Given j, n, t are the decomposition level, oscillation index, and time index,
respectively, the DWPT is given by W(j,n,t) = sum(u(n,l) * W( j-1, floor(n/2),
2t+1-l mod N(j-1) ) ) and g and h are the scaling filter and wavelet filter,
respectively. Each filter is of length L. 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:
,
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,
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.
EXAMPLES:
## calculate the DWPT of an electrocardiogram
## sequence out to 3 levels using Daubechies least
## asymmetric 8-tap filter set
result <- wavDWPT( ecg, wavelet = "s8", n.levels = 3 )
## plot the transform
plot( result )
## summarize the transform
summary( result )