Generalized Brushlet Packet Transform

DESCRIPTION:

Computes a generalized brushlet packet transform. This function is defunct.

USAGE:

gbpt(x, partition, taper = "poly2", n.taper=8, boundary="periodic")
igbpt(x)

REQUIRED ARGUMENTS:

x
a time series or a numeric vector, or, for igbpt only, an object of class gbpt.
partition
a vector specifying the partition of the input x. The brushlet packets are computed for each specified partition. The end of points of the partition vector are 0 and length(x) and need not be specified. See below for details.

OPTIONAL ARGUMENTS:

taper
a character string, indicating the taper function: "boxcar", "poly1", "poly2", "poly3", "poly4", "poly5", or "trig". See the function bp.table for details.
n.taper
a non-negative integer. The length of the taper will be 2*n.taper.
boundary
a character string, available boundary rules: "reflect", "periodic" and "zero". See the function bp.table for details.

VALUE:

an object of class gbpt.

DETAILS:

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.

REFERENCES:

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.

SEE ALSO:

EXAMPLES:

## 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)