Torsional vibration is key information in monitoring the condition of the shaft system. Using the vector superposition principle, the relationship between the rotation motion and the torsional vibration of the shaft is analyzed. This paper proposes a generalized incremental encoder model and constructs a piecewise function to describe the principle of the pulse output type speed measuring device. The incremental encoder uses a fixed angular increment to stamp the time component of the angular motion of the shaft, thereby establishing a discrete relationship between the angular motion of the shaft and the time component. The relationship between the angular resolution of the encoder and the torsional vibration signal sampling theorem is deduced. The asymmetric under-sampling of the torsional vibration signals is explained from the perspective of signal sampling. According to the index period invariance of the reconstruction of the encoder disk angle sequence, a dual-period instantaneous angular speed (IAS) calculation method is proposed, which uses all the time stamps, avoiding the sampling bandwidth idle caused by the single-period method, causing the torsional vibration signal to obtain more detailed information, and its analysis bandwidth is twice that of the single-period method. Simulation and experiment verified the correctness and superiority of the research content. Finally, the calculation method was packaged as a functional module and embedded in an online torsional vibration monitoring device applied to two 1000 Mw nuclear power turbine generator sets.