# wavMODWPT: The maximal overlap discrete wavelet packet transform... In wmtsa: Wavelet Methods for Time Series Analysis

## 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.

## Usage

 ```1 2 3``` ```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()) ```

## Arguments

 `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"`.

## Value

an object of class `wavTransform`.

## References

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`.
 ``` 1 2 3 4 5 6 7 8 9 10``` ```## 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) ```