG after completely removing baseline noise American Journal of Biomedical Engineering 2016, 6(6): 180-201 185 3.3. Equiripple Lowpass Filter Used to Remove Power Interference Noise Due to improper grounding, power line noise interferes with EKG signal. This interference adds up 50 or 60 Hz (depends on power frequency standard that is used). The power interference noise appears as spike in frequency components analysis (FFT) Fig.6 at 50 Hz. This frequency component can be removed by using notch filter. However, all other frequency components which exceeds this value (50 Hz) are not important and does not contribute to the important features that we are looking for. Therefore, lowpass filter is adequate for this purpose. FIR equiripple lowpass filter is used with filter order of 506. The cutoff frequency is at 40 Hz. This filter is followed also by another filter with zero phase for avoiding time delay using same Matlab function filtfilt. Fig.8 shows the magnitude (in dB) and phase response of the designed filter. these algorithms are easy to be implemented while others are complicated. Nevertheless, Haar wavelet transform is selected to be the method that is used to extract the EKG features. This decision was not arbitrary, in fact, based on many research papers, Haar wavelet is outstanding and promising. It provided high accuracy when it is applied to signals to detect important features. 4.1. Haar Wavelet Transform Haar wavelet first introduced by Alfred Haar in 1910. Then, many definition and generalization follow it [7]. Haar wavelet is widely used in image coding, edge extraction, and feature extraction. The advantage of wavelet transform over the Fourier transform is that the wavelet transform can keep track of both time and frequency while in Fourier transform the high frequency in a short time is hard to be detected. Haar wavelet decomposes the processed signal into two sub-signals of half of its original length. In fact, there are two main functions that form wavelet analysis. The scaling function Φ and the wavelet Ψ. Figure 10 shows the basic Haar scaling function. Y 1 X 0 1 Figure 8. Magnitude and phase response of the designed equiripple lowpass filter Figure 9 shows the resultant signal after removing the power interference noise using FIR Equiripple Lowpass filter. Figure 10. Haar Scaling Function multiresolution analysis. The Haar scaling function as follows [8]: Φ ( x ) = 1,  0, if 0 ≤ x < 1 elsewhere (12) The same signal can be shifted over any finite set of integers. Let V0 is the function that is shifted and scaled as follows (figure 11 shows elements in V0): ∑ V0 = akφ(x − k) ak ∈ R (13) k∈z Y a a Figure 9. EKG signal after removing power interference noise 4. Features Extraction Now, the EKG signal is ready to be processed for features extraction. In this stage, there are many methods and algorithms can be used to extract the EKG features. Some of a - 0123 X a a Figure 11. V0 Components 186 Saleh Alomari et al.: EKG Signals – De-noising and Features Extraction 4.2. General Form of Haar Wavelet Assume i is a positive integer, Vi is the space spanned by the following set: {........., φ(2i x +1), φ(2i x), φ(2i x −1),.........} (14) A function in V0 is contained in V1 and so forth. V0 ⊂ V1 ⊂ Vi−1 ⊂ Vi ⊂ Vi+1 (15) Vi has all information up to scale 2-i. when i become larger, the resolution become finer. The fact that Vi ⊂ Vi+1 indicates that there is no information is missed when the resolution become finer. The representation of Φ (2i x) is spike of width (1/2i). Thus, when i is large, the Φ (2i x) is just spike that it might be filtered out if we desired to. For filtering noises, the wavelet Ψ must be part of Haar wavelet to isolate those spikes that is mentioned previously. The main concept is to decompose the Vi as an orthogonal sum of Vi and its complement. To clarify this, let i = 1. Thus, we have V1 and V0. V0 is found by Φ and its shifted form. Therefore, V1 must be orthogonal and generated by the mother function Ψ. Ψ function must satisfy certain condition to be valid as a complement for V0. Ψ must be contained in V1. Hence, it can be expressed as: ∑ ψ(x) = aKϕ(2x − K) (16) K ∫ ψ(x)φ(x − k)dx = 0 (17) The simplest Ψ(x) that is satisfy both conditions is the following function: ψ(x) = φ(2x) − φ(2x −1) (18) It is obvious that this function satisfies the first condition (Ψ is contained in V1) as well as the second condition (Ψ is orthogonal to V0) as it is proofed in the following equation: +∞ 1/ 2 1 ∫ ∫ ∫ ψ(x)φ(x) = 1dx − 1dx = 0 (19) −∞ 0 1/ 2 Thus, Ψ(x) is called Haar wavelet. Figure 12 represents haar wavelet that has the amplitude of 1 (a1 = 1) at ϕ (2x) and amplitude of -1 (a2 =-1) at ϕ (2x-1). 