Signal Decomposition
DESCRIPTION:
Decomposes a signal or an image into components determined by the given basis or molecules.

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:

cpt, cp.molecule, dwt, nd.dwt, rob.dwt, wpt, wp.molecule.

USAGE: 
decompose(x, top=NULL, data=NULL, order.crystal="energy")
REQUIRED ARGUMENTS:
x:
an object of cpt, cp.molecule, dwt, nd.dwt, rob.dwt, wpt, wp.molecule.
OPTIONAL ARGUMENTS:
top:
number of coefficients (atoms) in x used in the decomposition, in effect only if x is an object of class "molecule". By default, use all the coefficients in x. See details below.
data:
if provided, residual term will be computed and attached at the end of the decomposition. This argument used only if x is an object of class "molecule". See details below.
order.crystal:
a character string: "dwt" (for the DWT decomposition only), "energy" (the decomposition components will be ordered by energy), and "frequency" (in depth.first order).
VALUE:
an object of class decompose. See decompose.object for details.
DETAILS:
The function decompose produces a decomposition which is a sum of components where each k-th component represents the contribution of the k-th crystal (when x is of class cpt or wpt) or the atom associated with the k-th largest coefficient (when x is of class "cp.molecule" or "wp.molecule") to the signal.

When x is of class "cpt" or "wpt", all atoms with non-zero coefficients are included in the decomposition, the sum of the components yields the original series.

When x is of class "cp.molecule" or "wp.molecule", if data is provided, the sum of the components yields an approximation of the data with a (non-trivial) residual term attached at the end of the outcome matrix. The bigger the top, the closer the approximation to the original signal; if data is missing, the sum of the components only yields an approximation to the original signal.

SEE ALSO:
cpt , decompose.object , dwt , molecule , mra , mrd , top.atoms , wpt .
EXAMPLES: 
xx <- make.signal("ramp", 1024)
par(mfrow=c(2,2))
plot(xx, type="l", xlab="")
xx.dwt <- dwt(xx, wavelet="s8", n.levels=4)
plot(xx.dwt)
xx.dec <- decompose(xx.dwt)
plot(xx.dec)
xx.top <- top.atoms(xx.dwt, n.atoms=10)
xx.dec1 <- decompose(xx.top, data=xx)    # decompose signal on the top 10 atoms
plot(xx.dec1)