To solve the problem of noise pollution in the measured spindle displacement signals， a sparse representation feature extraction algorithm （sparse algorithm for short） is proposed on the basis of the sparse representation algorithm theory. The algorithm consists of two steps： constructing the dictionary set and solving the sparsity coefficient， for constructing the cosine dictionary according to the periodic characteristics of the rotor signal， and for solving the sparsity coefficient according to the maximum inner product principle by using the matching pursuit algorithm. The proposed algorithm is used to extract single frequency and multiple frequency components of low SNR simulation signals， and each the extracted signal waveform almost completely coincides with the corresponding ideal one， thus verifying the effectiveness of the proposed algorithm. Then， it is used to purify the axis trajectories of the rotor of the large-scale sliding bearing test bed， and the result is better than harmonic wavelet algorithm. The axis orbits obtained by the proposed algorithm are clear and concentrated. Furthermore， the friction and misalignment faults of the rotor are successfully identified. In addition， the proposed algorithm is also suitable for the state recognition of other rotating machinery.