云计算-基于中国余数定理及全相位理论的高精度频率估计算法研究.pdf

ABSTRACT

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

s

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

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;

robustness to noise.

Key words：

目 录..................................................................................................................... I

第一章 绪 论....................................................................................................... 1

第二章 中国余数定理重构算法及其改进算法................................................... 5

2.1 引言.......................................................................................................... 5

2.2 经典中国余数定理重构算法.................................................................. 6

2.2.1 中国余数定理的由来................................................................... 6

2.2.2 经典中国余数定理算法............................................................... 8

2.6 本章小结................................................................................................ 17

第三章 结合全相位谱分析法的多普勒偏移估计............................................. 19

3.1 引言........................................................................................................ 19

3.2 全相位谱分析原理................................................................................ 20

3.2.1 离散傅里叶变换（DFT）在测定相位和幅度中的缺陷 .......... 20

3.3 相位差频率校正法................................................................................ 28

3.4 多普勒偏移估计方案............................................................................ 29

3.4.1 多普勒偏移估计的理论原理..................................................... 29

3.4.2 多普勒偏移估计具体实施方案................................................. 31

3.5 本章小结................................................................................................ 37

II

4.3 结合全相位谱分析法的频率估计方案................................................ 42

4.3.1 频率估计总流程......................................................................... 42

4.3.2 各处理步骤的详细过程............................................................. 43

4.4 本章小结................................................................................................ 47

第五章 结合 FFT 谱分析法的高频余弦信号的频率估计 ................................ 48

5.2.2 频率估计子过程分析................................................................. 50

5.3 本章小结................................................................................................ 53

第六章 实验结果及分析..................................................................................... 55

6.1 结合全相位谱分析法的多普勒偏移估计方案.................................... 55

6.1.1 性能指标..................................................................................... 55

6.2.2 实验结果及其分析..................................................................... 58

6.3 结合 FFT 谱分析法的高频余弦信号的频率估计方案 ....................... 62

6.3.1 性能指标..................................................................................... 62

6.3.2 实验结果及其分析..................................................................... 62

6.4 本章小结................................................................................................ 67

第一章 绪 论