The traditional principal component analysis (PCA) method selects the primary components according to the prior knowledge. In light of this shortcoming, the covariance matrix eigenvalue difference spectrum is introduced to describe the differences between the primary and secondary components. First, a square relation between singular value and eigenvalue is discovered by theoretical deduction. Second, the principle of PCA signal processing with the Hankel matrix is further studied by difference spectrum theory. Finally, a PCA algorithm based on differential spectrum theory is proposed, and the effectiveness of the algorithm is verified by simulation. The results show that the number of active principal components can be selected automatically according to the maximum peak of the difference spectrum of the eigenvalues of the covariance matrix, and different frequency components can be extracted from the combination of the component signals between different spectral peaks. The PCA algorithm is used to purify the axis trajectory of the rotor of a large sliding bearing testbed and present better performance than that of the traditional PCA algorithm.