IUWPFBT - Inverse Undecimated Wavelet Packet Filterbank Tree

Usage

f=iuwpfbt(c,info);
f=iuwpfbt(c,wt);

Input parameters

Output parameters

Description

f = iuwpfbt(c,info) reconstructs signal f from the wavelet packet coefficients c using parameters from info struct. both returned by the uwpfbt function.

f = iuwpfbt(c,wt) reconstructs signal f from the wavelet packet coefficients c using the undecimated wavelet filterbank tree described by wt.

Please see help for wfbt description of possible formats of wt.

Filter scaling:

As in uwpfbt, the function recognizes three flags controlling scaling of filters:

'sqrt'

Each filter is scaled by 1/sqrt(a), there a is the hop factor associated with it. If the original filterbank is orthonormal, the overall undecimated transform is a tight frame. This is the default.

'noscale'

Uses filters without scaling.

'scale'

Each filter is scaled by 1/a.

If 'noscale' is used, 'scale' must have been used in uwpfbt (and vice versa) in order to obtain a perfect reconstruction.

Scaling of intermediate outputs:

The following flags control scaling of the intermediate coefficients. The intermediate coefficients are outputs of nodes which ale also inputs to nodes further in the tree.

'intsqrt'

Each intermediate output is scaled by 1/sqrt(2). If the filterbank in each node is orthonormal, the overall undecimated transform is a tight frame. This is the default.

'intnoscale'

No scaling of intermediate results is used.

'intscale'

Each intermediate output is scaled by 1/2.

If 'intnoscale' is used, 'intscale' must have been used in uwpfbt (and vice versa) in order to obtain a perfect reconstruction.

Examples:

A simple example showing perfect reconstruction using the "full decomposition" wavelet tree:

f = greasy;
J = 7;
wtdef = {'db10',J,'full'};
c = uwpfbt(f,wtdef);
fhat = iuwpfbt(c,wtdef);
% The following should give (almost) zero
norm(f-fhat)