UWFBT Undecimated Wavelet FilterBank Tree
Usage: c=uwfbt(f,wt);
[c,info]=uwfbt(...);
Input parameters:
f : Input data.
wt : Wavelet Filterbank tree
Output parameters:
c : Coefficients stored in L xM matrix.
UWFBT(f,wt) computes redundant time (or shift) invariant
representation of the input signal f using the filterbank tree
definition in wt and using the "a-trous" algorithm.
Number of columns in c (*M*) is defined by the total number of
outputs of nodes of the tree.
[c,info]=UWFBT(f,wt) additionally returns struct. info containing
the transform parameters. It can be conviniently used for the inverse
transform IUWFBT e.g. fhat = iUWFBT(c,info). It is also required
by the PLOTWAVELETS function.
If f is a matrix, the transformation is applied to each of W columns
and the coefficients in c are stacked along the third dimension.
Please see help for WFBT description of possible formats of wt and
description of frequency and natural ordering of the coefficient subbands.
Filter scaling
--------------
When compared to WFBT, the subbands produced by UWFBT are
gradually more and more redundant with increasing depth in the tree.
This results in energy grow of the coefficients. There are 3 flags
defining filter scaling:
'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' has to be used in IUWFBT (and vice
versa) in order to obtain a perfect reconstruction.
Examples:
---------
A simple example of calling the UWFBT function using the "full decomposition" wavelet tree:
f = greasy;
J = 8;
[c,info] = uwfbt(f,{'sym10',J,'full'});
plotwavelets(c,info,16000,'dynrange',90);
Url: http://ltfat.github.io/doc/wavelets/uwfbt.html
See also: iuwfbt, wfbtinit.
Package: ltfat