## 2 Methodology
### Data Pre-Processing  
A total of 767,324 synchronized EMG and GRF datapoints in 1918 strides, including 640 uphill, 704 level walking and 574 downhill, were selected. The pre-processing of the EMG and GRF signals was performed in MATLAB.  
The raw EMG signal needs to be filtered before it can be used for further analysis because it is interfered with by noise. For the high-frequency region, most of the energy of the EMG signal mainly concentrates within 0-500 Hz [46], and the high-frequency region (500-1000 Hz) of the EMG signal is likely to be interfered with by aliasing, according to [47; 48]. For the low-frequency region, the frequency range of the movement artifacts, which is a type of noise caused by the movement of the cable and the interface between the detection surface of the electrode and the skin, is typically 1-10 Hz [49]. Therefore, the raw EMG signal was filtered by a finite impulse response (FIR) bandpass filter with cutoff frequencies of 10 (low) and 500 Hz (high) [41; 50; 51; 52].  
After denoising, we applied normalization to the EMG amplitude to reduce the inter-subject variability of the EMG signals. The widely applied normalization references include the peak of EMG from the ensemble average, the mean of the ensemble average, and maximal isometric voluntary contraction (MIVC) [53]. In this work, a MVC was chosen because it is less likely to be affected by joint kinematics like knee or ankle flexion. Furthermore, different levels of MVC have been researched, and 50% has been proven to be an optimal point as it is easier to be reached and maintained by the experiment participants, according to [54; 55]. Hence, the EMG amplitude in this work was normalized by 50% MVC. Furthermore, we also calculated the linear envelope (LE) of the EMG signal, which is an intuitive processing method of EMG reflecting the muscle force level [56]. Specifically, a full-wave  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Relevant Work** & **Ramp Angle** \\ \hline
[22] & 4.78 degree \\
[27] & 10 degree \\
[31] & 10 degree \\
[19] & 12 degree \\
[35] & 8.5 degree \\ This work & 5.2 degree \\ \hline \hline \end{tabular}
\end{table}
Table 2: Ramp angles selected in other relevant studies and comparison with our work.  
rectification and a lowpass filter with a cutoff frequency of 3 Hz were used to obtain the LE, as previous research has evidenced the ability of the 3 Hz cutoff frequency to provide good relations with muscle force [56; 57; 58; 59; 60].  
The GRF data was normalized to the body weight of each participant [61]. An important function of the GRF signal is for segmenting the collected data sequence into complete stride sequences. Here, the GRF data (without normalization) were binarized with a threshold of 300 g [43]. The timing of the binarized data, changing from 0 to 1, of the heel was considered as the timing of the heel strike (HS), and the interval of the two consecutive HSs was seen as the duration of a complete gait [62; 63]. In this way, the GRF and EMG data were segmented into a group of strides.  
Finally, we generate the profiles of the EMG, LE and GRF curves in each stride by calculating the ensemble average of the signals from all the participants. The ensemble average is obtained by the following procedure: Firstly, the stride time divided by the HS was normalized to 100%, and then all the EMG, LE and GRF curve data at each consecutive 1% of the normalized stride time were selected and averaged, producing the ensemble average [56]. Finally, a standard deviation (SD) band of \(\pm\)1 about the average was calculated to quantify the variability of each stride [56].