# An ECG Signal De-Noising Approach Based on Wavelet Energy and Sub-Band Smoothing Filter
## 1 Introduction  
ECG signals record the electrical activity of the heart, which can reflect its state. Therefore, ECG signals are widely used in heart disease diagnosis [1]. However, an ECG signal is easily degraded by various noises in the acquisition process, which reduces the application value of ECG. There are many reasons for ECG signal degradation, such as electromyographic (EMG) interference, respiratory interference, frequency interference, etc. Due to the different types of ECG signal noise sources, filtering becomes a difficult problem [2]. Therefore, the pre-processing and de-noising of ECG signals is a crucial process before the analysis and diagnosis of ECG.  
At present, there are many methods to filter and pre-process ECG signals. [PERSON] et al. [3] introduced a new signal analysis method called empirical mode decomposition (EMD), which iswidely applied to de-noise ECG signals. [PERSON] et al. [4] exploited the empirical mode decomposition method to remove noise from ECG signals. [PERSON] et al. [5] adopted a modified extended Kalman filter (EKF) structure to de-noise and compress ECG signals. [PERSON] et al. [6] proposed a revised scheme for ECG signal denoising based on a recursive filtering methodology. [PERSON] et al. [7; 8] proposed a sub-band adaptive shrinkage function for ECG signal de-noising. [PERSON] et al. [9] proposed a de-noising algorithm based on empirical mode decomposition and moving average filter. Discrete Wavelet Transform (DWT) is one of the widely used de-noising techniques, which provides an important solution to de-noise ECG signals. At present, threshold techniques using different sets of wavelet coefficients and wavelet transform are also proposed. [PERSON] et al. [10; 11] proposed a wavelet threshold de-noising method based on discrete wavelet transform for non-stationary signals. [PERSON]. [12] proposed an approach based on the threshold value of ECG signal determination using Wavelet Transform coefficients. [PERSON] et al. [13] presented a new ECG de-noising approach based on noise reduction in empirical mode decomposition (EMD) and discrete wavelet transform (DWT) domains. [PERSON] et al. [14] proposed a new threshold estimation method for ECG signal de-noising based on wavelet decomposition, in which the maximum and minimum wavelet coefficients of each stage are used to calculate the threshold. [PERSON] et al. [15] presented an ECG signal de-noising method based on Ensemble EMD Thresholding and Higher Order Statistics (HOS). [PERSON] et al. [16] adopted empirical mode decomposition and adaptive switching mean filter to de-noise ECG signals. Among the existing de-noising approaches, singular spectrum analysis (SSA) is a recently developed method to separate the signal of interest from various noises effectively [17; 18; 19; 20].  
In the light of the above factor, an approach based on wavelet energy and sub-band smoothing filter is proposed in this paper. The wavelet coefficients that required to be de-noised are determined by wavelet energy and other wavelet coefficients remain unchanged. Moreover, the quality of ECG signal is further improved by a sub-band smoothing filter. The remainder of this paper is organized as follows: the next section briefly overviews discrete wavelet transform. The proposed approach is explained in detail in Section 3. The experimental results are reported in Section 4 and the conclusion will be summarized in Section 5.