# Blockwise PPG Enhancement Based on Time-Variant Zero-Phase Harmonic Notch Filtering

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## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Adaptive Comb Filter

_{1j}= (1 + r

_{j})cos(jθ), a

_{2j}= −r

_{j}, b

_{1j}= −2cos(jθ), and k

_{j}= (1 + r

_{j})/2. j represents the order of harmonics. jθ represents the j-th notch frequency, and θ is the fundamental frequency (instantaneous HR). The parameter P is the number of harmonic components, and r

_{j}is the pole-zero contraction factor (0 < r

_{j}< 1). According to a decrease of the value of r

_{j}from 1 to 0, the frequency response of the j-th notch filter becomes wider. Because the variance of a high-order harmonic frequency is larger than that of a low-order harmonic frequency, it is necessary to filter out high-order harmonic components using a wide bandwidth filter to address the HR estimation error caused by the variation of HR. Hence, with increasing harmonic order j, r

_{j}need to be smaller, so in this study we define r

_{j}, with a positive small value δ (typically 0.02~0.04) as follows:

_{ACF}[n] is acquired as follows:

#### 2.2. Zero-Phase Line Enhancer

^{jω}) are written as

**y**

_{ZLE}as follows:

**u**= [u[0], u[1], u[2], … u[N−1]]

^{T}and

**w**= [w[0], w[1], w[2], … w[N−1]]

^{T}. N is the length of the input sequence. As a result, we can construct the ZLE, which combines the time-variant forward-backward harmonic notch filter with a frequency estimator, as seen in Figure 5. In this study, we employed the ALNF as the frequency estimator.

#### 2.3. Real-Time Implementation of Zero-Phase Line Enhancer

#### 2.4. Performance Comparison under Colored Noise Interference

#### 2.5. Data Acquisition

^{®}PPG100C) from one female and seven male subjects (27.1 ± 3.4). Two PPG sensors were mounted on the right and left index fingers, and all subjects were instructed to move their right hand randomly to measure the contaminated PPG and to hold their left hand motionless for the reference PPG. Eight subjects participated in the experiment with 3 different experimental conditions: finger bending, elbow bending, and arm swing. In total, 24 datasets were collected at a 100 Hz sampling frequency over 3 min, and preprocessing was performed with a bandpass filter (0.5–10 Hz) using a third-order Butterworth IIR bandpass filter. Because the frequency estimator (ALNF) requires time to converge, we excluded the initial 1000 samples (10 s) in each data set for our analysis. The institutional review board of the Gwangju Institute of Science and Technology approved all procedures in this study.

## 3. Results

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

MA | Motion artifact |

PPG | Photoplethysmogram |

ECG | Electrocardiogram |

HR | Heart rate |

RR | Respiratory rate |

HRV | Heart rate variability |

ANC | Adaptive noise canceller |

ICA | Independent Component Analysis |

CFSA | Cycle by cycle Fourier series analysis |

SSA | Singular spectrum analysis |

ACF | Adaptive comb filter |

IIR | Infinite impulse response |

FIR | Finite impulse response |

ZLE | Zero-phase line enhancer |

ALNF | Adaptive lattice notch filter |

MAE | Mean absolute error |

Se | Sensitivity |

PPV | Positive predictive value |

SNR | Signal-to-noise ratio |

LTV | linear time-variant |

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**Figure 3.**Direct form 2 implementation of j-th IIR notch filter of harmonic IIR notch filter. a

_{1j}= (1 + r

_{j})cos(jθ(n)), a

_{2j}= −r

_{j}, b

_{1j}= −2cos(jθ(n)), and k

_{j}= (1 + r

_{j})/2.

**Figure 4.**Bode plot for ACF. The shape of the frequency response of ACF is determined by δ in Equation (2). The annotation δ↑ indicates the increment of the value of δ.

