内容：

摘   要

信号的频谱分析是研究信号特性的重要手段之一，对于确定性信号，可以用 Fourier 变换来考察其频谱性质，而对于广义平稳随机信号，由于它一般既不是周期的，又不满足平方可积，严格来说不能进行 Fourier 变换，通常是求其功率谱来进行频谱分析。
功率谱估计在近 30 年中获得了飞速发展。涉及到信号与系统、随机信号分析、概率统计、随机过程、矩阵代数等一系列学科，广泛应用于雷达、声纳、通信、地质、勘探、天文、生物医学工程等众多领域。
实际中，数字信号的功率谱只能用所得的有限次记录的有限长数据来予以估计，这就产生了功率谱估计这一研究领域。功率谱的估计大致可分为经典功率谱估计和现代功率谱估计。经典谱估计的两个主要方法为周期图法和自相关法。针对经典谱估计的分辨率低和方差性能不好等问题提出了现代谱估计。现代谱估计大致可以分为参数模型谱估计和非参数模型谱估计。基于参数建摸的功率谱估计是现代功率谱估计的重要内容，其目的就是为了改善功率谱估计的频率分辨率，它主要包括 AR 模型、 MA 模型、 ARMA 模型，其中基于 AR 模型的功率谱估计是现代功率谱估计中最常用的一种方法。
理论分析及 MATLAB 仿真结果表明：经典谱估计方法得到的功率谱出现了许多虚假的谱峰，频率分辨率很低，而现代谱估计方法得到的功率谱较为真实，没有明显的频率偏移和假峰，并且具有较高的频率分辨率，尤其是频率带宽性能得到了明显的改善。
关键词： 功率谱估计； AR 模型； MATLAB ； Levinson-Durbin 算法； Burg 算法

ABSTRACT

Signal spectral analysis is one of the most important means to examine the characteristics of signal. Fourier transform can be used to study the quality of the spectrum of the certainty signal. For general stochastic signal, it is neither a cycle in general, nor in line with the square  integration  .Strictly speaking, general stochastic signal cannot be transformed by Fourier transform. So the power spectrum is  generally  used for signal spectral analysis.
In the last 30 years Power spectral estimation was rapidly developed. It related to a range of disciplines such as Signals and systems, stochastic signal analysis, probability and statistics, stochastic processes and Matrix algebra. And it is widely used in radar, sonar, communications, geology, exploration, astronomy, biomedical engineering and many other fields.
Actually, the power spectrum of digital signal can only be estimated by finite length data derived from the limited records, which produced the study area of power spectrum estimation. Power spectral estimation can be broadly divided into classical power spectral estimation and modern power spectral estimation. Two main methods of Classical power spectral estimation are period gram method and auto-correlation method. For the issues such as low resolution and poor variance performance in Classical spectral estimation, modern spectral estimation is proposed. Modern Spectral Estimation can be broadly classified into non-parametric spectral estimation and spectral estimation model. Modeling based on parameter estimation of the power spectrum is important content of modern power spectral estimation, and its purpose is to improve the problem of frequency resolution in classical power spectral estimation, which mainly includes the AR model, MA model, ARMA model. Modern power spectral estimation based on AR model is the most commonly used methods.
Theoretical analysis and MATLAB simulation results demonstrate that: the power spectrum approached by the classic spectral estimation has many false peaks, and the frequency resolution is very low, while the power spectrum approached by the modern spectral estimation methods to be more true .And in the modern spectral estimation methods there is no significant frequency deviation and false peak, and have a high frequency resolution, especially the frequency bandwidth performance significantly improved.
Keywords :  power spectrum estimation, AR model, MATLAB ,  Levinson-Durbin algorithm,
 Burg algorithm

目   录

   第 1 章   绪论      1
1.1  功率谱估计概述及发展现状       1
1.1.1  功率谱估计概述       1
1.1.2  功率谱估计的发展现状       1
1.2 论文结构       2
第 2 章  MATLAB 简介      3
2.1 MATLAB 的发展概述       3
2.2 MATLAB 的功能       3
2.3 MATLAB 的技术特点       4
2.4 GUI       5
第 3 章   经典谱估计      7
3.1  自相关函数的估计       7
3.1.1  自相关函数的直接估计       7
3.1.2  自相关函数的快速计算       7
3.2 经典谱估计简介       8
3.3  直接法及 MATLAB 仿真结果       8
3.3.1  直接法理论分析       8
3.3.2  直接法的 MATLAB 仿真结果       9
3.4  间接法及 MATLAB 仿真结果       11
3.4.1  间接法理论分析       11
3.4.2  间接法的 MATLAB 仿真结果       11
3.5  直接法和间接法的关系       14
3.6  直接法估计的改进       15
3.6.1 Bartlett 法       15
3.6.2 Welch 法       16
第 4 章   现代谱估计      17
4.1 现代谱估计简介       17
4.2 平稳随机信号的参数模型       17
4.3 AR 模型的构建       19
4.4 AR 模型阶数的选择       20
4.5 AR 模型的稳定性分析       20
4.6 Levinson-Durbin 算法及 MATLAB 仿真       22
4 .6.1 Levinson-Durbin 算法的理论分析       22
4.6.2 Levinson-Durbin 算法的 MATLAB 仿真       23
4.7 Burg 算法及 MATLAB 仿真       24
4.7.1 Burg 算法的理论分析       24
4.7.2 Burg 算法的 MATLAB 仿真       25
4.8  经典谱估计与现代谱估计性能比较       27
4.8.1 经典谱估计与现代谱估计性能比较的理论分析       27
4.8.2 经典谱估计与现代谱估计性能比较的 MATLAB 仿真       27
第 5 章   总结与展望      29
5.1  总结       29
5.2  不足之处与未来展望       29
参考文献      31
致   谢      32
附   录：   部分程序代码      33 

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