Inverse Transform Operator
DESCRIPTION:
Reconstructs (synthesizes) a signal from transform coefficients

This function is generic (see Methods); method functions can be written to handle specific classes of data. Classes which already have methods for this function include:

atrous, cp.crystal, cp.crystal.2d, cpt, cpt.2d, decompose, dwt, dwt.molecule, molecule, nd.dwt, rob.dwt, wp.crystal, wp.crystal.2d, wp.nd.crystal, wpt, wpt.2d.

USAGE: 
reconstruct(x, rob.resid=F)
REQUIRED ARGUMENTS:
x:
a transform object. The classes of objects which can be transformed are listed above.
OPTIONAL ARGUMENTS:
rob.resid:
logical flag indicating if robust residuals should be included in reconstruction. For rob.dwt objects only.
VALUE:
for 1-D transforms, a reconstructed vector with the same attributes as the original signal (data). If the original signal was a time series object, then the reconstructed signal will also be a time series object.

For 2-D transforms, a reconstructed image with the same dimensions as the original image.

DETAILS:
For decimated wavelet and wavelet packet transforms and crystals, the inverse transform is obtained by applying the appropriate synthesis wavelet filter operators.

For the non-decimated wavelet transform and crystals, the reconstructed signal is the average of the reconstructions from low-pass and high-pass filters, which is equivalent to the average over the decimations.

For cosine packet transforms and crystals, the inverse transform is obtained by applying the inverse DCT followed by the appropriate untapering operator.

For molecules and atoms, the inverse transform is obtained by first converting the molecule or atom to a wavelet packet or cosine packet transform, and then inverting that transform.

See the section "Pyramid Algorithm" and the chapter "Algorithms and Filters" of the S+WAVELETS User's Manual for more details about inverse transforms.

SEE ALSO:
best.basis , best.level , cpt , cpt.2d , cp.crystal, cp.crystal.2d , decompose , dwt , rob.dwt , nd.dwt , molecule, wpt , wpt.2d , wp.crystal .
EXAMPLES: 
xx <- rnorm(511)                   # white noise of length 511
yy <- dwt(xx, wavelet="bs2.4", boundary="reflection")
zz <- reconstruct(yy)              # reconstruct from wavelet coefficients
vecnorm(xx-zz)                     # check perfect reconstruction


yy <- make.signal("twochirp", 129)
ww <- wp.table(yy, wavelet="s8", boundary="zero", n.level=3)
bb <- best.basis(ww)               # select the best basis
zz <- reconstruct(bb)              # reconstruct from the best basis
vecnorm(yy-zz)                     # check perfect reconstruction