Calculation of Wavelet Packet Energy Spectrum

Wavelet packet energy spectrum calculation is a signal processing technique that performs detailed frequency-band decomposition of signals through wavelet packet transform, extracting energy from each frequency band as features. This method is widely applied in pattern recognition, fault diagnosis, and related fields.

### Core Methodology Wavelet Packet Decomposition: Multi-level wavelet packet decomposition of the original signal yields sub-signal components across different frequency bands, offering more flexible frequency-band partitioning compared to traditional wavelet decomposition. Energy Calculation: Compute the squared sum of wavelet packet coefficients for each node (frequency band) to obtain the corresponding frequency band energy, reflecting the signal's distribution intensity within that frequency range. Normalization Processing: Typically, divide each frequency band's energy by the total energy to eliminate the influence of signal amplitude variations, facilitating cross-comparison between different signals. Feature Vector Construction: Arrange normalized energy values in frequency band order to form a feature vector, serving as input for subsequent classification or recognition tasks.

### Application Extensions Fault Diagnosis: Identify abnormal states such as bearing wear by analyzing energy spectrum changes in rotating machinery vibration signals. Biosignal Processing: Extract energy features from specific frequency bands in EEG/ECG signals to assist in disease classification. Noise Reduction Optimization: Adaptively select effective frequency bands for signal reconstruction based on energy distribution characteristics.

The key advantage of this method lies in its ability to capture both high-frequency and low-frequency information simultaneously, making it particularly suitable for feature extraction from non-stationary signals. In practical applications, attention should be paid to the impact of parameters such as wavelet basis function selection and decomposition levels on the results.