When Wavelet Meets HMM WHMT for 1D Signal Denoising and Classification in MATLAB

1D Signal Two-Level Wavelet Decomposition Overview Two-Level Approximation Decomposition: The original signal is averaged every 4 values to capture the approximate components at this level. Two-Level Detail Decomposition: The difference between every 2 consecutive values in the original signal provides the detailed components at this level. One-Level Detail Decomposition: The difference between the odd and even-indexed values of the original signal is calculated to extract finer details. Signal Recovery: After the decomposition, the signal can be reconstructed by combining the approximations and details from each level. In MATLAB, you can implement these wavelet decompositions to analyze various signals effectively, applying discrete wavelet transform (DWT) functions for both decomposition and reconstruction steps.

This tutorial demonstrates how to perform 1D matrix classification for 2-class and 3-class problems using a Self-Organizing Map (SOM) neural network. It includes a matrix-based AND gate example with input samples of sizes 12 and 3. The approach uses machine learning principles to classify the data, making it suitable for tasks such as pattern recognition and clustering. The MATLAB code provided helps implement and visualize the classification process in a straightforward manner. The classification results can be interpreted using the SOM algorithm, which adjusts the map neurons based on the input data features.

用于1D AEM（或任何1D模型）反演的Matlab Trans-D代码示例，运行仅需在Matlab路径中包含/ include目录和子目录，按照编号顺序运行命名脚本。基于Blatter等人（2018）和Ray等人（2013，2012）的工作，来自机载瞬态电磁数据的跨维贝叶斯反演泰勒冰川。

This function implements linear 1D convolution using the overlap-and-add method. It is fully optimized, and the main loop avoids memory allocation. The function automatically computes the best DFT window for performance. It supports three output modes: Full, Same, and Valid, which align with MATLAB's conv() function. The package also includes a frequency-domain implementation and performance comparisons with two other methods.

本方法采用平移变换进行信号去噪，有效消除Gibbs效应。通过MATLAB编写，提高信号处理的质量和效率。

这里提供了基于FDTD方法的四个MATLAB代码示例，逐步深入探讨电磁场中的Ex和Hy场分量在z方向的传播，包括吸收边界条件（ABC）的应用、脉冲与介质相互作用的模拟，以及正弦波与介质相互作用的仿真。

该程序生成一个图形，用于说明相位干涉测量，其中一个辐射(E,B)在远场区被认为准时的电磁源正以传感器间距的半波长d=λ/2撞击N个元件的均匀线性阵列。在该图中，注意到了连续的相位delta_i，以及阵列的辐射方向图被描述为E(theta)，因此该图可用于课程、演示或科学论文。

这段代码能够计算在给定样本下，两个均匀概率分布之间的1-Wasserstein距离和2-Wasserstein距离。从图形上来看，它衡量了输入向量的（归一化）直方图之间的距离。详细信息可参阅GitHub存储库。

基于 MATLAB 的图像 二维小波变换，以及图像 重建。通过小波变换，可以有效地对图像进行压缩和去噪，从而提高图像质量。将介绍如何使用 MATLAB 实现这一过程，包含相关代码示例和关键步骤的详细说明。