Wavelet Packet Energy Spectrum Calculation

The calculation of the wavelet packet energy spectrum is a method used for frequency band analysis and feature extraction of signals, applicable to pattern recognition. Wavelet packet analysis is a mathematical tool that decomposes signals into sub-signals across different frequency bands and computes the energy spectrum for each band, enabling detailed signal analysis. By applying wavelet packet energy spectrum calculation techniques, a more comprehensive understanding of signal characteristics can be achieved, providing a more accurate foundation for pattern recognition. In implementation, key steps include: 1. Decomposing the signal using wavelet packet transforms (e.g., via MATLAB's `wpdec` function) to generate a tree of sub-bands. 2. Calculating the energy of each sub-band node, often using squared norm or variance metrics, such as `norm(node_coeffs, 2)^2`. 3. Normalizing energies to form a relative energy distribution for robustness against signal amplitude variations. This approach allows adaptive frequency partitioning compared to traditional wavelet analysis, making it valuable in signal processing and pattern recognition applications, such as fault diagnosis or biomedical signal classification.