As an important characteristic information in incipient fault diagnosis of rotating machinery, the fault impulse signal is hard to be monitored due to the low signal amplitude and system disturbance/noise. Based on bilateral spectrum and precession energy difference density spectrum for the incipient fault diagnosis of rotating machinery, a novel diagnosis method is proposed in this paper to overcome this key problem. Compared with the existing methods to extract transient impulses from the vibrate signals, this paper designs a new fault feature parameter-precession energy difference density to characterize the feature of transient impulse. Furthermore, the complex signal and the negative frequency are introduced into the spectrum analysis and the forward and backward precession characteristics, which can be directly gained through the bilateral spectrum and relieves the problems not to be overlooked, such as high calculation, high error and time consuming. Finally, the feasibility and effectiveness of the proposed methods are demonstrated via a case study of a vertical mill reducer.