## 2 Dataset and Feature Extraction
### Autocorrelation Function-Based Power Spectral Feature Extraction Process  
Preprocessing steps produced resampled wave signals from the PPG dataset for feature extraction, as shown in the boxes on the left side of Figure 1. Subsequently, the autocorrelation for feature extraction was calculated, as shown in the eighth box in Figure 1. The autocorrelation can be used to determine the periodicity in the time domain. The autocorrelation function relies on the difference between the discrete times \(n\) and \(n+m\). If \(m=0\) (lag 0), the autocorrelation denotes the maximum value representing the total energy of the input value. Given the measurements \(z=\{z_{n}\}_{n=1}^{N}\) at a discrete-time lag \(m\), in practice, we define the autocorrelation function as  
\[\rho_{m}(z)=\frac{\sum_{n=1}^{N}(z_{n}-\mu_{z})(z_{n+m}-\mu_{z})}{\sum_{n=1}^{ N}(z_{n}-\mu_{z})^{2}} \tag{1}\]  
where \(z\) denotes a data point obtained from the segmented wave signal and \(\mu_{z}=\sum_{n=1}^{N}z_{n}\) denotes the mean. The power spectral is a fast Fourier transform of the autocorrelation  
Figure 2: Upper panel (**a**) is an example (10 breath per minute) 4 th record PPG signal, and lower panel (**b**) is an example (50 breath per minute) 24 th record PPG signal, where the 4 th record represents the 4 th of 192 records.  
function and effectively represents information about the time series of a biological signal [41]. The time-axis correspondence of a power spectral denotes an autocorrelation function because the time-axis autocorrelation function is equal to the square of the amplitude spectrum. Hence, we obtained the power spectral of all components within 0.1-2.5 Hz. The CAGBA model extracts relevant features from the power spectral, automatically learns, and subsequently estimates RR. A low frequency (\(\leq\)0.5) with each spectral power can be an efficient feature for estimating RR. Each record had a length of 210 s, and the sampling frequency (Fs) was 500 Hz. Thus, 105,000 experimental sampled data points were prepared for each subject, as shown in Figure 2a,b. Figure 2 shows examples of PPG signals extracted for only 30 s out of 210 s of the 4 th and 24 th subject's PPG signals. After preprocessing, a clean wave signal was prepared, as shown in Figure 3a. Next, the clean waveform (6 ppm) was split using a 32 s window, as shown in Figure 3b. The 32 s window did not overlap. Figure 3c shows that the segmented waveform is converted to an autocorrelation coefficient. Subsequently, the power spectral was obtained, as shown in Figure 3d. Finally, the features were acquired by connecting the six power spectral in Figure 3e. In addition to the aforementioned method, power spectral features can be obtained, as shown in Figure 3e, by connecting six power spectral in Figure 3d, which are the signals obtained from the 2 th subjects. Specifically, we obtain the resample wave signal from the PPG signals 210 s and reshape into (6 \(\times\) 32 s window). Next, we acquire the autocorrelation and obtain the power spectral 6 \(\times\) 256 (=1542) data points using FFT as shown in Figure 3e.  
Figure 3: Top panel (**a**) is a resampled wave signal from the 2 nd subject PPG signal, panel (**b**) is a segmented wave signal from the resampled wave signal (**a**), panel (**c**) denotes an autocorrelation signal from the segmented wave signal (**b**), panel (**d**) is a power spectral from (**c**) the autocorrelation signal, and bottom panel (**e**) denotes the power spectral feature (PSF) from the power spectral (**d**).