Abstract An automatic tool-changing system (ATCS) is one of the key sub-systems for realizing automatic tool changing in machining centers. Each step in a tool-changing cycle tends to result in impacts, and thus generates transients in the vibration signal. The impact features often reflect important operational information related to the ATCS dynamics, and a crucial problem for impact-feature extraction is how to effectively represent the transients. A novel method for extracting impact features from an ATCS is proposed, based on sparse representation theory. A parametric multiple-impulse dictionary is constructed by the unit impulse-response function of a damped multiple-degree-of-freedom system, whose modal order, amplitudes, natural frequencies, relative damping ratios and initial phases are directly identified from the vibration signal by an improved state-space method. This leads to high similarity between atoms and impact-induced transients. To improve the calculation speed, a split augmented Lagrangian shrinkage method is used to obtain optimal sparse coefficients. With the proposed method, both the moments of impact occurrence and the time intervals between transients can be effectively identified, and thus the impact features can be extracted. The effectiveness of the proposed method is validated by simulated signals as well as practical ATCS vibration signals. A comparison study shows that the proposed method is superior to empirical-mode decomposition, ensemble-empirical-mode decomposition and variational-mode decomposition when used for impact-feature extraction.