Wavelet Packet Transform Power Spectrum

This article discusses the MATLAB implementation of wavelet packet transform power spectrum analysis and its differences from conventional wavelet transforms. While standard wavelet transforms are commonly used in signal processing, wavelet packet transforms provide superior advantages by decomposing signals into more sub-bands, thereby achieving higher resolution for better characterization of signal features and properties. The MATLAB implementation typically involves key functions such as wpdec() for wavelet packet decomposition, wprcoef() for reconstruction of coefficient nodes, and custom power spectrum calculation routines. The algorithm follows a tree-structured decomposition approach where both approximation and detail coefficients are recursively divided, creating a complete binary tree representation of the signal. Wavelet packet transforms find applications across multiple domains including image processing (through 2D wavelet packet decomposition using wpdec2()), audio signal analysis (featuring adaptive frequency band selection), and vibration analysis (enabling precise time-frequency localization). The program demonstrates practical implementation scenarios while highlighting the transform's capability to capture subtle signal characteristics through its flexible time-frequency partitioning.