This article proposes a novel three-stage condition assessment scheme of rotating machinery using internal encoder data rather than traditional external vibration data. In this article, periodical group sparse derivatives (PGSD)-based signal denoising method is proposed to suppress the background noise, which incorporates the periodical group sparse derivative property of encoder signal and can be considered as an optimization problem. Moreover, the convexity condition of optimization problem is thoroughly investigated and an effective iterative algorithm is derived. After the PGSD-based signal denoising method, difference method (DM), and autoregressive (AR) filter are employed to convert the denoised encoder signal into intelligible speed information and remove the operation-related harmonic components. With the proposed method PGSD-DMAR, the periodical transient features are effectively extracted and the health condition of rotating machinery is successfully identified. The effectiveness and superiority of the PGSD-DMAR are verified via simulated signal and experimental data.