The behavior of High-Impedance Faults (HIFs) in power distribution systems depends on multiple factors, making it a challenging disturbance to model. If enough data from real staged faults is provided, signal processing techniques can help reveal patterns from a specific type of fault. Such a task is implemented herein by employing the Shift-Invariant Sparse Coding (SISC) technique on a data set of staged vegetation high-impedance faults. The technique facilitates the uncoupling of shifted and convoluted patterns present in the recorded signals from fault tests. The deconvolution of these patterns was then individually studied to identify the possible repeating fault signatures. The work is primarily focused on the investigation of the under-discussed high-frequency faults signals, especially regarding voltage disturbances created by the fault currents. Therefore, the main contribution from this paper is the resulted evidence of consistent behavior from real vegetation HIFs at higher frequencies. These results can enhance phenomena awareness and support future methodologies dealing with these disturbances.