<p>Automatic tool changers (ATCs) facilitate high-frequency tool exchanges in machining centers, which significantly improve tool change efficiency. However, among all subsystems of a machining center, ATCs exhibit the highest failure rate, directly affecting the machine tool’s utilization. For effective fault diagnosis, fault prediction and health management of ATCs, obtaining a pure monitoring signal is the prerequisite. Unfortunately, measured transient impact signals often contain multiple noise components due to frictional collisions between mechanical parts and external vibrational interferences, including both band-limited noise and stochastic noise. Traditional linear time-invariant (LTI) filters and sparsity-based denoising algorithms demonstrate limited effectiveness in removing these multi-component noise from transient impact signals. To address this challenge, a novel denoising method integrating LTI filtering and overlapping group sparsity is proposed. This method first reformulates the transient signal recovery problem into a convex optimization framework, which is then solved using a majorization-minimization algorithm. Experimental validations through both simulated and measured signals demonstrate that the proposed approach outperforms several state-of-the-art denoising techniques, particularly in terms of signal fidelity preservation and noise suppression. The proposed method not only can be effectively applied to the denoising transient impact signals for ATCs, but also contributes to the theoretical advancement of sparse signal processing in industrial scenarios.</p>