Main Content

Multisignal 1-D wavelet packet transform

returns the
terminal (final-level) nodes of the discrete wavelet packet transform (DWPT) of
`wpt`

= dwpt(`X`

)`X`

. The input `X`

is a real-valued vector, matrix,
or timetable. By default, the `fk18`

wavelet is used, and the decomposition
level is `floor(log`

, where
_{2}(*Ns*))*Ns* is the number of data samples. The wavelet packet transform
`wpt`

is a 1-by-*N* cell array, where

.*N* =
2^floor(log_{2}(*Ns*))

`[`

also returns the transform levels of the nodes of `wpt`

,`l`

,`packetlevels`

] = dwpt(___)`wpt`

using any of the
previous syntaxes.

`[`

also returns the center frequencies of the approximate passbands in cycles per sample using
any of the previous syntaxes.`wpt`

,`l`

,`packetlevels`

,`f`

] = dwpt(___)

`[`

also returns the relative energy for the wavelet packets in `wpt`

,`l`

,`packetlevels`

,`f`

,`re`

] = dwpt(___)`wpt`

using
any of the previous syntaxes. The relative energy is the proportion of energy contained in
each wavelet packet by level.

`[___] = dwpt(___,`

specifies options using name-value pair arguments in addition to the input arguments in the
previous syntaxes. For example, `Name,Value`

)`'Level',4`

specifies the decomposition
level.

The `dwpt`

function performs a discrete wavelet packet transform and
produces a sequency-ordered wavelet packet tree. Compare the sequency-ordered and normal
(Paley)-ordered trees. $$\tilde{G}(f)$$ is the scaling (lowpass) analysis filter, and $$\tilde{H}(f)$$ represents the wavelet (highpass) analysis filter. The labels at the bottom
show the partition of the frequency axis [0, ½].

[1] Wickerhauser, Mladen Victor.
*Adapted Wavelet Analysis from Theory to Software.* Wellesley, MA: A.K.
Peters, 1994.

[2] Percival, D. B., and A. T. Walden.
*Wavelet Methods for Time Series Analysis*. Cambridge, UK: Cambridge
University Press, 2000.

[3] Mesa, Hector. “Adapted Wavelets
for Pattern Detection.” In *Progress in Pattern Recognition, Image Analysis and
Applications*, edited by Alberto Sanfeliu and Manuel Lazo Cortés, 3773:933–44.
Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. https://doi.org/10.1007/11578079_96.