c=uwfbt(f,wt); [c,info]=uwfbt(...);
| f | Input data. |
| wt | Wavelet Filterbank tree |
| c | Coefficients stored in \(L \times M\) 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.
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.
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);