1 x 0 1/2 1 -1 Figure 12. Haar Wavelet Ψ(x) The previous function is a form of Haar wavelet that consists of the wavelet Ψ(x) and the scaling function ϕ . Those two functions used to decompose a given signal and reconstruct it. The scaling function can be controlled to give wider or thiner scale that is called multiresolution analysis of a signal which helps to deeply diagnose the signal and filter out an undesirable component or noise [8]. 4.3. Haar Wavelet Decomposition Algorithm For a given function f, Vi is the nested spaces such that: …V-2 ⊂ V-1 ⊂ V0 ⊂ V1 ⊂ V2… (20) Assume Wi is the orthogonal of Vi with respect to subsequent space Vi+1. Therefore, Vi= +1 Vi ⊕ Wi (21) That is, Wi has all missing details from Vi to obtain Vi+1. Therefore, by repetition, any space Vi can be obtain by following formula [9]: Vi = Wi ⊗ Wi-1 ⊗ Wi-2 ⊗ Wi-3 … (22) Assuming f is a function in Vi, then, f can be decomposed as following equation: =f wr−1 + wr−2 + ⋅⋅⋅ + w0 + f0 (23) wr denote spikes of (f) that has the width 1/(2j+1). For r large enough, these spikes are narrow enough to represent noise, assume spike of width 0.001 denotes noise; then, 2-10 < 0.001< 2-9. Therefore, any wr with r ≥ 9 denotes noise, to remove these noises, these components (wr) set to zero value. The remaining components represents the signal that is free of noise [8]. 5. Detecting Important Features through Applying Haar Wavelet to EKG In many research papers that compared many methods used for features extraction, wavelet transform in general and Haar wavelet in specific has introduced the highest accuracy. Haar wavelet produce multiresolution analysis for a signal. Using this method, R Peaks detection is easily obtained. Haar wavelet transform generate two coefficients called approximation and detail coefficients. In the second detail coefficient, R peaks are dominant since the QRS complex has a higher frequency in a shorter time. Figure 13 shows the decomposed EKG signal second detail coefficient using Matlab function wavdec and detcoef. Hence, R peaks are easy to be detected using Haar wavelet transform. In this stage, the amplitude threshold is applied. Signal that has at least 60% of the maximum value is maintained and other samples are set to zero (see figure 14). The result was a bunch of values that are adjacent and repeated every period. Those values are representing the R peaks. Nonetheless, R peak should be represented by a unique value not by a bunch of values. Therefore, the highest American Journal of Biomedical Engineering 2016, 6(6): 180-201 187 amplitude value of each bunch of values is selected to be unique R peak. However, R peaks locations might be different in Haar wavelet from locations in the original signal. Therefore, a window of 100 samples of width is used to being searched through in the original signal after each R peaks location is multiplied by 4. This multiplication because in the second detail coefficient, the signal length is reduced by 4; this is the Haar wavelet property. Figure 15 shows the detected R peaks in the original EKG signal. Based on R peaks which are successfully detected, The P, Q, S, and T waves are being searched for with reference to R peaks locations. The number of beats per minute is calculated using the following formula: Number of beats = R peaks * length of signal (number of samples) / (Fs *60 seconds) Figure 16 shows the successfully detected R peaks with calculated heart rate per minute. Figure 13. Haar Wavelet Transform Second