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Figure 1. Ideal ECG signal. (Source: Zhao et al, 2011).

ECG signal noise removal is the process of isolating the essential signal component from unwanted signals to obtain a noise free ECG signal that provides more accurate diagnosis. The earlier method of ECG signal analysis was established on time domain only (Singh and Kaur 2013; Limaya and Deshmukh 2016). But this is not enough to analyze all the characteristics of the ECG signal. The frequency components of a signal are necessary. To achieve this, Fast Fourier Transform (FFT) method is used. But the restriction of the FFT is that the method cannot give information concerning the exact location of frequency components. Hence, the use of the Short Term Fourier Transform (STFT) as a solution. However, the main restriction of the STFT is that the tuning of time - frequency is not an optimum solution. Therefore, we decided to experiment what we felt should be a more appropriate method to solve this problem. The wavelet transform seems to be the most effective method for this purpose (Akujuobi and Baraniecki 1994; Akujuobi et al 2001; El-Dahshan 2010). 

Some of the methods used for noise removal of the ECG signals are adaptive filtering (Zhao et al 2011), FIR filtering (Rani et al 2011; Chinchkhede 2011), and Wavelet transform (El-Dahshan 2010; Tikkaren 1999; Banerjee et al 2012). Adaptive filtering is the most commonly used method for noise removal. Wavelet transform is the recent approach with different types of wavelet families. Wavelet transform methods provide the best performance for non-stationary signals that make them appropriate for ECG signal analysis. This paper compares two namely Daubechies-4 and Symlet types of wavelets and then determines which type gives the better performance.

 The objectives of this research are to:

•  To develop an ECG noise removal method based on Discrete Wavelet Transform (DWT).

•  To evaluate and determine which wavelet type gives better noise removal performance between the different types of the two wavelet families by calculating the Signal-to-Noise Ratio, Peak Signal-to-Noise Ratio, Mean Square Error, and Maximum Squared Error and compare the results.

•  To calculate the heart beat rate (beats per minute) in order to determine which type of cardiac arrhythmia the patient may have.

The earlier methods for noise filtering were based on digital filters (Mbachu et al 2011). proposed a technique using the FIR filter with Kaiser window in order to remove the noises in the ECG signal. They have designed Kaiser window based low pass filter to remove high frequency noise, high pass filter to remove low frequency noise like baseline wander and notch filter to remove power line frequency noise in the ECG signal with sampling frequency of 1KHz and the order of the filter that they used was 100. They also designed the cascade of all these filters. Bai et al (2004) made a comparison of a general notch filter, comb notch filter, and equiripple notch filter. They evaluated the performance with respect to mean square error. The results show that the equiripple notch filter successfully kept the detail of the signal at the expense of higher filter order. The comb and general notch filters degrade the features of the ECG signal.

Rani et al (2011) made a comparative study of the use of FIR and IIR filters in removing baseline noises present in ECG signal. Chinchkhede et al (2011) investigated the improvement of raw and noisy ECG signals by various window based FIR filters. The Power Spectral Density and spectrogram analysis were carried out to study the effect of noise on ECG. In order to measure the performance of noise removal, they calculated SNR of the processed ECG, and determined the correlation coefficient to find the mismatch between raw ECG and filtered noisy ECG. The designed FIR filter with Kaiser window worked excellently well as they compared them to the Blackman, Blackman-Harris, and Gaussian filters in removing baseline wandering and power line interference under different noisy conditions.

There are two main types of source separation methods, independent component analysis (ICA) and principal component analysis (PCA). Independent component analysis considers the noise signals as an independent entity in the ECG signal, on the other hand, principal component analysis considers it as a statistical tool that decorrelates the different signal components from ECG data. Chawla (2011) proposed a method that deals with principal component analysis followed by different versions of independent component analysis application for ECG segmentation. 

Recently, the wavelet-based analysis is one of the common methods for ECG denoising, because of its high accuracy in time-frequency resolution. In discrete wavelet transform (DWT), the signal is analyzed with different frequency bands in which a combination of different coefficients can be used to identify the noise components in order to eliminate them to get a clean signal. Banerjee et al (2012) proposed a dyadic DWT decomposition and reconstruction using Daubechies wavelet with faily good results. Their technique provided a quick and easy noise removal method for bandwidth and muscle noise. Wavelet-based noise removal method can effectively remove the noise components. In wavelet-based thresholding methods, the coefficients are adjusted after wavelet decomposition by the use of threshold values that can be set as hard thresholding or soft thresholding.

