DENOISING OF ECG SIGNALS USING WAVELETS
AND CLASSIFICATION USING SVM
Shivanesan S M. 1, Pradheep M. 1, Sharath K. 1, Aravind Prasad. 1, Manoj M. 1
Ganesan M. 2

Abstract- Electrocardiogram is the recording of the electrical potential of heart versus time. The analysis of ECG signal has great importance in the detection of cardiac abnormalities. In this paper we have dealt about the removal of noises in ECG signals and arrhythmia classification of the signal. The inputs for our analysis is taken from MIT-BIH database (Massachusetts
Institute of Technology Beth Israel Hospital database). The denoising is done through wavelet transform and thresholding.
Confirmatory tools such as Poincare plot and Detrended
Fluctuation Analysis (DFA) are used to find out the healthiness of the signal. Then Support Vector Machine (SVM) is used to find out what type of arrhythmia is present in the signal.
Keywords- Classification, DFA Electrocardiogram, MIT-BIH database, Poincare, SVM , Wavelets.

I. INTRODUCTION
In today’s environment there has been lot of threats due to heart disease and no proper diagnosis With the recent developments in technology, physicians have powerful tools to observe the working of the heart muscle and thus to establish their diagnosis. Among cardiovascular examinations, electrocardiogram (ECG) analysis is the most commonly used and very effective too. This is due to the fact that ECG presents useful information about the rhythm and the electrical activity of the heart. Thus, it is used for the diagnosis of cardiac arrhythmias worldwide. For effective diagnostics, the study of the ECG signal must be carried out for several hours. For this reason, researchers have been interested in enabling computers to classify the abnormal ECG signals. During the last five decades the analysis of ECG signals evolved from simple visual examinations to totally automated analysis [1, 2, 3].
A noise free signal is necessary in any type of signal analysis and classification [4]. Several algorithms have been proposed for denoising of the biomedical signals, especially
ECG signals. Advancement have been done to various fields for denoising and classification of ECG signals. ECG signal is one of the bio signals that is considered as a non-stationary signal and needs a hard work to denoise [5, 6]. An efficient technique for such a non-stationary signal processing is the wavelet transform. The wavelet transform can be used as a decomposition of a signal in the time frequency scale plane.
There are many applications of wavelet transform such as sub-band coding data compression, characteristic point’s detection and noise reduction. In order to reduce the noise of
ECG signal many techniques are available like digital filters
(FIR or IIR), adaptive method and wavelet transform thresholding methods. However, digital filters and adaptive methods can be applied to signal whose statistical characteristics are stationary in many cases. Recently the

wavelet transform has been proven to be useful tool for nonstationary signal analysis.
Thresholding is used in wavelet domain to smooth out or to remove coefficients of wavelet transform. The denoising method that applies thresholding in wavelet domain has been proposed by Donoho as a powerful method [7].
Before classification of these signals to find out the arrhythmia, the need to know whether the signals is abnormal or not becomes necessary. To find out the healthiness of the signal we used two methods Poincare plot and Detrended
Fluctuation analysis (DFA) [8, 9, 10]. After confirming with the abnormality of the signal simple Support Vector Machine
(SVM) is used to train the signals and find out the exact arrhythmia in the ECG signal. In [11], two classification systems based on the support vector machines (SVM) approach are implemented.
1Shivanesan S M, Pradheep M., Sharath K, Aravind Prasad, Manoj M. are students of ECE department, Amrita Vishwa Vidyapeetham, Coimbatore
641112, India. e-mail: shiva.rathna@gmail.com
2Ganesan M., (Assistant Professor) is with Department of ECE, Amrita
Vishwa
Vidyapeetham,
Coimbatore
641112,
India.
e-mail: meetganesan@gmail.com The signals for analysis are taken from the MIT-BIH database [12]. We have discussed about how wavelet can efficiently denoise the obtained from the database. The
Poincare plot and Detrended fluctuation analysis are done in order to confirm the abnormality of the signal. The classification of the ECG signal is based on the major arrhythmias that causes threats to human life viz. Bradycardia
Tachycardia, cardiac and ventricular. SVM trains, classifies and finds out what type of abnormality is present.
The article is organised as follows: section II tells about the principle behind wavelet transform and thresholding. Section
III describes about the Poincare plot and Detrended fluctuation
Analysis (DFA). Section IV tells about the SVM classification of arrhythmia. Section V discusses about the results obtained and tabulation. We present our conclusions and future work in the section VI. The overall block diagram is depicted in Fig. 1.

