Table A1.

Pseudo-code of the ENVELOPE and SLOPE beat detection algorithms. Bold type in variable names indicates arrays.

ENVELOPE

SLOPE

# PPG PROCESSING Compute:      x’(t) = first derivative of the PPG signal      emin(t) = inferior envelope of x’(t)      emax(t) = superior envelope of x’(t)      x’norm(t) = min-max normalization of x’(t) as in                        Equation (4) # HEARTBEAT DETECTION Define:      thENV = threshold for the identification of                    heartbeats from x’norm(t); set to 0.8 Find:      tpeaks = occurrence time of the local maxima of            x’norm(t) exceeding thENV # FALSE POSITIVES REDUCTION Define:      $\overline{IBI}$= median peak-to-peak distance between all              the elements in tpeaks      N = number of peaks in tpeaks      i = 1 While i < N Take the occurrence time of the i-th peak (ti) Calculate the difference between ti and the occurrence time of all the other elements in tpeaks: ti − t1, ti − t2, …, ti − tN Compare these differences to $\overline{IBI}$ by using Equation (2), from which d = [d1, d2, …, dN] is obtained For each i < k ≤ N, find the lowest dk and define:   j = k-th peak that minimizes d Discard all the peaks included between i and j-1 from tpeaks, if any, as they are false positives Update $\overline{IBI}$ as in Equation (4) and set i = j for the next iteration End # IBI CALCULATION Compute:      IBIENV = difference between consecutive elements             of the remaining occurrence times in tpeaks

# PPG PROCESSING Define:      x(t) = PPG signal      N = number of samples in x(t) # HEARTBEAT DETECTION Define:      RP = refractory period; initialized to 0.6 s      RPchange = multiplier for RP updates; set to 0.6      slope = slope coefficient for the adaptive threshold;        initialized to 0.2*max(x(t))      tinit = occurrence time of the first increasing        segment found in x(t)      th(t) = adaptive threshold, initialized to x(tinit)      i = sample of x(t) corresponding to tinit While i < N Increase i until a peak is found on x(t); define j as the sample of x(t) corresponding to this peak Add tj (occurrence time of the peak) to the array of the peaks found so far (tpeaks) Make th(t) = x(t) until the j-th sample is reached Update the slope parameter as shown in Equation (2) of [41] Linearly decrease th(t) starting from the peak found on x(t), using the updated slope When th(t) intersects x(t):      If RP has passed       Proceed to step 7      Else       Continue to linearly decrease th(t) and       repeat this check at the next point of       intersection      End Compute the average IBI ($\overline{IBI}$) from the tpeaks found so far and update RP for the next iteration: RP = RPchange ∗ $\overline{IBI}$ Update i to the sample where th(t) intersected x(t) and proceed with the next iteration End # IBI CALCULATION Compute:      IBISLOPE = difference between consecutive            elements of tpeaks