c=uwpfbt(f,wt); [c,info]=uwpfbt(...);
| f | Input data. |
| wt | Wavelet Filterbank tree |
| c | Coefficients in a \(L \times M\) matrix. |
c=uwpfbt(f,wt) returns coefficients c obtained by applying the undecimated wavelet filterbank tree defined by wt to the input data f using the "a-trous" algorithm. Number of columns in c (M) is defined by the total number of outputs of each node. The outputs c(:,jj) are ordered in the breadth-first node order manner.
[c,info]=uwpfbt(f,wt) additionally returns struct. info containing the transform parameters. It can be conviniently used for the inverse transform iuwpfbt e.g. fhat = iuwpfbt(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.
The following flags control scaling of intermediate outputs and therefore the energy relations between coefficient subbands. An intermediate output is an output of a node which is further used as an input to a descendant node.
- '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. This is necessaty for the wpbest function to correctly work with the cost measures.
- 'intscale'
- Each intermediate output is scaled by 1/2.
If 'intnoscale' is used, 'intscale' must be used in iuwpfbt (and vice versa) in order to obtain a perfect reconstruction.
When compared to wpfbt, the subbands produced by uwpfbt 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' must be used in iuwpfbt (and vice versa) in order to obtain a perfect reconstruction.
A simple example of calling the uwpfbt function using the "full decomposition" wavelet tree:
[f,fs] = greasy;
J = 6;
[c,info] = uwpfbt(f,{'db10',J,'full'});
plotwavelets(c,info,fs,'dynrange',90);