Non-decimated Discrete Wavelet Transform

DESCRIPTION:

Applies the non-decimated (over-sampled) discrete wavelet transform to a time series or a vector.

USAGE:

nd.dwt(x, wavelet="s8", n.levels=6, dual=F, 
       analysis.filter=NULL, synthesis.filter=NULL, 
       filter.reverse=F) 

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 all available wavelet names. For user-provided filter, 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, then n.levels is set to ml and a warning message is given. The max.level function is used to compute ml.
dual
logical flag indicating if dual filter is used for analysis instead of synthesis. This argument applies only for biorthogonal wavelets. See wavelet for details.
analysis.filter
for user-defined analysis filter, see filter argument in wave.filter for details.
synthesis.filter
for user-defined synthesis filter, see filter argument in wave.filter for details. When analysis.filter is provided, then the default synthesis.filter is also analysis.filter.
filter.reverse
logical flag indicating should wavelet filters be reversed.

VALUE:

an object of class nd.dwt, inheriting from the classes dwt , wpt, wp and crystal.vector. or an object of class nd.dwt.list, inheriting from the classes dwt.list , wpt.list, wp.list and crystal.list. See crystal.vector.object and crystal.list.object for details.

DETAILS:

The non-decimated discrete wavelet transform is non-orthogonal variant to the classical DWT. With the non-decimated DWT, starting with n sample values, you end up with (J+1) n coefficients. Unlike the classical DWT, which has fewer coefficients at coarse scales, each scale for the non-decimated DWT has n coefficients. The non-decimated wavelet transform can be inverted using the reconstruct function. Refer to the section "Non-Decimated Wavelets" in the S+WAVELETS User's Manual for more details about the nd.dwt function. All the default optional arguments can be reset using function wavelet.options . See wavelet.options for details.

BUGS:

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

REFERENCES:

Mallat, S. and Hwang, W. L. (1992). Singularity Detection and Processing with Wavelets. IEEE Transactions on Information Theory, 38 (2), 617-643. 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:

, , , , , .

EXAMPLES:

xx <- make.signal("doppler") 
nd <- nd.dwt(xx, n.levels=4) 
eda.plot(nd)