Repetitive transients are typical vibration fault components of rotating machinery, and researchers have paid much attention to the extraction of repetitive fault transients. Though classic methods such as Kurtogram, Blind deconvolution, and signal decompositions have been extensively applied for this purpose, problems such as amplitude distortions and tricky parameter tuning still impede the precision extraction of repetitive fault transients. Besides, many works ignore the existence of multiple repetitive fault transients existing in different frequency bands, and they are designed to only extract one repetitive fault transients. To solve these problems, the authors recently proposed a new signal decomposition method named impulsive mode decomposition (IMD). IMD is established based on an iterative frequency band searching model that takes a new cycle-embedded sparsity measure as the optimization objective function. As a specialized method for the extraction of impulsive signal components (e.g., repetitive fault transients), several case studies demonstrated its superior performance in automatically determining the number of impulsive modes and further extracting and separating them.