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: pcosts, pcosts.2d, ptable.

best.basis(x, type="wp", J=NULL, costs=attr(x, "pcosts"),
           data=NULL, ...)

x:

a numeric vector, a univariate time series, a matrix, an image, or an object of pcosts, pcosts.2d, ptable.

type:

one of the character strings "wp" or "cp" indicating whether to perform wavelet packet analysis or cosine packet analysis. This argument will be ignored when x is an object of ptable, pcosts or pcosts.2d.

J:

maximum depth of tree-search. This argument applies only for when x is an object of ptable or pcosts. Levels beyond J will be ignored in the best basis selection process. The default is n.levels.

costs:

a numeric vector of length 2^min(J, n.level). The best basis will be selected based on the costs vector. This argument applies only for when x is an object of ptable. The vector costs is typically created by pcosts applied to a ptable object.

data:

the image to be analyzed. Only for when x is a pcosts.2d object. If present, coefficients of the best basis are returned (a matrix of the same size as data), otherwise, a character vector of crystal.names representing the best basis is returned.

...:

additional arguments for wp.table or cp.table when x is a numeric vector; additional arguments for wp.costs.2d or cp.costs.2d when x is a matrix. See wp.table, cp.table, wp.costs.2d, cp.costs.2d for details.

Otherwise, a wavelet packet transform object or a cosine packet transform object is returned. 1-D wavelet packet transforms have class wpt inheriting from classes wp and crystal.vector (if boundary is not infinite) or crystal.list (if boundary=infinite). 1-D cosine packet transforms have class cpt inheriting from classes cp and crystal.vector. See crystal.vector.object and crystal.list.object for details.

2-D wavelet packet and cosine packet transforms have class wpt.2d and cpt.2d, and inherit from class crystal.matrix. See crystal.matrix.object for details.

If x is a numeric vector or univariate time series, then best.basis will first compute a wavelet packet or cosine packet table (according to type="wp" or "cp) and then select the best basis from the table.

If x is a matrix or an image, then best.basis will first compute a 2D wavelet or cosine packet cost vector (according to type="wp" or "cp) and then select the best basis from the cost vector.

For more details, refer to the section "The Best Basis Algorithm" of the S+WAVELETS User's Manual for details. See also Coifman and Wickerhauser (1992) and Chapter 8 of Wickerhauser (1994).

Wickerhauser, M. V. (1994). Adapted Wavelet Analysis -- from theory to software.

yy <- make.signal("linchirp", 512)    # a linear chirp
yw <- wp.table(yy, wavelet="s8", n.levels=4)
bb <- best.basis(yw)                  # select the best basis
eda.plot(bb)

yc <- cp.table(yy, taper="trig", n.levels=4)
bc <- best.basis(yc)
eda.plot(bc)

x <- phone-mean(phone)
wcost <- wp.costs.2d(x, wavelet="s8", n.levels=3)
bb2 <- best.basis(wcost, x)
eda.plot(bb2)

ccost <- cp.costs.2d(x, taper="poly1", n.levels=3)
bb3 <- best.basis(ccost, x)
eda.plot(bb3)