MATLAB Implementation of Wavelet Analysis

In this discussion, we further explore the principles and applications of wavelet analysis. Wavelet analysis represents a sophisticated signal processing technique that decomposes signals into wavelet basis functions across different scales. By applying transformations and analysis to these scale-dependent basis functions, we can extract critical frequency and energy information from signals. The implementation typically involves using MATLAB's Wavelet Toolbox functions such as wavedec for multi-level decomposition and wrcoef for reconstruction. Wavelet energy spectrum analysis, built upon fundamental wavelet analysis, enables deeper understanding of signal frequency distributions and energy patterns through algorithms that compute coefficient energies at each decomposition level. By leveraging wavelet analysis and energy spectrum techniques with MATLAB code implementations - including key steps like selecting appropriate wavelet families (e.g., Daubechies, Coiflets), determining optimal decomposition levels, and calculating energy percentages - researchers can conduct more profound signal investigation and processing, leading to enhanced accuracy and comprehensive results across various engineering and scientific domains.