We propose a novel measurement system that evaluates the frequency stability of high-precision oscillators such as atomic oscillators. This measurement system consists of a pair of high-speed analog-to-digital converters (ADCs) and digital-signal-processing (DSP) circuits on a field programmable gate array. The pair of high-speed ADCs simultaneously digitizes the two sinusoidal-voltage outputs from the oscillator under test and a reference oscillator. The DSP circuits calculate the phase difference between the two sinusoidal voltages. The frequency stability evaluated as the Allan deviation sigmay(tau) is calculated from the phase difference. The main advantage of this system is that the hardware configuration is much more compact than the conventional systems using a dual mixer and a local oscillator. Nonetheless, the system noise floor of the prototype at the nominal frequency of 5 MHz is sigmay(1000 s) = 6.8 times 10-17, which is sufficient to evaluate a commercial hydrogen maser oscillator and is better by a factor of 5 than our previously reported system. We have verified that the measurement accuracy of the prototype depends on the nominal frequency and the level of the sinusoidal voltages, but it does not depend on the initial phase difference and offset frequency.