Detail Coefficient Figure 14. Detected R Peaks from the Second Detail Coefficient Figure 15. Detected R peaks in Original EKG Signal Figure 16. Calculated Heart Rate Based on Detected R Peaks Creating windows and searching within these windows is the method that is used to detect other waves. To detect P peaks location, window of 160 samples is created. This window extends from 200 samples to 60 samples to the left of each R peaks. Within these windows, P peaks are located at the samples that have the maximum amplitude value. The same manner, Q peaks are detected with reference to R peaks locations. Windows of 90 samples extend on ranges start 100 samples on the left side of R peaks location and end 10 samples away from R peaks locations. In these windows, the minimum amplitude values are the Q peaks. S peaks are detected the same way; yet, instead of searching on the right side of R peaks, the left side is searched through windows of 95 samples. These windows start 5 samples on the right of R peaks and end at 100 samples away from R peaks. In these windows, minimum amplitude values are the S peaks. Figure 17 shows detected QRS complex and the time of these complexes for every single beat in EKG signal. T waves are the farthest waves from R peaks. They are detected using windows of 300 samples of width. These windows start at 100 samples on the right of R peaks and end at 400 samples away from R peaks. In these windows the maximum amplitude value are the T waves. Thus, all peaks are successfully detected. Figure 18 shows detected T waves. However, there was a problem that urged through processing some EKG signals. Location of Windows that are created to detect waves peaks, in some signal, have some of negative values. Those negative values are used as arrays indices. However, Matlab does not allow for zero or negative values as indices. Therefore, some errors appeared with some EKG signals. To overcome this obstacle, the Matlab 188 Saleh Alomari et al.: EKG Signals – De-noising and Features Extraction code that is developed, search the first peak of P wave and Q wave which are on the right side of R peak separately outside the main for loop function that is used for other peaks. If statement is set to measure the length of the first window. Then the minimum location is found. If the minimum location has zero or negative value, the window is narrowed down. Then, it is tested again. If it still has zero or negative value, it is narrowed down again and so forth. Figure 17. Detected QRS Complex with Its Time Duration for Every Single Beat instead of checking for zero or negative indices, the indices that exceed the EKG signal length (10000 sample) is checked using find the maximum value command instead of minimum. This strict algorithm, searching windows that are always within the range. The algorithm and matlab code being smart and able to handle any EKG signal regardless of how and when the signals are recorded. After all, waves and peaks are found. The code measures the QRS complex duration, P wave duration and T wave duration. To have these waves duration measured, onset and offset for every single wave should be found. Using if condition nested inside for loop for every type of wave (P, QRS, T), the onset and offset are found. If condition checks for sample that proceed the sample which is bigger than zero and follow sample which is less than zero. The search for every peak duration starts from the peaks itself. For peaks onset, windows are created to the right of peaks. Within each window, the value that is satisfy the if statement condition is consider the wave onset. However, in some waves, sample that satisfy if condition is not unique. Hence, the first sample that satisfy if condition is considered and ignore other samples with help of break command. In fact, the closest sample to the wave peak is considered. That is, the first zero crossing sample is considered to be onset. The same way that offset for every single wave is measured; yet, instead of searching to the left side of the peak, the right side of the peak is the point of