An Efficient and Robust Frequency Estimator Dealing With Short-Observation Under-Sampled Waveforms

Frequency estimation of a noisy signal in under-sampled conditions is a challenging problem, which has proved to be effectively solved by Chinese remainder theorem (CRT). To enhance the estimation efficiency and robustness to noise, an improved CRT estimator based on spectrum correction is proposed. Based on a comprehensive error analysis of the CRT-based frequency reconstruction model, it is emphasized that, for different signal-to-noise ratio (SNR) cases, the two main errors (discrete Fourier transform (DFT) resolution error and noise error) exert distinct effects on the original CRT-based estimator. For the purpose of removing DFT resolution error, the Tsui corrector is suggested to be incorporated into the proposed estimator. Moreover, the proposed estimator can achieve a high efficiency since it employs small-sized DFT. Numerical results show that the proposed estimator not only can achieve a high estimation accuracy but also can lower the SNR threshold for successful reconstruction, which present the vast potential in the frequency estimation of short-observation and undersampling cases.