An Improved R-Peaks Marking Method Using Fourier Decomposition and Teager Energy Operator

The ECG signal is evolved as an extensively used rapid investigation tool to monitor cardiac abnormalities. It can give useful information about the functionality of the cardiovascular system. The threat of cardiovascular diseases is growing in India. The occurrence of cardiovascular diseases in India was estimated to be 5.45 cores in the year 2016 [1]. The ECG signal analyses and accurate detection of feature points take a big part in the identification of cardiac abnormalities. The standard ECG signal consists of five characteristic waves: P wave, Q wave, R wave, S wave and T wave. Ascertaining accurate R-peaks becomes a benchmark for the extraction of remaining all fiducial points [2]. Nonetheless, Morphology of the ECG gets affected owing to the variation in the characteristic waves and noise interference. So, computer-aided diagnosis is required to precisely delineate the R-wave to assist physicians and doctors with appropriate medical intervention. Conventionally, the wave functions were identified by both time and frequency domain signal processing technique [3, 4].

In recent developments, various wavelets transform techniques [5], time-frequency distribution of S-transform [6, 7], Circulant matrix-based continuous wavelet transform [8]. and convolution window [9] was used for ascertain R-peaks. However, correct marking of the R-peaks remains an open problem.

The primary objective of this work is to emphasizing the R wave and suppressing the effect of other wave functions while delineating the R-waves. In this work simple and efficient FDM is used for preprocessing of the ECG signal. The combination of Teager Energy Operator (TEO), Hilbert Transform (HT) and Zero Cross Detector (ZCD) is used for implementing the peak finding Logic. In our proposed work, FDM has applied for denoise the ECG signal by suppressing the BW and PLI. In the subsequent stage, TEO is calculated to enhance the R-waves. At last, Hilbert Transform and Zero Cross Detector are used for reliable estimation of R-waves and its peak positions.

The reminder of the paper has been ordered as follows. We will present the previous research concerning to field of R-peak identification in the second section. Section 3, presented proposed R-peak identification methodology. Performance assessment this work and shown results in Section 4. In section 5 the work is concluded.

The proposed method for accurate identification of R-Peaks is depicted in Figure 1. It consists of four different stages i.e. cleaning of ECG signal, Emphasizing the QRS complex, Peak finding logic and R-peaks detection. Initially, Fourier Decomposition Method (FDM) is applied as a part of preprocessing to remove the noise. The FDM uses DFT and IDFT based zero-phase filter bank, to break down the given signal into multiple frequency bands and regenerate filtered signal from the required frequency components. Furthermore, FDM is the most effective way of cleaning the ECG signal. It can be done by eradicating the BW and PLI [21]. An amplitude normalization and Teager Energy Operator (TEO) is calculated in the second stage to emphasize the QRS complexes. TEO gives instantaneous frequency of the signal and also more sensitive to sudden changes. Initially, it was used for nonlinear signal processing and found many applications in speech signal analysis. It will also reduce th­e effect of P- peak and T-peak while detecting R-peaks. The generated TEO Signal enhances the R-wave function and plays a significant part in finding the R-peaks in the proposed algorithm. The third stage is designed using the combination of HT and ZCD for detection of R-peaks. Accurate detection of local maxima is possible by finding Zero cross points on the Hilbert Transformation of TEO signal. Finally, the original R-peaks on ECG signal can be detected by projecting zero cross points on to the original ECG signal. The following subsections describe all the stages in detailed.

3.1 Fourier decomposition method for noise suppression

The ECG signals can be distorted by multiple noise sources, which include PLI, BW, electrode contact noise and motion artifacts, etc. Owing to these noises the reliable identification of R-Peaks becomes complicated. Different methodologies are formulated in the literature over the years to remove PLI and BW from the ECG signal. Some of these methods use high pass filters for removing PLI and low pass filters to remove BW. However, these methods generate computational delays and nonlinear phase distortion [22-25]. This can be addressed by exploiting the advantage of Zero phase filter bank [26]. Another popular approach is signal decomposition using discrete wavelet transforms [27-29] for ECG denoising, but noise is present at various levels of detailed coefficients. Thus, removing these coefficients eliminates the noise and sometimes it leads to loss required information also. In this paper, we are using FDM which clearly outperformed all other methods. FDM decomposes the given signal into a set of various frequency bands [21].

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Figure 1. Block diagram of improved R-peak marking method

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Figure 2. Block diagram of Frequency Decomposition Method

The Discrete Fourier Transform (DFT) based zero-phase filter bank is used for implementing the FDM. The block diagram of the FDM technique using Zero phase filtering is described in Figure 2.

