## 1 Introduction
The distance between S1\({}^{\prime}\) and S2\({}^{\prime}\) within the same cardiac cycle is shorter than that of S2\({}^{\prime}\) from the current beat and S1\({}^{\prime}\) from the next beat. We can use these facts to get individual pairs of S1\({}^{\prime}\) and S2\({}^{\prime}\). This can be easily done with a low heart rate. A series of AO timings can be used to calculate heart rate. Furthermore, researchers also use AO to estimate blood pressure based on pulse transit time (PTT) between biosignals, such as ECG, and accelerometer data from, for example, the carotid artery on the neck [8]. Figure 1: Typical SCG signal measured from the chest. Each heartbeat consists of S1\({}^{\prime}\) and S2\({}^{\prime}\), which are close to each other, like those in PCG. Although the signal under the shaded area, around 13-14 s, is corrupted, both S1\({}^{\prime}\) and S2\({}^{\prime}\) are still visible. Thus, AO detection is of high interest and requires robust algorithms to handle noisy signals resulting from motions and vibrations caused by factors other than cardiac activity. A list of weaknesses of SCG, compiled by [PERSON] and [PERSON], includes complex waveforms that are difficult to interpret [1]. SCG signals also vary by age, sex, heart condition and body position [5; 9]. However, these facts open various opportunities to develop new signal processing algorithms and improve sensor and instrumentation technology. Researchers around the globe have been working to find good methods to detect AO automatically. The easiest way to detect AO is using ECG, especially R-peak, as a guideline. [PERSON] et al. evaluated four different methods, namely, cardiac sound characteristic waveform (CSCW), Shannon, absolute and Hilbert, to get the envelope of SCG signals by utilizing their high-frequency (>20 Hz) and low-frequency (<30 Hz) parts [10]. [PERSON], in turn, used modified signal energy thresholding, empirical mode decomposition (EMD) and empirical wavelet transform to detect AO [11]. [PERSON] et al. measured SCG from adults in a supine position without any tasks and aimed to detect peaks in the systolic phase [12]. The main problem with the abovementioned methods is that they rely on the availability of ECG signals. However, ECG sensor instrumentation is more demanding than that of SCG. It usually uses several electrodes placed on the subject's body with good skin-electrode contact. If the main goal is to measure HRV or heartrate (HR), then accelerometers provide easy instrumentation at an affordable price. This calls for methods to detect various important peaks in SCG in the absence of ECG. Attempting to exclude ECG signals from AO detection, researchers have used cardiac cycle envelope (CCE) detection estimated from SCG as a guide [13; 14; 15; 16] in combination with signals measured by a 3D gyroscope [17], a machine learning algorithm [18], a match-filter [8] and simple moving average (SMA) [19]. Although the results are promising, the proposed algorithms suffer from various parameter settings and only work well for good SCG signals, characterized by low noise, clear separation between adjacent cardiac beats and higher peak in the systolic than in the diastolic phase. In addition, most of these algorithms were evaluated against SCG signals measured from mainly healthy adults in a supine position, thereby limiting their applicability. Some algorithms were also too complex and might not be suitable for real-time analysis. In this paper, we proposed and evaluated two methods to detect AO from only SCG signals for real-time application. The methods relied on the discrete wavelet transform (DWT) either to guide SCG segmentation for each cardiac cycle, prior to AO detection, or to find AO detection directly without segmentation. SCG signals were measured from both children/infants and adults at resting state by using an accelerometer placed on the chest. In addition to a normal resting situation, the developed algorithms were tested using various breathing tasks (adults only).