Wavelet Entropy MATLAB Algorithm

Calculating signal wavelet entropy is a method used to analyze signal complexity and information content. By performing wavelet transform on a signal and computing the entropy of wavelet coefficients, we obtain a measure of the signal's complexity and information richness. Wavelet entropy finds applications in various fields such as signal processing, image processing, and data compression. It helps us understand signal characteristics and structure, and can be used in various signal analysis and processing applications. Implementation typically involves the following MATLAB workflow: First, perform wavelet decomposition using functions like wavedec() to obtain wavelet coefficients across different frequency bands. Then calculate the energy distribution for each decomposition level. Finally, compute the Shannon entropy using the formula -sum(p.*log(p)) where p represents the normalized energy distribution. This entropy value quantifies the signal's randomness and complexity - higher entropy indicates more complex signal content while lower entropy suggests more ordered patterns. Key MATLAB functions involved include: wavelet family selection (db1, sym2, etc.), decomposition level determination, and entropy calculation algorithms. The method is particularly useful for non-stationary signal analysis where traditional Fourier-based methods may be insufficient.