Wavelet packet decomposition

In the DWT, each level is calculated by passing only the previous wavelet approximation coefficients (cAj) through discrete-time low- and high-pass quadrature mirror filters.

[1][2] However, in the WPD, both the detail (cDj (in the 1-D case), cHj, cVj, cDj (in the 2-D case)) and approximation coefficients are decomposed to create the full binary tree.

[5] There are several algorithms for subband tree structuring that find a set of optimal bases that provide the most desirable representation of the data relative to a particular cost function (entropy, energy compaction, etc.).

[1] [2] There were relevant studies in signal processing and communications fields to address the selection of subband trees (orthogonal basis) of various kinds, e.g. regular, dyadic, irregular, with respect to performance metrics of interest including energy compaction (entropy), subband correlations and others.

In contrast, the discrete-time subband transform theory enables a perfect representation of already sampled signals.