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Sparsity is becoming a more and more important topic in the area of machine learning and signal processing recently. One big family of sparse measures in current literature is the generalized l p/l q norm, which is scale invariant and is widely regarded as normalized l p norm. However, the characteristics of the generalized l p/l q norm are still less discussed and its application to the condition monitoring of rotating devices has been still unexplored. In this study, we firstly discuss the characteristics of the generalized l p/l q norm for sparse optimization and then propose a method of sparse filtering with the generalized l p/l q norm for the purpose of impulsive signature enhancement. Further driven by the trend of industrial big data and the need of reducing maintenance cost for industrial equipment, the proposed sparse filter is customized for vibration signal processing and also implemented on bearing and gearbox for …