**Figure 7.**Simulation results. Dotted line, dashed line, asterisks, and solid line represent the results of wavelet de-noising method, CFSA, ACF and ZLE, respectively. (

**a**) Correlation coefficient; (

**b**) F1; (

**c**) MAE.

**Figure 8.**Reference, raw, and reconstructed PPG. Dashed line, dotted line, and solid line represent reference, raw, and reconstructed PPG, respectively. (

**a**) Wavelet de-noising method; (

**b**) CFSA; (

**c**) ACF; (

**d**) ZLE.

**Figure 9.**Periodogram power spectral density for PPG. Dashed line, dotted line, and solid line represent spectrums of reference, raw, and reconstructed PPG, respectively.

**Figure 10.**Distribution of correlation coefficient between reference and filtered PPG reconstructed by each MA reduction method. Upper and lower boxes represent the distribution of correlation coefficients from 25th to 75th percentiles. Top and bottom line indicate the 90th and 10th percentiles. (

**a**) Wavelet de-noising method; (

**b**) CFSA; (

**c**) ACF; (

**d**) ZLE.

**Figure 11.**Distribution of F1 scores for filtered PPG reconstructed by each MA reduction method. Upper and lower boxes represent the distribution of correlation coefficients from 25th to 75th percentiles. Top and bottom line indicate the 90th and 10th percentiles. (

**a**) Wavelet de-noising method; (

**b**) CFSA; (

**c**) ACF; (

**d**) ZLE.

**Figure 12.**Distribution of MAE for filtered PPG reconstructed by each MA reduction method. Upper and lower boxes represent the distribution of correlation coefficients from 25th to 75th percentiles. Top and bottom line indicate the 90th and 10th percentiles. (

**a**) Wavelet de-noising method; (

**b**) CFSA; (

**c**) ACF; (

**d**) ZLE.

**Table 1.**Correlation coefficients according to motions and methods. Data are expressed as mean ± standard deviation.

Wavelet | CFSA | ACF | ZLE | |
---|---|---|---|---|

Finger Bending | 0.8237 ± 0.0716 | 0.7405 ± 0.0945 | 0.7824 ± 0.1082 | 0.8728 ± 0.0976 |

Elbow Bending | 0.8777 ± 0.0548 | 0.8357 ± 0.0569 | 0.8619 ± 0.0523 | 0.9262 ± 0.0287 |

Arm Swing | 0.8352 ± 0.0822 | 0.7956 ± 0.0929 | 0.8198 ± 0.1000 | 0.9043 ± 0.0526 |

Total | 0.8455 ± 0.0713 | 0.7906 ± 0.0890 | 0.8214 ± 0.0924 | 0.9011 ± 0.0670 |

Wavelet | CFSA | ACF | ZLE | |
---|---|---|---|---|

MAE (ms) | 1.5078 ± 0.5645 | 1.5400 ± 0.5570 | 1.5582 ± 0.5499 | 1.4371 ± 0.5625 |

Se (%) | 93.1247 ± 7.2786 | 91.5446 ± 8.1233 | 89.8683 ± 8.7489 | 96.2713 ± 4.4469 |

PPV (%) | 93.8799 ± 6.5653 | 93.6469 ± 6.3911 | 91.8527 ± 7.7115 | 96.5478 ± 4.1635 |

F1 (%) | 93.4971 ± 6.9150 | 92.5655 ± 7.2395 | 90.8341 ± 8.1817 | 96.4068 ± 4.2807 |

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Park, C.; Shin, H.; Lee, B.
Blockwise PPG Enhancement Based on Time-Variant Zero-Phase Harmonic Notch Filtering. *Sensors* **2017**, *17*, 860.
https://doi.org/10.3390/s17040860

**AMA Style**

Park C, Shin H, Lee B.
Blockwise PPG Enhancement Based on Time-Variant Zero-Phase Harmonic Notch Filtering. *Sensors*. 2017; 17(4):860.
https://doi.org/10.3390/s17040860

**Chicago/Turabian Style**

Park, Chanki, Hyunsoon Shin, and Boreom Lee.
2017. "Blockwise PPG Enhancement Based on Time-Variant Zero-Phase Harmonic Notch Filtering" *Sensors* 17, no. 4: 860.
https://doi.org/10.3390/s17040860