gbpt(x, partition, taper = "poly2", n.taper=8, boundary="periodic") igbpt(x)
igbpt only, an object of class
gbpt.
"boxcar", "poly1", "poly2", "poly3", "poly4", "poly5", or
"trig".
See the function
bp.table for details.
2*n.taper.
"reflect", "periodic"
and
"zero".
See the function
bp.table for details.
gbpt.
This algorithm is a generalized version of the Brushlet Packet Transform (See
bpt
). Whereas in
bpt the only kinds of partitions that can be defined are
dyadic partitions (partitions corresponding to powers of 2), in this function
any kind of partition (not neccesarily dyadic) can be defined.
In case the partitions are dyadic, the resulting
transform will be identical to the Brushlet Packet Transform.
The algorithms for the taper functions are given in the
S+WAVELETS User's Manual,
in the section "Cosine Packet Algorithms". They are discussed in
greater depth in Wickerhauser (1994).
The default optional arguments
taper, boundary
can be reset using function
wavelet.options, see
wavelet.options for
details.
Meyer, F.G. and Coifman, R.R. (1997), Brushlets: A tool for directional image analysis and image compression Applied and Computational Harmonic Analysis, Academic Press Publishers.
Wickerhauser, M. V. (1994). Adapted Wavelet Analysis from Theory to Software. A. K. Peters Ltd, Wellesley, MA.
## create a linear chirp sequence
lc <- make.signal("linchirp", n=1024)
## compute the generalized brushlet packet transform for a dyadic partition
lc.gbpt <- gbpt(lc, partition=c(256, 512, 768), n.taper=8)
## the above transform is the same as obtained by the following bpt function
lc.bpt <- bpt(lc, n.levels=2, n.taper=8)
## to reconstruct the signal apply the igbpt function
recon <- igbpt(lc.gbpt)
## we can also compute the gbpt for a non-dyadic partition
lc.gbpt <- gbpt(lc, partition=c(25, 47, 100, 717, 930), n.taper=8)