II. WAVELET TRANSFORM
A. Discrete Wavelet Transform:
The wavelet transform is similar to the Fourier transform.
For the FFT, the basis functions are sines and cosines. For the wavelet transform, the basis functions are more complicated called wavelets, mother wavelets or analysing wavelets and scaling function. In wavelet analysis, the signal is broken into shifted and scaled versions of the original (or mother) wavelet.
The fact that wavelet transform is a multiresolution analysis

makes it very suitable for analysis of non-stationary signals such as the ECG signal [13].
The discrete wavelet transform (DWT) is an implementation of the wavelet transform using a discrete set of the wavelet scales and translations obeying some defined rules. In other words, this transform decomposes the signal into mutually orthogonal set of wavelets. The DWT can be realized in terms of high pass and low pass filters. The approximation properties of filter banks and their relation to wavelets are presented in the paper [14]. The output of the low pass filter gives the approximation coefficients and the output of the high pass filter gives the detailed coefficients.
Inputs
MIT-BIH database Denoising by wavelets

Feature extraction PP & DFA

Arrhythmia classification using SVM

Fig. 1. Overall block diagram
The DWT of an discrete signal x(n) of length M-1 is given in the below equation.
() = ∑ ( , ) 0, () + ∑∞
=0 ( , ) , () (1)
Here Wφ( , ) and Wψ( , ) are called the wavelet coefficients. ,() and 0,() are orthogonal to each other.
Hence we can simply take the inner product to obtain the wavelet coefficients.
1
∑ () 0, [] [0 , ] =
(2)
√
1

∑ () 0, [] [, ] =
(3)
√
The coefficients Wφ( ,k) are called the approximation coefficients and the coefficients Wφ( , ) are called the detailed coefficients. The DWT can be realized in terms of high pass and low pass filters. The approximation properties of filter banks and their relation to wavelets are presented in the paper
[14]. The output of the low pass filter gives the approximation coefficients and the output of the high pass filter gives the detailed coefficients. Computation of the wavelet coefficients at every possible scale is a fair amount of work and it generates an awful lot of data. Selection of a subset of scales and positions based on powers of two (dyadic scales and positions) results in a more efficient and accurate analysis.
B. Wavelet Decomposition and Thresholding:
The DWT decomposes the signal into approximate and detail information as discussed. The wavelet decomposition process can be iterated, so that one signal is broken down into many lower resolution components. This is called the wavelet decomposition tree. x(n) cA1 cA2 cAn

