：从经典功率谱估计周期图法原理入手，从理论上分析了其存在的局限性，借助Welch算法对其进行修正。依靠 Matlab强大的数值分析和信号处理能力，进行实验仿真，比较不同的窗函数，不同的数据长度对Welch法谱估计质量的影 响，并分析了造成这些影响的原因。

psd和welch方法的改进及其应用，并对两者进行了对比

此提交提供了使用 Welch 方法计算功率谱密度 (PSD) 的可能性。 该文件基于使用信号处理工具箱的 Matlab 实现。 我排除了计算机密间隔的可能性。 如果需要，请发表评论，我会更新必要的依赖项。 WelchPowerSpectralDensity.m 文件的标题中给出了一个使用示例。 另外两个文件 Hann.m 和 Hamming.m 提供了算法所需的两种可能的窗口函数。

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隐马尔可夫模型c++实现程序，采用Baum-Welch (ML)算法进行训练。

Baum-Welch算法(模型训练算法) 目的：给定观察值序列O，通过计算确定一个模型l ， 使得P(O| l)最大。 算法步骤： 1. 初始模型（待训练模型） l0, 2. 基于l0 以及观察值序列O，训练新模型 l； 3. 如果 log P(X|l) - log(P(X|l0) < Delta，说明训练已经达到预期效果， 算法结束。 4. 否则，令l0 ＝ l ，继续第2步工作

经典功率谱估计 Welch法 自己编写的程序，可以直接使用

功率谱估计示意weltch方法和Thomson多窗估计法原创分享-welch_mtm.m 程序示意weltch方法参数改变和mtm方法参数改变时对频谱图的影响 weltch方法 Figuer 1 示意随分段长度（窗函数时域长度）增加，方差特性变差 welch.jpg welch方法Figure 1 MTM多窗估计法 Figure 2 示意随窗函数增多，方差特性改善，但频率分辨率下降 MTM.jpg mtm方法Figure 2

基于matlab的_welch法功率谱估计.pdf

功率谱估计，直接法，welch算法求取信号功率谱，包含FFT直接法估计功率谱，求取的结果和matlab的库函数pwelch完全一致，信号默认采用hamming窗，可自行修改。