In hard thresholding, the coefficient values that are below the threshold are set to zero, therefore, eliminating the noise associated with those components of the signal. In soft thresholding, the values that are below the threshold are reduced by the same magnitude from their original values. We studied the Daubechies-4 and the Symlet types of wavelet transforms and did a comparative analysis of the two and their suitability for the noise removal of the ECG signals.

Theory and Method

Traditionally, the Fourier transform has been a useful method to analyze the frequency components of the signal. However, Fourier transform is good for stationary signals but not for non-stationary or transient signals hence the use of Short Time Fourier Transform (STFT). But STFT uses a constant window in its analysis of the signals hence introducing errors. Wavelet transform overcomes these shortcomings with its translation and localization properties. The translated version wavelets locate the areas of concern, whereas the scaled version wavelets give us the ability to analyze the signal in different scales, (Akujuobi and Baraniecki 1994; Akujuobi, et al 2001; El-Dahshan 2010). 

 The wavelet transform is the most recent solution to overcome the restrictions of the Fourier transform and the STFT. The window is translated along the signal and for every location, the spectrum is calculated. Then this process is repeated with a slightly shorter (or longer) window for every new cycle. Eventually, the result will be a collection of time-frequency representations of the signal, all with different resolutions that represent the multiresolution analysis.

Multi-Resolution Analysis (MRA)

One of the main advantages of wavelet transform is its ability to express a signal f(t) as a limit of successive approximations, each level of the signal is more accurate than the level before. These successive approximations identify different resolution levels. A multi-resolution analysis (MRA) is a technique to construct the signal with different resolution levels. This involves a sequence {Vm : m _ integers} of embedded subspaces of L2 that satisfies the following relations:

Each subspace included in the one before as the following:

V-2 _ V-1 _ V0 _ V1 _ V2 · · · Vm _ Vm+1                                                                             (1)

The union of all subspaces spans the entire L2 space so that:

 is dense in L2                               (2)

The intersection of subspaces is the empty set so that:

                                           (3)

Each subspace gives a specific resolution so that f(x) _ Vm if and only if f(2x) _ Vm+1 for all integers m.

There exists a function  such that

                                          (4)

is an orthogonal basis for V0 so that

                                                                                 (5)

The function 

 is called the scaling function or father wavelet.

In the multi-resolution analysis, we can use the wavelet basis functions as a complete expansion basis for a given function f(x) in L2. More than that, it connects between the scaling function 

(x) and wavelet function (mother wavelet) and constructs a wavelet basis to use. For wavelet analysis, the principle is to establish an advantage of certain features of the system so that it gives a qualified time-frequency representation (Akujuobi and Baraniecki 1994; Akujuobi, et al 2001; El-Dahshan 2010). 

Discrete Wavelet Transform (DWT)

The discrete wavelet transform is a type of wavelet transform for which the wavelets are discretely sampled. Like other wavelet transforms, one of the main advantage of DWT that it has over Fourier transforms is a temporal resolution: it captures both frequency and location information. We can solve the problems of redundancy and impracticality by discretizing the time-scale parameters. In discrete wavelet transform (DWT), the signal is analyzed to different frequency bands in which a combination of different coefficients can be used to identify the noise components in order to eliminate them to get a clean signal. Suppose we have an original signal (the signal with the noise), we apply a high pass filter and a low pass filter on the samples based on convolution techniques.

We apply the high pass filter in order to preserve the high frequency components and apply the low pass filter in order to preserve the low frequency components. Then we apply downsampling on the high frequency components to get the detail coefficients, and also we apply downsampling on the low frequency components to get the approximation coefficients, this process called decomposition as we can see in Figure 2.

To reconstruct the signal, the inverse is applied. The signal is reproduced by upsampling the detail coefficients and then applying a high pass filter to get the high frequency components. We also do the upsampling for the approximation coefficients then apply a low pass filter to get the low frequency components. We then do the summation between the high frequency and low frequency components in order to get the original signal or the reconstructed signal. This is called the reconstruction process as we can see in Figure 3.