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This article studies the sparse decomposition algorithm, constructs a cyclic dictionary suitable for composite faults using the concept of cyclic matrices, and improves the problem of low computational efficiency in the orthogonal matching pursuit algorithm. A fault feature extraction method called Cyclic Sparse Decomposition (CSD) is proposed to enhance the amplitude of reconstructed signals. Then, spectral analysis and envelope analysis are combined with fault feature frequencies to discriminate fault locations, and comparative simulation analysis is conducted.