The resolvers can output amplitude-modulated signals which contain angular position information of the rotor. Through the demodulation by Resolver to Digital Converter, a digital format of angular position can be obtained, but it is difficult to obtain high precise angular velocity. In order to get the velocity signal, an estimation method based on the angular position need to be designed. Compared with the difference algorithm, the state observer method can greatly suppress noise interference, however, the accuracy of angular velocity estimation is still affected by the un-modeled dynamics, and the effect of measurement noise is not fully analyzed. In this paper, an m-order state observer is designed to estimate angular velocity, and then, the influences of un-modeled dynamics and measurement noise on the estimation results of observer are analyzed. Simultaneously, the relationships between the performance of velocity observer and observer order, observer gain are analyzed from the perspective of frequency-domain characteristics. In the end, the angle-measuring channel with resolver is modeled, and the simulation verification is carried out after the discretization of state observer. The obtained conclusion can provide a theoretical guidance and reference for the design of velocity observer in servo motor control.