IUFWT - Inverse Undecimated Fast Wavelet Transform

Usage

f = iufwt(c,info)
f = iufwt(c,w,J);

Input parameters

Output parameters

Description

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)