# PPG and Bioimpedance-Based Wearable Applications in Heart Rate Monitoring--A Comprehensive Review
## 5 Heart Rate Monitoring
### With supplementary acceleration signals  
Several algorithms in the literature require reference accelerometer signals to remove MAs from a PPG signal. Other references in the form of a gyroscope [86], piezoelectric sensor [87] or LED/PD [88] signals have also been used. The adaptive filtering family of methods include different variations of the least squares algorithm, for example, least mean squares (LMS) [89], normalized least mean squares (NLMS) [90], and recursive least squares (RLS) [91]. A combination of the above-mentioned algorithms has been used in [92]. Frequency content of MAs can be found both inside and outside of the spectral range of human heart rate. In order to remove the outside spectral component of MA, a fourth-order Butterworth band-pass filter with a cut-off frequency band from 0.5 Hz to 3.5 Hz was applied in [71], while the range of 0.4 Hz to 4 Hz was used in [93; 94]. The authors explained that this range translates to 0.6 Hz-3.3 Hz of heart rate, covering subjects of all ages at different intensities of physical activity. On the other hand, the in-band spectral component of MA was canceled by employing a fourth-order LMS filter with a step size of 0.01. The advantages are as follows [71]:  
* Low computation complexity allows for a real-time signal processing. The drawbacks are as follows [9]:
* The correlation between the reference signal and the motion spectrum has to be sufficiently high, which is impossible in practice. * Very high computational requirements. Another adaptive filtering method is Fourier decomposition (FD). FD decomposes the signal into a Q-number of orthogonal or linearly dependent and energy preserving Fourier intrinsic band functions (FIBFs) within the desired frequency band  
\[S[n]=C_{0}+\sum_{l=1}^{Q}X_{l}[n] \tag{10}\]  
where \(C_{0}\) is the mean of the signal \(S[n]\), \(X_{l}[n]\) denotes the Qth FIBF. FIBFS themselves are obtained from a the inverse discrete cosine transform (IDCT)-based zero-phase filter bank as depicted in Figure 12(a). \[FIBS_{l}=\sqrt{\frac{2}{n}}\sum_{k=0}^{N=1}\sigma_{k}H_{l}[k]X_{c2}\cos\left( \frac{\pi k(2n+1)}{2N}\right) \tag{11}\]  
where \(X_{c2}[k]\) is the N-length DCT of the signal \(S[n]\), \(H_{l}[k]\) is the zero-phase filter and the normalization factor \(\sigma_{k}\) is given by \(\sigma_{k}=\frac{1}{\sqrt{2}}\) if \(k=0\) and 1 if \(k\
eq 0\)[9]. FIBFs are derived from the input data; thus, they are data-dependent. As the data changes, the FIBFs adapt to the transition and change their values accordingly. The FIBFS obtained from a PPG signal are shown in Figure 12(b). FIBF0 and FIBF1 contain low-frequency signal information, such as respiratory signals. FIBF2 through FIBF6 represent the MA components and FIBF7 and FIBF8 contain most of the information of the PPG signal which can be used for signal reconstruction without the MAs [9]. Even though the FD overcomes the drawbacks of EMD in terms of mathematical complexity, detrend uncertainty, and mode mixing [9], there are some drawbacks. Specifically, the drawbacks include the following [95; 96]: the process is time-consuming; a large number of data samples for data processing are needed, making it unfeasible in mobile device applications. In case the frequency of the MA is close to that of the feature we are interested in (for example, heart rate), the MA cannot be suppressed [9]. The adaptive detection threshold method (ADT) uses a threshold that reacts to PPG waveform amplitude in order to detect peaks and valleys [97; 98]. Compared to FD, ADT is more flexible, less time-consuming and not dependent on baseline drift. In addition, a peak correction technique was also used to ignore the unwanted diastolic peaks. In the ADT method, two different adaptive thresholds are created to detect PPG peaks \((V_{max})\) and PPG valleys \((V_{min})\). Starting from a peak of the signal, the upper threshold is decreased with a slope parameter until it crosses the PPG signal. Afterwards, this threshold follows the waveform of a signal until it reaches the inflection point \((V_{max})\).