Wavelet Analysis Theory: Reference Code Routines and Implementation Examples

The following routines from wavelet analysis theory are provided as reference examples. These code implementations demonstrate key concepts and applications of wavelet transforms, including decomposition/reconstruction algorithms, filter bank implementations, and multi-resolution analysis techniques. Each routine contains practical MATLAB/Python code snippets with explanations of underlying mathematical operations, such as discrete wavelet transform (DWT) computation using filter convolution methods, wavelet coefficient thresholding for denoising applications, and inverse transform reconstruction processes. These examples are designed to help readers better understand wavelet analysis concepts through hands-on code examination, supporting both learning and research activities in signal processing and time-frequency analysis. The routines include implementations of Daubechies wavelets, Haar transforms, and wavelet packet decomposition with detailed comments on algorithm parameters and performance considerations.