摘要：功率谱估计是数字信号处理和分析重要研究内容之一。功率谱估计在分析平稳随机信号频率成分领域被广泛应用，并且已被成功应用到雷达信号处理、故障诊断等实际工程中。一般来说，功率谱估计方法可分为经典功率谱估计方法和现代功率谱估计方法。经典功率谱估计方法的方差性能较差，分辨率较低，主要原因是无法实现功率谱密度原始定义中的求均值和求极限的运算和相关假设不符合实际产生了较差的分辨率。现代功率谱估计是以参数模型为基础，内容较为丰富，涉及的学科及应用领域也相当广泛，因其解决了经典谱估计的问题而被广泛的应用。现代谱估计常用的模型ARMA模型、AR模型和MA模型，其中AR模型，又称为自回归模型，应用较多，具有代表性。本文的功率谱估计设计采用自回归模型，理解并分析Levinson-Durbin提取参数算法，通过用MATLAB进行算法编写，实现自回归模型谱估计在计算机上的仿真。

关键词：功率谱估计；AR模型；算法；MATLAB

Abstract：Power spectrum estimation is one of the important research contents of digital signal processing and analysis.The power spectrum estimation is widely used in the analysis of the frequency components of stationary random signals, and has been successfully applied to practical engineering such as radar signal processing and fault diagnosis.In general, the power spectrum estimation method can be pided into classical power spectrum estimation method and modern power spectrum estimation method.The variance performance of the classical power spectrum estimation method is poor and the resolution is low. The main reason is that the calculation of the mean and the limit of the power spectral density in the original definition does not accord with the actual resolution.Modern power spectrum estimation is based on the parameter model, the content is more abundant, involving a wide range of disciplines and applications, because it solves the problem of classical spectrum estimation and is widely used.The ARMA model, the AR model and the MA model, which are commonly used in modern spectral estimation, are also known as autoregressive models, which are more representative and representative.In this paper, the power spectrum estimation design uses the autoregressive model to understand and analyze the Levinson-Durbin extraction parameter algorithm. The algorithm is written by MATLAB to realize the simulation of the autoregressive model spectrum estimation on the computer.

Keywords: Power spectrum estimation; AR model; algorithm; Matlab

目 录

第一章绪论 1

1.1发展历程 1

1.2研究的现状和意义 1

1.3主要研究内容 2

1.4论文的主体内容 2

第二章自回归模型功率谱估计 3

2.1平稳随机信号的参数模型 3

2.2自回归模型的正则方程 5

2.3自回归模型和线性预测的关系 6

2.4Levinson-Durbin算法 8

2.5本章小结 10

第三章自回归模型阶次的选择和性质 11

3.1自回归模型阶次的选择 11

3.2自回归模型谱的分辨率 13

3.3自回归模型的稳定性 16

3.4自回归模型谱的匹配性质