## 2 SEMG Space Extend  
This study proposes a space-to-space (SPS) framework for extracting features from sEMG signals, with the aim of describing specific signals by extracting structural characteristics from each sEMG channel. This framework is capable of extracting information from channel combinations, providing cross-channel patterns and background information on potential muscle synergy. The general procedure of the proposed method and the structure of SPS is shown in Figure 1.  
In traditional methods, after signal down-sampling, a lot of information is lost along with the reduction in signal data. Among the lost information, there is a lot of potentially valuable information.  
The extending operation mentioned in this paper is derived from the common down-sampling operation in images. For details, refer to SPD-Conv [22]. In ref. [22], the feature map of the original image is down-sampled to reduce the image resolution and avoid the loss of fine-grained information in the image. This paper refers to the idea of spatial conversion to depth and down-samples the original EMG segment according to time. Then, the down-sampled data are concatenated, releasing the time and space information in the EMG signal by transforming the EMG signal segment in space, and enriching the spatial domain information. The specific execution Equation (1) is as follows:  
\[\begin{split} f_{1}&=X[1:c,1:scale:n],\\ f_{2}&=X[1:c,2:scale:n],\\ &\ldots,\\ f_{scale}&=X[1:c,scale:scale:n]\end{split} \tag{1}\]  
In Equation (1), the function \(f(\dots)\) signifies the specific down-sampling operation, extending the original signal segment into scale parts and ultimately merging them into the newly expanded sEMG signal segment. By transforming the original signal feature segment \(X(c\times n)\), where \(n\) represents the length of the signal feature segments and \(c\) represents the number of signal channels, through signal folding, the original signal feature segment is transformed into \(X^{\prime}((c\times scale)\times\frac{n}{scale})\), where \(scale\) represents the extension factor (the extension factor can only be selected as a number that can be divided by \(n\), and it is necessary to ensure that the folded signal feature segment \(\frac{n}{scale}>c\times scale\).  
Taking \(scale=2\) as an example shown in Figure 1, for a signal segment \(X(c\times n)\) with current time length \(n\) and channel count \(c\), within \(f_{1}(\dots)\), starting at time point 0 for each of the \(c\) channels, a sampling operation occurs at intervals of \(scale\) units until reaching the boundary of the time segment. Subsequent operations \(f_{2}(\dots),\cdots,f_{scale}(\dots)\) mirror \(f_{1}(\dots)\). By iteratively applying these steps and concatenating the down-scaled \(f(\dots)\), the final result is the spatially expanded sEMG signal segment \(X^{\prime}((c\times scale)\times\frac{n}{scale})\), forming the basis for subsequent feature extraction.  
For the extended EMG signal segment, extract the temporal and frequency domain and the spatial information between channels. It can more effectively extract the hidden feature information within a single channel, and then provide multi-perspective information for subsequent feature extraction.  
Figure 1: The general procedure of the proposed method. The bottom is the structure of space-to-space (SPS).