论文总字数：37053字

摘 要

信号频率估计是信号处理的重要研究方向，这一问题的研究有重要的理论和现实意义。基于水下声呐被动探测未知敌方信号的背景，本文主要针对被动探测到的水下的脉冲信号进行频率估计的研究和分析。

本文研究了两种水下脉冲信号模型的频率估计方法：CW信号和LFM信号。对于CW信号，研究了Rife算法和基于Rife原理的各种改进算法，包括缩小估计频点的搜索区间和搜索步长以达到提高准确度的M-Rife算法和I-Rife算法；利用最大幅值点及其左右相邻两点幅度的关系，推导出频率估计偏差来实现精准频率估计的Candan算法；只使用最大幅值点左右两点的幅度，巧妙利用信号补零和频谱插值来进行频偏估计，以实现频率估计修正的Fang算法。对于LFM信号，研究了基于短时傅里叶变换的瞬时频率估计方法，将LFM分段转化为CW信号进行瞬时频率估计；还研究了一种基于线性调频信号频率特性的快速频率估计法，利用信号的自相关解调首先实现调频率的估计，再进一步构造信号完成初始频率的估计，从而获得完整的频率关系，并分别讨论了I-Rife算法以及信号长度和延时量取值对估计性能的影响。仿真验证了上述方法的有效性。

关键词：脉冲信号，线性调频信号，频率估计，Rife算法，自相关解调

Abstract

Signal frequency estimation is an important research direction of signal processing, and the research of this problem has important theoretical and practical significance. Based on the background of passive detection of unknown enemy signals by underwater sonar, it should be mainly studied and analyzed that the passive detection of underwater pulse signals.

In this paper, two types of receiving signal models, CW signals and LFM signals, are amply studied for exact estimation of frequency to achieve the precise analysis of signals. For CW signals, it can start with the simplest Rife algorithm, and then it would learn more various improved algorithms based on Rife which should be more precise, including M-Rife algorithm and I-Rife algorithm, which reduce the region of searching and the time interval for the estimated frequency to improve accuracy; Candan algorithm which uses the amplitude peak and the relationship between its left and right adjacent points, is derived to achieve accurate frequency estimation by frequency estimation bias. Fang algorithm only uses the amplitude of the two points which are on both sides of the amplitude peak, then ingeniously uses signal nulling and spectral interpolation to realize the estimation of deviation and the correction of estimated frequency. For LFM signals, the method of instantaneous frequency estimation based on short-time Fourier transform is studied initially, which converts LFM into CW signal in segments for instantaneous frequency estimation. Then it learns about the fast demodulation method for the estimation of frequency which can be realized by autocorrelation demodulation. In view of the special frequency characteristics of LFM signal, it can firstly accomplish the estimation of modulation rate, and then the initial frequency estimation is completed by constructing signal and the results can be used to achieve the complete frequency characteristics. The influence of I-Rife algorithm, and different values of signal length and delay of correlation for estimation precision is also discussed respectively. The simulation results verify the effectiveness of the above methods.

KEY WORDS: Pulse signal, LFM signal, frequency estimation, Rife algorithm, autocorrelation demodulation,

目 录

摘要 ……………………………………………...….......……………………………………………………………………………Ⅰ

Abstract ……….....…………………………….………………………………………………………………………………… Ⅱ

第一章 绪论 ………………………………………………….………………………………………………………………………1

1.1研究背景及目的 …………………………….………………………………………..……………………………1

1.2 国内外研究现状 …………………………………………………………………………………………..………2

第二章 频率估计基础 ………………………………………………………………………………………………..………..4

2.1 信号模型 ………..…………………………………………………………………………………………...………4

2.1.1 CW–脉冲信号 ..………..............................................................................…...4

2.1.2 LFM–线性调频信号 ....................................................................................4

2.2 频率估计原理 ...........................................................................................................5

2.2.1 参数估计的基本理论 ...................................................................................5

2.2.2 基于最大似然准则的频率估计方法 ...........................................................5

2.2.3 参数估计性能的指标 ...................................................................................6

第三章 CW信号频率估计 .......................................................................................................8

3.1 Rife算法、M-Rife算法和I-Rife算法 ....................................................................8

3.1.1 Rife算法 ........................................................................................................8

3.1.2 M-Rife算法 ...................................................................................................9

3.1.3 I-Rife算法 ...................................................................................................11

3.2 Candan法和Fang法 .............................................................................................12

3.2.1 Candan法 ....................................................................................................12

3.2.2 Fang法 ........................................................................................................14

3.3 仿真实验 ...............................................................................................................15

3.4 本章小结 ...............................................................................................................18

第四章 LFM信号频率估计 ...................................................................................................20

4.1 STFT法 ...............................................................................................................20

4.2 相关解调法 ...........................................................................................................20

4.3 改进的相关解调法 ...............................................................................................21

4.3.1 I-Rife法改进相关解调 ...............................................................................21

4.3.2 改进的L与取值方法 ..............................................................................22

4.4 仿真实验 ...............................................................................................................23

4.5 本章小结 ...............................................................................................................26

第五章 全文总结 ....................................................................................................................27

参考文献（References） …..........................................…………………………………………………………..29

致谢 …………………………………………………………………………...................................................………..30

第一章 绪论

随着人类文明和科技的发展，人类对海洋资源的需求也变得更加迫切，海洋的战略地位也随之上升。各国的科技对海洋探测的重视也逐渐加强，本文讨论的水下脉冲信号的频率估计，正是海洋探测中的重要环节之一——对探测信号的有效分析，这同样也是信号处理领域里的研究重点。

1.1研究背景及目的

地球能孕育出如此种类繁多，灿烂辉煌的生物文明，最重要的因素有三点：阳光，空气和水。如果说，阳光是地球生命的催化剂，为生命的孕育提供合适的条件和合理的可能，而空气是地球生命最坚实的保护层，抵御了宇宙中过多的辐射，那么水，则更是地球生命孕育的温床，亿万年前最初的生命体，一切生物文明的开始，就是从海洋中诞生。

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