Research Of High-accuracy Frequency Estimation Algorithm Based On Chinese Remainder Theorem And All-phase Theory

The frequency estimation and detection of high-frequency signal is one critical issue in signal processing such as Radar communications, sonar, seismic monitoring, fault diagnosis, Medical Health Care and so on. However, limited by the Nyquist theorem, estimating the frequency of one real-valued signal accurately requires at least two samples in one signal cycle, indicating that the sampling rate must be equal to or larger than twice the frequency of the measured high-frequency signal. Therefore, the hardware cost is very high. This dissertation aims to solve the problem of high-accuracy frequency estimation of the high-frequency signal, under the condition of multiple undersampled signal paths(if signal frequency is f0, it requires that the sampling rate fs<<2f0). To achieve this goal, the ancient Chinese Remainder Theorem(CRT) is introduced in this dissertation.Frequency estimation based on the reconstruction algorithm of Chinese remainder theorem is one of the frontier focuses in the fields of signal processing, electromagnetism and optics etc. However, the existing studies can only realize the rough frequency estimation of complex exponential signals. So this dissertation firstly needs to complete accurate frequency estimation of the complex signals. Therefore the original all-phase FFT spectrum analysis theory is introduced. Through employing apFFT/FFT phase difference spectrum correction method to provide the exact frequency remainders to the Chinese Remainder Theorem, this dissertation realizes accurate frequency estimation of complex exponential signal. This algorithm is also successfully applied to the Doppler shift estimation.In order to further generalize undersampling frequency reconstruction from complex exponential signals to sinusoidal signals, this dissertation presents two remainder screening methods based on two different measures of correcting spectrums. Then, the accurate frequency estimation of sinusoidal signals can be realized in combination with them. The proposed estimation scheme process is as follows:(1) Detect zero crossing point on the high-frequency sinusoidal waveform to determine the phase information;(2) Implement Fast Fourier Transform(or All-phase Fast Fourier Transform) on each path's undersampled signal, and then use Candan estimator(or All-phase-based ratio spectrum correction) to correct the frequencies at the peak FFT(or apFFT) 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 estimate of the original signal. Additionally, this dissertation also deduces the theoretic expressions of the frequency estimation variance. Numerical result not only verifies the correctness of this theoretic expressions, but also reflects that the proposed scheme possesses high precision and high robustness to noise.