A Trous Wavelet Transform
DESCRIPTION:
Applies the a trous wavelet transform to a time series or a vector.
USAGE: 
atrous(x, wavelet="s8", n.levels=6, dual=F, analysis.filter=NULL)
REQUIRED ARGUMENTS:
x:
a vector or time series object.
OPTIONAL ARGUMENTS:
wavelet:
a character string giving the name of the wavelet, e.g. "d4", "s8". See wavelet for a list of all available wavelet names. For user-provided filters, input the values in analysis.filter below.
n.levels:
a non-negative integer specifying number of multi-resolution levels. If n.levels is bigger than ml, where ml is the maximum possible level, computed from the max.level function, then n.levels is set to ml and a warning message is given.
dual:
logical flag indicating if dual filter is used for analysis.
analysis.filter:
for user-defined filter, see filter argument in wave.filter for details.
VALUE:
an object of class atrous, inheriting from the classes nd.dwt, dwt, wpt, wp, and crystal.list. See crystal.list.object for details.
DETAILS:
The atrous transform is closely related to the non-decimated discrete wavelet transform. Refer to the function nd.dwt and the section "Non-Decimated Wavelets" in the S+WAVELETS User's Manual for more details about the atrous function.
BUGS:
Subscripting is not fully supported. Cannot reconstruct from [[.

Signal x is assumed to be periodic. Other boundary rules are not available for atrous.

REFERENCES:
Dutilleux, P. (1987). An Implementation of the "algorithme a trous" to Compute the Wavelet Transform. In Wavelets: Time-Frequency Methods and Phase Space. Edited by Combes, J. M. and Grossman, A., Tchamitchian, Ph., Springer-Verlag.

Shensa, M. J. (1992). The Discrete Wavelet Transform: Wedding the A Trous and Mallat Algorithms. IEEE Transactions on Signal Processing, 40 (10), 2464-2482.

SEE ALSO:
max.level , nd.dwt , wave.filter , wavelet.options , crystal.list.object .
EXAMPLES: 
z1 <- atrous(glint, wavelet="s8", n.levels=5)
z2 <- nd.dwt(glint, wavelet="s8", n.levels=5)
par(mfrow=c(1,2))
plot(z1)                          # plot A Trous coefficients
plot(z2)                          # plot non-decimate DWT coefficients