Wavelet Packet Transform

The wavelet packet transform (WPT) represents a generalization of the wavelet methods and it has recently been applied to various science and engineering fields with great success. Here are some tips about WPT from Matlab tutorial.

From WT to WPT:

In wavelet analysis, a signal is split into an approximation and a detail. The approximation is then itself split into a second-level approximation and detail, and the process is repeated. For an n-level decomposition, there are n+1 possible ways to decompose or encode the signal. More basic information about wavelet can be got here.

In wavelet packet analysis, the details as well as the approximations can be split.


The wavelet decomposition tree is a part of this complete binary tree. For instance, wavelet packet analysis allows the signal S to be represented as A1 + AAD3 + DAD3 + DD2.

Here is a sample transform of an EEG signal in our lab. The original waveform was decomposed into five waveforms in WPT method, db5 mother wavelet was employed and 7 levels decomposition was taken. We can see DELTA, THETA, ALPHA, BETA, GAMMA waves in this figure.