interest. Having all peaks of waves onset and offset measured, subtracting the offset from onset for every single wave result in the duration (in many samples) for every single wave. To convert the duration to be in time (seconds), the following formula is used: Duration in samples = offset - onset Duration in time = (Duration in samples * 1)/Fs Fs is the sampling frequency. The same method is used for both P and T wave durations. Figure 19 and 20 show the P and T waves onset and offset detection and duration respectively. Figure 18. Detected T Waves in EKG Signal This procedure is done iteratively till certain limit. If it still has zero or negative value, the window width is set to zero and consider the first peaks is not existing. As a matter of fact, this is true because in practical it is not guaranteed that the EKG signal which being recorded has the first P or Q peaks. in fact, it might be when the sensor is connected to the patient, the time of recording is exactly at the appearance of R peaks. In this case, the P or Q is not existing. The same method is used with S and T waves which are located on the right-hand side of R peaks. Nonetheless, instead of processing the first peak individually, the last peaks are processed separately and Figure 19. Detected P Waves and Their Duration American Journal of Biomedical Engineering 2016, 6(6): 180-201 189 No Patient’s EKG Signal 22 patient045_s0147_Ire 23 patient046_s0156_Ire 24 patient048_s0180_Ire 25 patient049_s0173_Ire 26 patient051_s0213_Ire 27 patient053_s0191_Ire 28 patient055_s0194_Ire 29 patient056_s0196_Ire 30 patient059_s0208_Ire 31 patient060_s0209_Ire 32 patient062_s0212_Ire 33 patient063_s0214_Ire Figure 20. Detected T Waves and Their Duration 34 patient065_s0226_Ire 35 patient066_s0225_Ire 6. Conclusions 36 patient068_s0228_Ire 37 patient070_s0235_Ire This algorithm has been tested on 108 EKG signals 38 patient071_s0236_Ire obtained from physionet website. Those signals are real 39 patient073_s0238_Ire signals collected from patients for research aim. The 40 patient074_s0406_Ire algorithm succeeded to detects all R peaks in each signal and 41 patient075_s0242_Ire all other important waves. In addition, the heart rate, the 41 patient077_s0254_Ire duration of P, QRS Complex, and T waves have been 42 patient078_s0259_Ire successfully and accurately calculated. The only wave that 43 patient079_s0269_Ire the algorithm fails to detect R peaks in it is the EKG obtained from the patient 146. This signal is extremely distorted. 44 patient080_s0260_Ire Table 2 shows the heart rate calculated for different patients. 45 patient084_s0281_Ire 46 patient084_s0281_Ire Table 2. Measured Heart rate for Some Patient’s EKG Signals’ 47 patient085_s0345_Ire No Patient’s EKG Signal Detected Heart Rate 48 patient088_s0339_Ire 1 patient001_s0010_re 78 49 patient090_s0356_Ire 2 patient002_s0015_Ire 78 50 patient091_s0353_Ire 3 patient003_s0017_Ire 78 51 patient097_s0380_Ire 4 patient006_s0022_Ire 84 52 patient099_s0388_Ire 5 patient010_s0036_Ire 96 53 patient100_s0399_Ire 6 patient012_s0043_Ire 54 54 patient101_s0400_Ire 7 patient015_s0057_Ire 78 55 patient105_s0303_Ire 8 patient016_s0076_Ire 54 56 patient106_s0030_re 9 patient018_s0082_Ire 72 57 patient108_s0013_re 10 patient021_s0065_Ire 72 58 patient111_s0203_re 11 patient023_s0081_Ire 66 59 patient115_s0023_re 12 patient024_s0094_Ire 78 60 patient118_s0183_re 13 patient026_s0088_Ire 78 61 patient121_s0311_Ire 14 patient029_s0122_Ire 84 62 patient125_s0006_re 15 patient033_s0113_Ire 60 63 patient127_s0342_Ire 16 patient034_s0109_Ire 120 64 patient130_s0166_re 17 patient037_s0120_Ire 72 65 patient131_s0273Ire 18 patient038_s0162_Ire 60 66 patient135_s0334Ire 19 patient040_s0131_Ire 72 67 patient138_s0005_re 20 patient041_s0136_Ire 84 68 patient141_s0307Ire 21 patient043_s0278_Ire 90 69 patient146_s0007_re Detected Heart Rate 108 102 72 78 66 78 108 66 90 84 72 72 66 78 84 78 66 66 72 84 78 72 66 102 78 66 66 78 54 84 84 84 114 108 72 78 78 84 60 84 84 84 72 54 102 72 90 78 36 (not accurate)

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