cD1 cD2 In this proposed method, the corrupted ECG signal x(n) is denoised by taking the DWT of raw and noisy ECG signal. A family of the mother wavelet is available having the energy spectrum concentrated around the low frequencies like the
ECG signal as well as better resembling the QRS complex of the ECG signal. We have used daubaches wavelet, which resembles the ECG wave. In discrete wavelet transform
(DWT), the low and high frequency components in x(n) is analysed by passing it through a series of low-pass and highpass filters with different cut-off frequencies.
This process results in a set of approximate coefficients (cA) and detail coefficients (cD). To remove the power line interference and the high frequency noise, the DWT is computed to level 4 using daubaches16 (DB16) mother wavelet function and scaling function. Then the approximate coefficients at level 5 (cA5) are set to zero. The residue of the raw signal and the approximate noise is obtained to get noise free ECG signal. The method is based on taking the discrete wavelet transform (DWT) of a signal, passing this transform through a threshold, which removes the coefficients below a certain value. = √2 ∗ log()
(4)
Where, T is threshold, n is the number of samples and is the noise standard deviation. Thresholding is applied at every loop to smooth out the signals and denoise the raw data
.
III. FEATURE EXTRACTION
Classification to find out the arrhythmia becomes unnecessary when the ECG signal is normal and does not contain any sort of abnormalities. To visually verify and find out whether the signals are normal or not we use two highly accurate methods.
The Poincare plot and the Detrended Fluctuation analysis
(DFA).
A. Poincare Plot:
The Poincare plot of RR intervals is one of the techniques used in heart rate variability (HRV) analysis. It is both a useful visual tool which is capable of summarizing an entire RR time series derived from an electrocardiogram in one picture, and a quantitative technique which gives information on the longand short-term HRV. A Poincare plot of RR intervals is composed of points ( , +1), that is each point in the plot corresponds to two consecutive RR intervals [15]. The resulting cloud of points is usually characterized by its length
(SD2) along the line of identity and its breadth across this line
(SD1). The visual inspection of the formed shapes of the
Poincare plot of RR intervals is a widely used method for analysing the quality of recorded ECG signals and to identify premature and ectopic beats, as well as technical artefacts. The plot of a healthy person will have a comet shaped structure along the line of identity [16]. Also the ratio of the Poincare descriptors (SD1, SD2) should be high for a healthy person.
Let RR, x and y vectors be defined as = (1, 2 … … . , +1 ), = (1 , 2 , … . . , ) = (1 , 2 , … … , ) = (1 , 2 , … . , , ) = (2 , 3 , … … , +1 ),
(5)

cDn

Fig. 2. Decomposition tree

1

1 = √ ∑ =1( 1 )2

(6)

1

2 = √ ∑ =1( 2 )2

1 =

( −̅ )−( − )
√2

,

(7)

2 =

( −̅ )+( − )
√2

(8)

The over bar stands for mean.
By calculating SD1 and SD2 from the eq. (6) & (7) and finding the ratio of the descriptors we could comment on the abnormality. But the ECG signals involve more than a b than two classes, so we need a classifier that is more than a binary classifier [16,
17]. The widely practised ones are one-against-all (OAA) and the one-against-one (OAO) strategies. The one against one
(−1)
constructs 2 decision functions for all the combinations of class pairs. Experimental results in [18] indicate that the oneagainst-one is more suitable for practical use. (More details appeared in [18]). We use OAO for ECG multi class classification. B. Detrended Fluctuation Analysis (DFA):

V. RESULTS AND TABULATION

This is also a plot analysis by which we could visually see and comment on the abnormality of the given ECG signal. The plot here is a double logarithmic plot. Its log F(n) versus log(n). The main objective of DFA is to extract the extrinsic fluctuations in order to allow the analysis of the signal’s variability associated exclusively with autonomic control. The integrated signal y(k) is then segmented into multiple windows of length n. For each of these windows, a least-squares firstorder approximation (a line segment) is calculated, representing the “trend” of that segment of the signal that has been found out. The trend signal yn(k) in Eq. (10), formed by the line segments, is an approximation to the integrated signal y(k). 1

() = √ ∑ =1 ()2 ,

(9)

A. Wavelet denoising:
The denoised signal is evaluated on the basis of SNR and correlation factor. Records or samples from MIT-BIH database were used. The tabulation below shows the records used and the SNR of the filters.DB16 was found to denoise effectively. ∑

2 () 2 ()
=0

= 10 ∑ =0

(13)

(n): the deformation in reconstructed ECG signal. (n): the original signal.
Table 1. SNR values of various records and filters

(10)
(11)

Where () is the duration of the i-th RR interval, is the mean interval, and k is the current output sample timeindex. The slope of the line (log F(n)& log (n)) gives us a coefficient called α which gives us the HRV fluctuations. The normal plot of DFA is shown in the Fig 3.

