Wavelet Decomposition and Wavelet Packet Decomposition

During our study, we will cover the following key aspects:

1) Detailed examination of the concepts of wavelet decomposition and wavelet packet decomposition, including their differences and interconnections. This foundation will enhance our understanding of fundamental wavelet analysis principles and their algorithmic implementations.

2) In-depth exploration of wavelet packet decomposition and reconstruction algorithms. We will investigate how wavelet packets decompose signals and utilize reconstruction algorithms to restore original signals, focusing on implementation approaches using filter banks and tree-structured decomposition techniques.

3) Practical implementation using MATLAB programming language to perform wavelet packet decomposition on signals and generate wavelet energy spectrum plots. This hands-on approach will involve using MATLAB's Wavelet Toolbox functions such as wpdec for decomposition and wenergy for energy calculation, helping bridge theoretical knowledge with real-world applications while improving programming skills.

Through these learning objectives, we will comprehensively master both theoretical foundations and practical applications of wavelet decomposition and wavelet packet decomposition, establishing a solid foundation for future research and professional work in signal processing.