Wavelet Packet Decomposition with Signal Reconstruction Problem

This MATLAB program implements wavelet packet decomposition and signal reconstruction functionality. Wavelet packet decomposition is a signal processing technique that decomposes signals into sub-signals of different frequencies, enabling better understanding of signal characteristics and structures. The program provides comprehensive decomposition and reconstruction capabilities, allowing users to obtain detailed signal information through these operations. The implementation utilizes MATLAB's Wavelet Toolbox functions, including wpdec for wavelet packet decomposition and wprcoef for reconstruction. Key algorithmic features include: - Multi-level decomposition tree structure management - Adaptive frequency band selection - Inverse transformation with perfect reconstruction properties - Customizable wavelet basis functions (Daubechies, Symlets, etc.) Testing has demonstrated excellent performance across various signal types. The program handles audio signals, image signals, and other data formats effectively, maintaining signal integrity throughout decomposition and reconstruction processes. To ensure reliability, the program has been validated using custom-collected datasets. These carefully processed datasets guarantee consistent performance across different data scenarios, with rigorous testing covering: - Boundary condition handling - Computational efficiency optimization - Reconstruction error minimization - Noise robustness assessment In summary, this MATLAB program provides a robust and powerful tool for wavelet packet decomposition and signal reconstruction. It enables researchers and engineers to perform detailed signal analysis, leading to accurate conclusions and data-driven decisions. The code includes comprehensive documentation and examples demonstrating proper usage patterns for various application scenarios.