DB4

DB6

DB16

Sym8

100

12.37

11.86

13.06

7.37

105

13.15

9.47

11.65

4.75

112

12.47

11.9

12.92

6.84

228

() = () − ().

() = ∑ =1[() − ]

SAMPLES
MIT-BIH

18.05

16.5

17.57

11.72

Table 2. Correlation values
SAMPLES
MIT-BIH

IV. SUPPORT VECTOR MACHINE
The support vector (SV) machine is a new type of learning machine. It is based on statistical learning theory. Support vector machines (SVMs) are becoming popular in a wide variety of biological applications. The main use of SVM is classification. They were used in cancer cells classification and now SVM’s are used widely in biomedical signal analysis.
Here we have employed SVM to classify the ECG signal and to find out the arrhythmia present in it. SVM finds the optimal separating hyper plane (OSH) with the minimum errors. The linear separation hyper plane is in the form of
() = + .
(12)

DB6

DB16

Sym8

100
Fig 3. Normal DFA plot.

DB4
0.8279

0.4599

0.9325

0.1120

105

0.3146

0.2935

0.5848

0.0662

112

0.6291

0.4878

0.6661

0.4522

228

0.6222

0.4826

0.7929

0.4882

From the Table 1 and Table 2 we found out that DB16 denoised the signal efficiently and can be used for effective denoising of ECG signals.
B. Poincare Plot:
The Fig 4 below shows the Poincare plot of the record 228 of the MIT-BIH database. From the figure we could see that

the shape is not comet shaped along the line of incidence
(LOI) as discussed in section three. So just by looking at graph of the Poincare plot we can tell that the signal is abnormal and contains some kind of artefact.

Record

Table 3. SVM arrhythmia classification
Normal/abnormal Type of arrhythmia

112

Abnormal

Bradycardia

219

Abnormal

Tachycardia

228

Abnormal

Bradycardia

VI. CONCLUSION AND FUTURE WORK
The results shown above are the outputs of the record 228.
Similarly other records from the MIT-BIH database were run and the outputs were verified and type of arrhythmia present in it was found and analysed. The Poincare plot and Detrended
Fluctuation Analysis (DFA) are highly accurate in determining the abnormality of the ECG signal. It’s fast and just by looking
Fig 4. Poincare plot of record 228 at the output plot of the ECG signal we can comment on the abnormality of the signal. This paper throws light on the
SD1= 317.2 method of denoising that can efficiently remove various noises
SD2= 317.0 like baseline wander, power line interference etc. from the ECG
1
= 1.0062 signal. We have also seen that the best filter for denoising ECG
2
signals was DB16 which has got the maximum number of
The ratio of SD1 and SD2 is very low and hence the signal is vanishing moments. The higher the vanishing moments higher will be the amount of denoising but not at the cost of losing the abnormal. original data from the signal. SVM has always been an accurate classifier and one against one (OAO) strategy is used for
C. Detrended Fluctuation Analysis: multiclass classification of ECG signals. Keeping in mind that
The fig 5 below shows the DFA plot of the record 228 of the ECG being a non-stationary signal, we have designed the entire
MIT-BIH database. Comparing the Fig 5 with the normal plot block that can handle the non-stationary ECG signal.
The inputs to the whole setup was taken from the MIT-BIH from the Fig 3 we see the plot is disfigured and the abnormality database and not real time ECG signals. In the future ECG is confirmed. signals can be acquired from the human and can be sent as the inputs and the type of arrhythmia can be found. Since it is going to be real time acquisition of data, the amount of noise present will be more, so care must be taken while denoising the real time signals.
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Fig 5. DFA plot of record 228

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α = 0.2783 (Anti-correlated)
D. Support Vector Machine:
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