## Wavelet packet decomposition

Purpose

Description

Macro Synopsis

Modules

Related Functions

References

### Purpose

Wavelet packet decomposition

### Description

The Wavelet packet decomposition extends the discrete wavelet transform in a
way that each octave *i* consists of boxes,
generated by a tree of lowpass and highpass operations, according to

(G : Lowpass, H: Highpass), where denotes a
convolution operation.

Therefore, the frequency bandwidth of a box decreases with growing
octave number. In other words: With increasing octave number the
frequency resolution becomes higher while the time
resolution is reduced.

The difference to the discrete wavelet transform is that we store all
result signals at octave i and apply to all these signals the filter
and subsampling procedure when we go from octave i to octave i+1.
Thus the ordinary wavelet decomposition is a subtree of the wavelet
packet decomposition.

The function's parameter is:

- number n of octaves (decomposition depth).

The tree of the b-signals is displayed with increasing octave from top
to bottom and increasing j from left to right.
The user can extract one of these b-signals (called boxes) via Extract box from WPD.
**Warning:** *Note that the information on the **shift* of the input signal is dropped in this function.

### Macro Synopsis

`y = WPD(x,n);`

signal x,y;

int n;

### Modules

Wavelet

### Related Functions

Define wavelet, Load wavelet,
Save wavelet, Decompose,
Reconstruct, Continuous wavelet transform.

### References

Vandenhouten [21].