# PPG and Bioimpedance-Based Wearable Applications in Heart Rate Monitoring--A Comprehensive Review
## 5 Heart Rate Monitoring
### With supplementary acceleration signals
In case of valleys, the process is identical, except that the slope parameter acts to increase the value of threshold until the threshold crosses the PPG signal and \(V_{min}\) is found. This process is repeated until all inflection points \(V_{max}\) and \(V_{min}\) are found. The initial and modified slope parameters are given by [36]\(slope_{int}\)=[0.2 \(\times\) argmaxPPG in peak \(V_{max}\) detection, 0.2 \(\times\) argminPPG in valley \(V_{min}\) detection] and \(slope_{k}=slope_{k-1}+s_{r}\frac{(V_{max}+\sigma_{PPG})}{f_{s}}\), respectively. Here, \(slope_{k}\) is the amplitude of the k-th slope, \(s_{r}\) is the rate of slope change (empirically selected as \(-\)0.6 and 0.6 for \(V_{max}\) and \(V_{min}\), respectively), \(V_{n-1}\) is the amplitude of the previous peak, \(\sigma_{PPG}\) is the standard deviation of an entire PPG signal, and \(f_{s}\) is the sampling frequency. The principle of the ADT method is illustrated in Figure 14. The period of a PPG signal is defined as an \"in-sensing period\" when the detection threshold conforms to the waveform of the signal, whereas in an \"out-of-sensing period\" the slope parameter of the threshold is fixed. In the spectral subtraction (SS) method, a spectrum of a supplementary acceleration signal is subtracted from a spectrum of a signal [99]. The authors in [69] suggested computing the correlation coefficient between normalized magnitudes of acceleration and PPG periodograms. When the correlation coefficient was smaller than a threshold value (set to 0.5), SS was not performed, as MAs were not dominant in the PPG signal. Otherwise, both acceleration and PPG signals were used. In [100], the SS method was performed in an asymmetric least squares manner to improve the outcome of MA removal. The drawbacks are as follows [69]: SS is only effective when the spectral components are matched. Otherwise, the use of SS could potentially lead to false spectral peaks. In [72], the Wiener filter was used to filter a measured PPG signal in frequency domain by SS according to  
\[P_{C}(i)\approx P_{S}(i)-P_{A/G}(i)=\left(\frac{P_{S}(i)-P_{A/G}(i)}{P_{S}(i)} \right)\times P_{S}(i)\approx\left(\frac{P_{C}(i)}{P_{C}(i)-P_{A/G}(i)}\right) \times P_{S}(i) \tag{12}\]  
where \(P_{S}(i)\) is the spectrum of the measured PPG signal containing MA, \(P_{C}(i)\) is the spectrum of the MA-free PPG signal and \(P_{A/G}(i)\) is the spectrum of acceleration or gyroscope signal. After the application of the Wiener filter, the MA removal results are as seen in Figure 15.  
Figure 13: Fourier decomposition of a PPG signal into Fourier intrinsic band functions (FIBS)—(**a**) zero-phase filter bank into (**b**) a set of ten FIBFs obtained after decomposition [9]. In case 1, the dominant frequency of \(P_{S}(i)\) overlaps only with that of \(P_{A}(i)\). Then the acceleration signal provides the correct MA reference, since the realization of SS subtracts the dominant frequency peak corresponding to MA. In case 2, the dominant frequency of \(P_{S}(i)\) overlaps only with that of \(P_{G}(i)\). Then, only the gyroscope signal provides the correct MA reference. Figure 14: Adaptive detection threshold method for detection of peaks of PPG signal and MA removal [36]. Figure 15: Cancellation of motion artifacts (MAs) using acceleration and gyroscope signals—Case 1 (**a–c**) when acceleration signal correctly cancels out MA; Case 2 (**d–f**) when gyroscope signal correctly cancels out MA [72].