Wavelet Transform Implementation for Vectors Using Daubechies 9/7 Wavelet

This program is designed to perform wavelet transformation on vector data. The implementation utilizes the Daubechies 9/7 wavelet based on the lifting scheme approach, which provides computational efficiency through in-place calculations and reduced memory requirements. The wavelet transform serves as a mathematical tool for extracting meaningful information in signal processing and data analysis applications. By decomposing signals into frequency components at different scales, the transform reveals both detailed features and overall trends within the data. The algorithm follows a multi-resolution analysis approach, implementing both forward (decomposition) and inverse (reconstruction) transformations through prediction and update steps characteristic of lifting schemes. This wavelet transformation capability finds extensive applications across various domains including image processing, audio compression, and pattern recognition. Consequently, this program's wavelet transform functionality enables users to better understand and analyze data characteristics when processing vector-based information, with particular advantages in handling boundary conditions and maintaining perfect reconstruction properties.