Haar Wavelet-Based Decomposition and Reconstruction Algorithm

This MATLAB-based implementation provides decomposition and reconstruction functions utilizing Haar wavelet transform. The code includes detailed inline comments explaining the algorithm logic and implementation process. Haar wavelet serves as a fundamental signal processing method that decomposes signals into different frequency sub-bands, enabling effective feature extraction and signal analysis. The implementation employs multiresolution analysis through iterative filtering operations, where decomposition involves applying low-pass and high-pass filters followed by downsampling, while reconstruction performs upsampling with corresponding inverse filters. Using this function library, users can conveniently perform signal decomposition and reconstruction operations in MATLAB environment, supporting various applications such as signal denoising, compression, and feature detection. The code structure includes main functions for wavelet decomposition (haar_decompose) and reconstruction (haar_reconstruct), with auxiliary functions handling boundary conditions and filter coefficient management.