## 1 Introduction  
Cardiovascular diseases are the main noncommunicable diseases and they contribute to more deaths than all other causes combined [1]. Cardiac auscultation is the most common and cost-effective noninvasive screening method for heart conditions. Despite its universality, auscultation is a difficult technique that requires sufficient experience. Only around 20% of medical interns can effectively perform auscultation [2, 3]. Automatic algorithms for auscultation can make the subjective experience of the auscultation technique objective and simplify the mastery of auscultation. The segmentation of heart sounds is important for improving algorithms for classifying heart sound diseases [4]. One heart sound cycle is generally divided into four states and the states have a fixed order comprising the first sound (S1), systole, the second sound (S2), and diastole, as shown in Figure 0(a). S1 is mainly caused by mitral and tricuspid valve closure, and S2 is mainly caused by aortic and pulmonary valve closure. Normally, no sounds appear during systole and diastole, but heart murmururs may appear in systole and diastole to indicate heart diseases, such as valve diseases [5], as shown in Figure 1b. The two main difficulties that affect heart sound segmentation (HSS) are individual differences and various types of noise. Individual differences such as the frequencies, amplitudes, and durations of heart states may vary according to the physical conditions. The noises introduced in the heart sound signal collection process include breath sounds, ambient noise, and friction sounds caused by shaking. In addition, heart sound signals can be affected by the filtering effects of electronic stethoscopes depending on the filter circuit, material, and shape of the sampling device employed. Thus, the HSS task requires extracting the unique features of S1 and S2 in the heart sound signals, and distinguishing them from various noises. The previously proposed HSS algorithms were divided into three steps comprising feature extraction, feature classification, and state annotation, and simplified summaries of these methods are shown in Table 1. Most algorithms mainly use envelope information and time-frequency information for feature extraction. The envelope and time-frequency features were extracted because the signal amplitudes of S1 and S2 were relatively strong in normal heart sounds, and the frequencies of S1 and S2 mainly fell within a certain range [2]. However, two problems may affect the search for peaks based on the envelopes. First, strong noises may be incorrectly identified as the peaks generated by S1 and S2. Second, S1 and S2 peaks with less sound may be omitted. The positions of S1 and S2 may not be found due to the overlapping of the noise spectrum in the time-frequency based methods. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Study** & **Feature Extraction** & **Feature Classification** & **State Annotation** \\ \hline \multirow{3}{*}{[6]} & \multirow{3}{*}{Shannon energy envelope} & \multirow{3}{*}{Threshold method for peaks} & Larger time intervals are the \\  & & & diastolic period; \\  & & & Corresponding time intervals \\  & & & vary more for diastole \\ \multirow{3}{*}{[7]} & \multirow{3}{*}{Homomorphic filtering envelope} & \multirow{3}{*}{Peak conditioning process} & K-means for time intervals \\  & & Duration-dependent hidden & \\ \cline{1-1}  & multiple frequency bands & & Markov model (DHMM) & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Brief summaries of some heart sound segmentation algorithms. Figure 1: Heart sounds with synchronous electrocardiogram and segmentation results for four states of the heart cycle (S1, systole, S2, and diastole): (**a**) normal heart sound (**b**) abnormal heart sound with heart murmur. Therefore, some algorithms aimed to improve the discrimination of S1 and S2 compared with other sounds by modifying the methods for extracting the envelope and frequency features.