Frequency estimation of undersampled sinusoidal signal based on chinese remainder theorem

Abstract

Frequency estimation based on the reconstruction algorithm of the Chinese remainder theorem(CRT) is one of the frontier focuses in the fields of signal processing, electromagnetism, and optics etc. Howerver, the existing studies can only realize a rough frequency estimation of complex exponential signals. Hence this paper generalizes the CRT-based frequency reconstruction from a rough frequency estimation of complex exponential signals to the accurate frequency estimation of sinusoidal signals. The procedure of the proposed estimation scheme is as follows: (1) Detect zero crossing point on the original high-frequency sinusoidal waveform so as to determine the ideal phase information; (2) implement fast Fourier transform(FFT) to each path's undersampled signal, and then use Candan estimator to correct the frequencies at the peak FFT spectral bins so that the frequency biases can be extracted to realize phase correction; (3) use the proposed classification method based on phase features to screen the corrected remainders; (4)substitute the filtered frequency remainders into the closed-form robust Chinese remainder theorem to obtain the high-accuracy frequency estimation of the original signal. Additionally, this paper also deduces the theoretic expressions of the frequency estimation variance, which is also verified through numerical simulation. And the experimental results also reflect that the proposed scheme possesses high precision and high robustness to noise.