idwpt

Inverse wavelet packet 1-D transform

Syntax

xrec = idwpt(wpt,l)

xrec = idwpt(wpt,l,wname)

xrec = idwpt(wpt,l,LoR,HiR)

xrec = idwpt(___, Boundary=extmode)

Description

xrec = idwpt(wpt,l) inverts the discrete wavelet packet transform (DWPT) of the terminal node wavelet packet tree wpt using the bookkeeping vector l. The idwpt function assumes that you obtained wpt and l using dwpt with the fk18 wavelet and default settings.

If the input to dwpt was one signal, xrec is a column vector. If the input was a multichannel signal, xrec is a matrix, where each matrix column corresponds to a channel.

xrec = idwpt(wpt,l,wname) uses the wavelet specified by wname to invert the DWPT. wname must be recognized by wavemngr. The specified wavelet must be the same wavelet used to obtain the DWPT.

xrec = idwpt(wpt,l,LoR,HiR) uses the scaling (lowpass) filter, LoR, and wavelet (highpass) filter, HiR. The synthesis filter pair LoR and HiR must be associated with the same wavelet used in the DWPT.

xrec = idwpt(___, Boundary=extmode) specifies the mode to extend the signal.

Examples

Inverse Discrete Wavelet Packet Transform

This example shows how to perform the inverse discrete wavelet packet transform using synthesis filters.

Obtain the DWPT of an ECG signal using dwpt with default settings.

load wecg
[wpt,l] = dwpt(wecg);

By default, dwpt uses the fk18 wavelet. Obtain the synthesis (reconstruction) filters associated with the wavelet.

[~,~,lor,hir] = wfilters("fk18");

Invert the DWPT using the synthesis filters and demonstrate perfect reconstruction.

xrec = idwpt(wpt,l,lor,hir);
norm(wecg-xrec,"inf")

ans = 
4.9236e-11

Change Boundary Extension Mode

Obtain the DWPT of an ECG signal using dwpt and periodic extension.

load wecg
[wpt,l] = dwpt(wecg,Boundary="periodic");

By default, idwpt uses symmetric extension. Invert the DWPT using periodic and symmetric extension modes.

xrecA = idwpt(wpt,l,Boundary="periodic");
xrecB = idwpt(wpt,l);

Demonstrate perfect reconstruction only when the extension modes of the forward and inverse DWPT agree.

fprintf("Periodic/Periodic : %f\n",norm(wecg-xrecA,"inf"))

Periodic/Periodic : 0.000000

fprintf("Periodic/Symmetric: %f\n",norm(wecg-xrecB,"inf"))

Periodic/Symmetric: 1.477907

Input Arguments

wpt — Terminal node wavelet packet tree

cell array

Terminal node wavelet packet tree, specified as a cell array. wpt is the output of dwpt with the FullTree set to false.

Example: [wpt,l] = dwpt(X,Level=3,FullTree=false) returns the terminal node wavelet packet tree of the three-level wavelet packet decomposition of X.

Data Types: single | double
Complex Number Support: Yes

l — Bookkeeping vector

vector of positive integers

Bookkeeping vector, specified as a vector of positive integers. The vector l is the output of dwpt. The bookkeeping vector contains the length of the input signal and the number of coefficients by level and is required for perfect reconstruction.

Data Types: single | double

wname — Wavelet

"fk18" (default) | character vector | string scalar

Wavelet to use in the inverse DWPT, specified as a character vector or string scalar. wname must be recognized by wavemngr. The specified wavelet must be the same wavelet used to obtain the DWPT.

You cannot specify both wname and a filter pair, LoD and HiD.

Example: xrec = idwpt(wpt,l,"sym4") specifies the sym4 wavelet.

LoR,HiR — Wavelet synthesis filters

real-valued vectors

Wavelet synthesis (reconstruction) filters to use in the inverse DWPT, specified as a pair of real-valued vectors. LoR is the scaling (lowpass) synthesis filter and HiR is the wavelet (highpass) synthesis filter. The synthesis filter pair must be associated with the same wavelet as used in the DWPT. You cannot specify both wname and a filter pair, LoR and HiR. See wfilters for additional information.

Note

idwpt does not check that LoR and HiR satisfy the requirements for a perfect reconstruction wavelet packet filter bank. To confirm your filter pair satisfies the requirements, use isorthwfb or isbiorthwfb.

extmode — Wavelet packet transform extension mode

"reflection" (default) | "periodic" | "zeropad"

Wavelet packet transform extension mode, specified as "reflection" , "periodic", or "zeropad". The idwpt function extends the wavelet packet coefficients at each level based on the corresponding mode in dwtmode:

• "reflection" — Half-point symmetric extension, "sym"

• "periodic" — Periodic extension, "per"

• "zeropad" — Zero padding, "zpd" (since R2025a)

You must specify the same mode used in the DWPT.

Example: xrec = idwpt(wpt,l,Boundary="periodic") and xrec = idwpt(wpt,l,"Boundary","periodic") both specify periodic extension.

References

[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.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• The input wname must be constant.

Version History

Introduced in R2020a

R2025a: Specify zero padding as an extension mode

The idwpt function now supports zero padding as an extension mode.

R2023b: Compute inverse DWPT of complex-valued data

The idwpt function can invert the DWPT of complex-valued data. The idwpt function assumes you computed the DWPT using dwpt.