The given ECG signal y[n] is break down into a set of orthogonal frequency bands using the following signal decomposition

$y[n]=b_{0}+\sum_{i=1}^{M} y_{i}[n]$     (1)

Here b₀ is average value of the Signal y[n], and {y₁[n], y₂[n], y₃[n], … y_k[n]} are Fourier intrinsic band functions. Consider frequency below 0.7 Hz as baseline wander frequency and 50 Hz and above as powerline interference. The frequency response of i^th band in the filter-bank can be obtained by defining H_i[k] = 1 for the required band of frequencies and zero for the range of noise frequencies (below 0.7 Hz and above 50Hz). Mathematically the filter bank can be defined as

$\left.\begin{array}{rl}

\mathrm{H}_{\mathrm{i}}[\mathrm{k}]=0, & \left(\mathrm{k}_{\mathrm{i}-1}+1\right) \leq \mathrm{k} \leq\left(\mathrm{N}-\mathrm{k}_{\mathrm{i}}\right) \\

=0, & \left(\mathrm{N}-\mathrm{k}_{\mathrm{i}}\right) \leq \mathrm{k} \leq \mathrm{N}-\mathrm{k}_{\mathrm{i}-1}-1 \\

=1, & \text { otherwise }

\end{array}\right\}$     (2)

where, i is 1, 2…M using inverse discrete Fourier transform (IDFT) operation, the signal components y_j[n] are obtained as

$\mathrm{y}_{\mathrm{i}}[\mathrm{n}]=\sum_{\mathrm{k}=0}^{\mathrm{N}-1}\left[\mathrm{H}_{\mathrm{i}}[\mathrm{k}] \mathrm{Y}[\mathrm{k}] \exp \left(\frac{\mathrm{j} 2 \pi \mathrm{kn}}{\mathrm{N}}\right)\right]$     (3)

where, Y[k] is discrete Fourier transform of y[n].

The proposed zero phase filter bank preserve the significant features like positions of all peaks. So that we can extract meaningful information from filtered ECG signal. However, the computational complexity also reduced by implementing the required DFT and IDFT using fast Fourier transform (FFT) algorithm. Figure 3 illustrate the performance of FDM for Denoising the ECG signal. Figure 3 (a) depicts the Original ECG signal y[n], Figure 3 (b) shows the 0.2Hz frequency noise which resembles the BW, Figure 3 (c) illustrate the 50Hz frequency noise which resembles the PLI, Figure 3 (d) shows the noise contaminated signal generated by adding all the above three signal. The filtered ECG signal is shown in Figure 3 (e) after applying FDM.

3.2 Amplitude normalization and Teager energy signal generation

This is the second step of the proposed method to identify R-peak. In this step, we implemented both amplitude normalization and generation of TEO signal for emphasizing the QRS complexes in the ECG signal. Normalization of the signal is useful for better discrimination of positive peaks and negative peaks. By doing this we can limit the signal amplitude to [-1, 1]. We normalize the signal y (n) by

$\check{\mathrm{y}}(\mathrm{n})=\frac{\mathrm{y}(\mathrm{n})}{\max _{\mathrm{n}-1}^{\mathrm{N}}(|\mathrm{y}[\mathrm{n}]|)}$      (4)

 

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Figure 3. Illustration of denoising ECG signal

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Figure 4. Identifying R-peaks using proposed method

where, each sample of y (n) is divided by maximum value of the signal. Amplitude normalization improves the detection of negative R-peaks. The primary purpose of generating TEO signal is to boost the original amplitudes of R-peaks. It was originally created by Kaiser [21]. TEO for a signal $\breve{\mathrm{y}}(\mathrm{n})$  in its discrete form can be generated by using following equation:

$\Psi_{y}[n]=\breve{y}(n)^{2}-\breve{y}(n-1) * \breve{y}(n+1)$     (5)

The TEO has been commonly used as a peak detector in many applications. Using TEO, it is possible to reduce the effect of P and T waves for reliable identification of R-peaks.

3.3 Accurate R-peak detection

From many years, the position of R-peaks is detecting by comparing the amplitude of the signal with the predefined threshold values. The secondary threshold value and search back methods are also exploited for reduction of errors. Nevertheless, in the case of diseased patient with varying wave function characteristics the search back mechanism with the second threshold value also does not give efficient results. In this work, HT and ZCD are used to construct a novel automatic R-peaks finding technique. The Figure 4 depicts how the HT signal identifies the R-peaks by marking its zero crossing points using Zero Cross Detector. This eliminates the complexity of comparison with various threshold values.

The HT of given signal z (t) is defined as

$\tilde{z}(t)=H[z(t)]=\frac{1}{\pi t} * z(t)=\frac{1}{\pi} \int_{-\alpha}^{\alpha} \frac{z(\tau)}{t-\tau} d \tau$     (6)

The process of finding R-peaks is depicted in Figure 4. Filtered ECG signal is shown in the Figure 4 (a). How the QRS complexes are enhanced in generated TEO signal is depicted in Figure 4 (b). Figure 4 (c) Illustrating the positive zero crossing points in the HT signal. Figure 4 (c) shows the identified R-peaks on the given ECG signal. Locating R-Peaks is difficult in the case of fragmented QRS complexes and low-frequency drift in the signal. To overcome this HT signal is passed through the Moving Average filter. The location of positive zero crossing points on the HT signal represents the R-peaks. which can resemble the positions of R-Peaks. By projecting these locations on the ECG signal, we can find the R-Peaks with ±20  samples. By searching the point which is more away from the zero-dc line in the searching window of ±20 samples of the identified R-peak locations in the previous test we can find the original R-peak locations.