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　1,3　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　the　purpose　of　condition　monitoring.　Based　on　the　results　from　the　industrial　implementations　in　this　paper,　the　proposed　method　has　been　found　to　be　a　promising　tool　for　impulsive　feature　enhancement,　and　the　superiority　of　the　proposed　method　over　previous　methods　is　also　demonstrated.　(C)　2017　Elsevier　Ltd.　All　rights　reserved.