Single channel (univariate) signal - Practical Biomedical Signal Analysis Using MATLAB - page 59

FIGURE 2.18: Structure of the time-frequency plane for discrete wavelets. The
wavelet function is dilated and translated.

2.4.2.2.5 Wavelet packets Wavelet packets (WP) are a modification of the dis-
crete wavelet decomposition. The decomposition into WP is achieved in two steps.
First is the modification of the filter/downsampling cascade. In the WP scheme
at each level of the cascade both branches—the approximation and the detail
coefficients—are further filtered and downsampled. As a result, a complete tree is
obtained as illustrated in Figure 2.19. The second modification is that from that tree
we can select the most suitable decomposition of a given signal, e.g., with respect
to an entropy-based criterion [Coifman and Wickerhauser, 1992]. This procedure is
called pruning of a decomposition tree.

A 2 0

↓

↓

h g

AA 2 − 1 AD 2 − 1

↓ ↓ h g ↓ h g ↓

AAA 2 − 2 AAD 2 − 2 ADA 2 − 2 ADD 2 − 2

↓

↓

h g ↓ h g ↓ h ↓ g ↓ h ↓ g ↓

... ... ... ... ... ... ... ...

FIGURE 2.19: Three levels of WP decomposition tree.

More detailed information on different aspects of wavelet analysis may be found
in [Mallat, 1999].