IUFWT Inverse Undecimated Fast Wavelet Transform
Usage: f = iufwt(c,info)
f = iufwt(c,w,J);
Input parameters:
c : Coefficients stored in L xJ+1 matrix.
info,w : Transform parameters struct/Wavelet filters definition.
J : Number of filterbank iterations.
Output parameters:
f : Reconstructed data.
f = IUFWT(c,info) reconstructs signal f from the wavelet
coefficients c using parameters from info struct. both returned by
UFWT function.
f = IUFWT(c,w,J) reconstructs signal f from the wavelet
coefficients c using the wavelet filterbank consisting of the J*
levels of the basic synthesis filterbank defined by w using the "a-trous"
algorithm. Node that the same flag as in the ufwt function have to be used.
Please see the help on UFWT for a description of the parameters.
Filter scaling
--------------
As in UFWT, 3 flags defining scaling of filters are recognized:
'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 UFWT (and vice
versa) in order to obtain a perfect reconstruction.
Examples:
---------
A simple example showing perfect reconstruction:
f = gspi;
J = 8;
c = ufwt(f,'db8',J);
fhat = iufwt(c,'db8',J);
% The following should give (almost) zero
norm(f-fhat)
References:
S. Mallat. A wavelet tour of signal processing. Academic Press, San
Diego, CA, 1998.
Url: http://ltfat.github.io/doc/wavelets/iufwt.html
See also: ufwt, plotwavelets.
Package: ltfat