RF-ECG:Heart Rate Variability Assessment Based on COTS RFID Tag Array.85:15 Attenuation ●0● Original Signal ∽MMM Filtered Signal ●0● Attenuation →A Fig.12.Illustration of DWT denoising flow. 4.4 DWT-based Denoising After eliminating the respiration signal caused by the moving effect,there still exist some noises in the remaining signals,as the approximated respiration signal derived from the moving effect cannot completely be consistent with the actual respiration signal.Hence,we use the Discrete Wavelet Transform(DWT)-based denoising method to further remove the noises from the remaining signals.Compared with other filtering techniques,the Discrete Wavelet Transform can analyze the signal in both time and frequency domain without making any assumption about the nature of the signal.It decomposes the signals into the approximation coefficients and the detailed coefficients.The approximation coefficients denote the low frequency signals,which correspond to the residual components of the respiration signals.The detailed coefficients denote the signal details of the heartbeat as well as the high frequency noises.As the heartbeat usually falls in the frequency range of 1~2Hz,we are able to further remove the residual noises by filtering out both the approximation coefficients and the detailed coefficients in higher frequency band. In particular,the DWT method includes three steps.1)Decomposition:We first run the DWT-based signal decomposition recursively by 9 levels with Symlet wavelet filter [33].The DWT generates the approximation coefficients yapp and a sequence of detailed coefficients yerye.,where yet has higher frequency than y)Filtering:We apply the filtering method to extract the components corresponding to the heartbeat frequency band.In particular,we remove the approximation coefficients yapp which is related to the large displacement from chest movement.Meanwhile,we keep the detailed coefficientsyunchanged, which correspond to the frequency about the heart beat(ranging from 0.7Hz to 5.6Hz).In regard to the other components,since they are mainly related to the noisy signal,we reduce them to 20%according to our empirical study,which can remove most noise and keep the sufficient details about heart beat.3)Reconstruction:By combining all the remaining coefficients(i.e.,the detailed coefficients after filtering),we reconstruct the final phase trends with the inverse DWT as follows:{0(1),...,0'(t)).The reconstructed measurements enable us to remove the noise components while keeping the heartbeat related phase signal.In Figure 12,we show an example to illustrate the DWT denoising flow.Note that after DWT,the original decreasing trend of the signals is removed,while the detailed heartbeat influence remains.Therefore,DWT facilitates accurate inter-beat interval estimation,when the respiration signal is not fully removed. 4.5 Signal Fusion from RFID Tag Array After denoising the signals based on DWT,we can observe fairly clear periodic pattern caused by the heartbeat from these signals.According to the model in Section 3.3,the current signals S,still contain two components,i.e., S.o.which is the mixture of LOS signal and reflection signal from the static background environment,and S.. which is the reflection signal from the heartbeat movement.Since it is difficult to measure the signal Sr.o like Section 3.3 by simply removing the heartbeat,we can select a sufficiently large time interval,and use the averaged Proc.ACM Interact.Mob.Wearable Ubiquitous Technol,Vol.2,No.2,Article 85.Publication date:June 2018.RF-ECG: Heart Rate Variability Assessment Based on COTS RFID Tag Array • 85:15 0 2 4 6 8 -0.4 -0.3 -0.2 -0.1 0 0 2 4 6 8 -0.1 -0.05 0 0.05 0.1 Original Signal Decomposing Filtered Signal Recomposing !"## ! ' $%& ! ( $%& ! ) $%& ! * $%& Attenuation Attenuation Fig. 12. Illustration of DWT denoising flow. 4.4 DWT-based Denoising After eliminating the respiration signal caused by the moving effect, there still exist some noises in the remaining signals, as the approximated respiration signal derived from the moving effect cannot completely be consistent with the actual respiration signal. Hence, we use the Discrete Wavelet Transform (DWT)-based denoising method to further remove the noises from the remaining signals. Compared with other filtering techniques, the Discrete Wavelet Transform can analyze the signal in both time and frequency domain without making any assumption about the nature of the signal. It decomposes the signals into the approximation coefficients and the detailed coefficients. The approximation coefficients denote the low frequency signals, which correspond to the residual components of the respiration signals. The detailed coefficients denote the signal details of the heartbeat as well as the high frequency noises. As the heartbeat usually falls in the frequency range of 1 ∼ 2Hz, we are able to further remove the residual noises by filtering out both the approximation coefficients and the detailed coefficients in higher frequency band. In particular, the DWT method includes three steps. 1) Decomposition: We first run the DWT-based signal decomposition recursively by 9 levels with Symlet wavelet filter [33]. The DWT generates the approximation coefficients yapp and a sequence of detailed coefficients y 1 det,y 2 det, · · · ,y 9 det , where y 1 det has higher frequency than y 9 det . 2) Filtering: We apply the filtering method to extract the components corresponding to the heartbeat frequency band. In particular, we remove the approximation coefficients yapp which is related to the large displacement from chest movement. Meanwhile, we keep the detailed coefficients y 5 det, · · · ,y 8 det unchanged, which correspond to the frequency about the heart beat (ranging from 0.7Hz to 5.6Hz). In regard to the other components, since they are mainly related to the noisy signal, we reduce them to 20% according to our empirical study, which can remove most noise and keep the sufficient details about heart beat. 3) Reconstruction: By combining all the remaining coefficients (i.e., the detailed coefficients after filtering), we reconstruct the final phase trends with the inverse DWT as follows: {θb′ i (1), · · · , θb′ i (t)}. The reconstructed measurements enable us to remove the noise components while keeping the heartbeat related phase signal. In Figure 12, we show an example to illustrate the DWT denoising flow. Note that after DWT, the original decreasing trend of the signals is removed, while the detailed heartbeat influence remains. Therefore, DWT facilitates accurate inter-beat interval estimation, when the respiration signal is not fully removed. 4.5 Signal Fusion from RFID Tag Array After denoising the signals based on DWT, we can observe fairly clear periodic pattern caused by the heartbeat from these signals. According to the model in Section 3.3, the current signals Sr still contain two components, i.e., Sr,0, which is the mixture of LOS signal and reflection signal from the static background environment, and Sr,1, which is the reflection signal from the heartbeat movement. Since it is difficult to measure the signal Sr,0 like Section 3.3 by simply removing the heartbeat, we can select a sufficiently large time interval, and use the averaged Proc. ACM Interact. Mob. Wearable Ubiquitous Technol., Vol. 2, No. 2, Article 85. Publication date: June 2018