A Three-Point Interpolation DFT-Based Frequency Estimation Algorithm for Temperature-Stable System in MEMS Oscillators

Microelectromechanical system (MEMS) oscillators are widely used in navigation systems because of their reliability. Real-time temperature changes will have a major impact on the stability of these systems, so calculating the output frequency of the MEMS resonator at different temperatures is particularly important for the stability of the system. Therefore, we propose a three-point interpolated discrete Fourier transform (IpDFT)-based frequency estimation algorithm for a temperature-stable system in MEMS oscillators. Because the temperature-stable technique can provide an unbiased estimate of the frequency of the signal that is more accurate and efficient for temperature compensation, it can effectively mitigate the frequency shift of the MEMS resonator due to temperature variation. The simulated result of the absolute temperature error is less than $0.01~^{\circ } $ C when the signal-to-noise ratio (SNR) is 40 dB. The absolute temperature error result is less than $0.01~^{\circ } $ C in the amplitude jitter and frequency jitter tests. The temperature-stable technique is applied to the MEMS resonator temperature compensation system. The measured frequency shift ratio of the signal processed by the temperature compensation system is less than 30 ppm, indicating that the oscillation frequency can be effectively stabilized at different temperatures.