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In this paper, a new resolver-to-digital conversion method is presented. This method is based on synchronous demodulation of resolver's output signals. A modified angle-tracking observer is proposed to extract the rotor angle in high speeds as well as in low speeds. An estimation algorithm, which is based on the sign and absolute values of sine and cosine of the rotor angle, is introduced to find an appropriate initial value for this observer. This method can be incorporated in a DSP-based motor drive system. The proposed method is simple and cost effective when an appropriate microcontroller is selected for motor control. This method has been successfully implemented in a DSP board. Several tests at different speeds and initial positions have been performed to evaluate the proposed method.