Wavelet Packet Analysis for Extracting Characteristic Frequencies from Vibration Signals

Wavelet Packet Analysis is a method used for extracting characteristic frequencies from vibration signals. It decomposes the signal into sub-signals across different frequency bands and performs energy spectrum analysis on each sub-signal to calculate characteristic frequencies. This analytical approach can more accurately capture frequency components within the signal and provide more detailed spectral information. In practical implementation using MATLAB or Python (with PyWavelets library), the process typically involves using functions like wpdec for wavelet packet decomposition, wprcoef for reconstruction, and subsequent FFT analysis for energy spectrum calculation. The algorithm first applies multi-level wavelet packet decomposition to partition the signal into fine frequency bands, then computes the energy of each node in the decomposition tree, and finally identifies characteristic frequencies by analyzing energy distribution patterns across frequency bands. Due to its precise frequency localization capabilities, Wavelet Packet Analysis has widespread application value in signal processing and vibration analysis fields, particularly for fault diagnosis in rotating machinery and structural health monitoring systems.