Resolvers are universally employed as absolute angle sensors in motor control systems. Detecting the synchronous envelopes is an essential step during the resolver-to-digital conversion (RDC) process when calculating the angle. However, conventional filter-based envelope detection could introduce enormous angle delay and peak capturing-based detection could lead to apparent quantization angle error. A novel all-digital RDC system is proposed in this article with the synchronous envelopes detected based on numerical synchronous integration method. The sine and cosine signals are oversampled and then multiplied by the excitation signal before integration to derive the envelopes. The angle delay and quantization errors could thus be largely reduced compared with RDC systems based on conventional envelop detections. In the experiment, angle error is limited to less than 30 arc min at the angular speed of 1000 r/min.