140:12·L.Wang et al. Rawg 0.5 20 40 080 100 120 40080100 120 40 80 100 120 Sample index Sample index Sample index (a)Raw signal (b)Level 1 (c)Level 2 0.5 D.5 a.s 0.5 20406080 100120 20 40 60 80 100 120 20 80100 120 Sample index Sample index Sample index (d)Level 3 (e)Level 4 (f)Level5 Fig.10.Five levels of DWT decompositions capturing process.These noises reduce the reliability of the raw SCG sequence.Figure 9(b)shows the correlation coefficients of the raw SCG sequences between the same five users as in Figure 9(a).A higher correlation coefficient means that the two samples are more similar to each other.We observe that some users,e.g.,user 3,the correlation coefficients between his/her own samples are low due to the noises in SCG.Therefore,directly using the raw SCG sequences as features leads to high false negative rate,where the user's own heartbeat may be wrongly rejected due to noises in the SCG signals. In this paper,we use Discrete Wavelet Transform(DWT)to extract features from the SCG signal.The DWT decomposes the signal into two parts of coefficients:the approximation coefficients that represent the low- frequency components and the detailed coefficients that represent the high-frequency components.By iteratively applying the wavelet decomposition on the approximation coefficients,the DWT can separate the original signals into multiple levels that contain components in different frequency ranges. In our system,we use the discrete Meyer wavelet to decompose SCG signals into five levels.With a sampling rate of 100Hz,level 1 to 5 represent signal components in the frequency range of 25 ~50 Hz,12.5~25 Hz, 6.25~12.5 Hz,3.13~6.25 Hz and 1.56~3.13 Hz,respectively.Figure 10 shows the reconstructed SCG signals from the detailed coefficients at the five levels. To reduce noises from imperfections of the built-in accelerometers,we remove the high-frequency components in level 1.For heart rates in the range of 50~120 BPM,the heartbeat frequency is in the range of 1 ~2 Hz Therefore,we can remove level 5 where the signal component has a frequency lower than 3.13 Hz,which may not contain useful detailed features within a heartbeat cycle.In this way,we also remove the low-frequency movement interferences in the SCG signals.For example,the respiration movements have low frequencies in the range of 0.2 ~0.4 Hz[60]. In summary,we use the detailed coefficients from the second level to the fourth level as the feature vector for heartbeat authentication.For a normalized heartbeat signal with 128 samples,the resulting DWT-based feature is a 56 dimensional vector.Our DWT-based feature extraction scheme has the following two advantages.First,by removing the coefficients in level 1 and below level 5,we reduce the noises in the SCG signal.Second,DWT has high time-resolution at levels representing the high-frequency components.Therefore,the high-frequency components retain the time intervals of sharp peaks in the SCG.For low-frequency components in the SCG, DWT is more tolerable in variations in the time domain.In this way,we achieve a balance between keeping the timing information and tolerating the variations in the heartbeat stages.Figure 9(c)shows the correlation coefficients of the DWT features for the five users.We observe that our DWT-based features outperform both the raw SCG features and the DTW based distance. Proc.ACM Interact.Mob.Wearable Ubiquitous Technol.,Vol.2,No.3,Article 140.Publication date:September 2018.140:12 • L. Wang et al. 0 20 40 60 80100120 Sample index -0.5 0 0.5 Acceleration (m/s 2 ) Raw signal (a) Raw signal 0 20 40 60 80100120 Sample index -0.5 0 0.5 Acceleration (m/s 2 ) Level 1 (b) Level 1 0 20 40 60 80100120 Sample index -0.5 0 0.5 Acceleration (m/s 2 ) Level 2 (c) Level 2 0 20 40 60 80100120 Sample index -0.5 0 0.5 Acceleration (m/s 2 ) Level 3 (d) Level 3 0 20 40 60 80100120 Sample index -0.5 0 0.5 Acceleration (m/s 2 ) Level 4 (e) Level 4 0 20 40 60 80100120 Sample index -0.5 0 0.5 Acceleration (m/s 2 ) Level 5 (f) Level 5 Fig. 10. Five levels of DWT decompositions capturing process. These noises reduce the reliability of the raw SCG sequence. Figure 9(b) shows the correlation coefficients of the raw SCG sequences between the same five users as in Figure 9(a). A higher correlation coefficient means that the two samples are more similar to each other. We observe that some users, e.g., user 3, the correlation coefficients between his/her own samples are low due to the noises in SCG. Therefore, directly using the raw SCG sequences as features leads to high false negative rate, where the user’s own heartbeat may be wrongly rejected due to noises in the SCG signals. In this paper, we use Discrete Wavelet Transform (DWT) to extract features from the SCG signal. The DWT decomposes the signal into two parts of coefficients: the approximation coefficients that represent the low￾frequency components and the detailed coefficients that represent the high-frequency components. By iteratively applying the wavelet decomposition on the approximation coefficients, the DWT can separate the original signals into multiple levels that contain components in different frequency ranges. In our system, we use the discrete Meyer wavelet to decompose SCG signals into five levels. With a sampling rate of 100Hz, level 1 to 5 represent signal components in the frequency range of 25 ∼ 50 Hz, 12.5 ∼ 25 Hz, 6.25 ∼ 12.5 Hz, 3.13 ∼ 6.25 Hz and 1.56 ∼ 3.13 Hz, respectively. Figure 10 shows the reconstructed SCG signals from the detailed coefficients at the five levels. To reduce noises from imperfections of the built-in accelerometers, we remove the high-frequency components in level 1. For heart rates in the range of 50∼120 BPM, the heartbeat frequency is in the range of 1 ∼ 2 Hz. Therefore, we can remove level 5 where the signal component has a frequency lower than 3.13 Hz, which may not contain useful detailed features within a heartbeat cycle. In this way, we also remove the low-frequency movement interferences in the SCG signals. For example, the respiration movements have low frequencies in the range of 0.2 ∼ 0.4 Hz [60]. In summary, we use the detailed coefficients from the second level to the fourth level as the feature vector for heartbeat authentication. For a normalized heartbeat signal with 128 samples, the resulting DWT-based feature is a 56 dimensional vector. Our DWT-based feature extraction scheme has the following two advantages. First, by removing the coefficients in level 1 and below level 5, we reduce the noises in the SCG signal. Second, DWT has high time-resolution at levels representing the high-frequency components. Therefore, the high-frequency components retain the time intervals of sharp peaks in the SCG. For low-frequency components in the SCG, DWT is more tolerable in variations in the time domain. In this way, we achieve a balance between keeping the timing information and tolerating the variations in the heartbeat stages. Figure 9(c) shows the correlation coefficients of the DWT features for the five users. We observe that our DWT-based features outperform both the raw SCG features and the DTW based distance. Proc. ACM Interact. Mob. Wearable Ubiquitous Technol., Vol. 2, No. 3, Article 140. Publication date: September 2018