| wavMODWPT {wmtsa} | R Documentation |
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.
wavMODWPT(x, wavelet="s8", n.levels=ilogb(length(x), base=2),
position=list(from=1,by=1,units=character()), units=character(),
title.data=character(), documentation=character())
x |
a vector containing a uniformly-sampled real-valued time series. |
documentation |
a character string used to describe the input
data. Default: character(). |
n.levels |
the number of decomposition levels.
Default: as.integer(floor(logb(length(x),base=2))). |
position |
a list containing the arguments
from, by and to which describe the position(s) of the input
data. All position arguments need not be specified as missing members
will be filled in by their default values. Default: list(from=1, by=1, units=character()). |
title.data |
a character string representing the name of the input
data. Default: character(). |
units |
a string denoting the units of the time series. Default: character() (no units). |
wavelet |
a character string denoting the filter type. See wavDaubechies for details. Default: "s8". |
an object of class wavTransform.
D. B. Percival and A. T. Walden, Wavelet Methods for Time Series Analysis, Cambridge University Press, 2000.
reconstruct, wavMRD, wavMODWT, wavDWT, wavDWPT, wavDaubechies, wavShift, wavZeroPhase.
## calculate the MODWPT of sunspots series out to ## 3 levels using Daubechies least asymmetric ## 8-tap filter set z <- wavMODWPT(sunspots, wavelet="s8", n.levels=3) ## plot the transform plot(z) ## summarize the transform summary(z)