The maximal overlap discrete wavelet packet transform (MODWPT).
USAGE:
wavMODWPT( x, wavelet = ``s8", n.levels = 3 )
DESCRIPTION:
Given j, n, t are the decomposition level, oscillation index, and time index,
respectively, the MODWPT is given by W(j,n,t) = sum(u(n,l) * W( j-1, floor(n/2),
t - 2^(j-1) * l mod N ) ) The variable L is the length of the filters defined by
u(n,l) = g(l) / sqrt(2) if n mod 4 = 0 or 3; u(n,l) = h(l) / sqrt(2) if n mod 4
= 1 or 2; for l = 0, ..., L-1 where g and h are the scaling filter and wavelet
filter, respectively. By definition, W(0,0,t) = X(t) where X is the original
time series.
REQUIRED ARGUMENTS:
x
A vector containing a uniformly-sampled real-valued time series.
OPTIONAL ARGUMENTS:
wavelet
A character string denoting the filter type. See wavDaubechies for details.
Default: ``s8".
n.levels
The number of decomposition levels. Default: the maximum level at which there
exists at least one interior wavelet coefficient.
VALUE:
result
An object of class WaveletPacket.
REFERENCES:
(1) D. B. Percival and A. T. Walden, ``Wavelet Methods for Time Series Analysis'',
Cambridge University Press, 2000.
SEE ALSO:
,
,
,
,
,
,
,
.
EXAMPLES:
## calculate the MODWPT of an electrocardiogram
## sequence out to 3 levels using Daubechies least
## asymmetric 8-tap filter set
result <- wavMODWPT( ecg, wavelet = "s8", n.levels = 3 )
## plot the transform
plot( result )
## summarize the transform
summary( result )