The singular spectrum decomposition (SSD) is an effective signal denoising tool and has been attracted much attention in fault diagnosis. However, the filtering effect and calculation efficiency of SSD are seriously affected by the embedding dimension of trajectory matrix. To overcome these disadvantages, the improved SSD (ISSD) is proposed in this paper. A length factor is designed to optimize the construction of trajectory matrix, which considers the fault information in both time-domain and frequency-domain. A series of analysis, including impulse response analysis and multi-components signal decomposition, demonstrate the ISSD lifts the performance of SSD. After that, a new indicator, named singular Gini index, is applied to select the optimal singular spectrum components (SSCs) decomposed by the ISSD. To further supplement the impulses extraction effect of the ISSD, the sparsity operation is improved by combing the morphological analysis to process the vibration and sound signals. The sparsity factor is updated in each iteration and the structure element in morphological analysis is determined adaptively. Benefiting from the virtues of ISSD and sparsity analysis, the fault impulses in the processed signal are more prominent. Finally, according to the information of bearing characteristic frequencies in the spectrum, the fault type of bearing is determined. The reliability and feasibility of the proposed method is identified by analyzing the different simulation and experimental cases.