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

Description Usage Arguments Value References See Also Examples

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.

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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)

         Min     1Q Median     3Q     Max   Mean     SD      Var    MAD
w0.0   0.000 15.700 42.000 74.925 253.800 51.266 43.449 1887.813 42.106
w1.0  -1.656 16.143 42.318 73.643 244.069 51.266 42.682 1821.750 41.465
w1.1 -36.132 -4.037 -0.116  4.020  46.084  0.000  8.128   66.063  5.955
w2.0  -1.422 15.312 43.220 73.699 230.014 51.266 42.006 1764.523 42.369
w2.1 -32.739 -3.860 -0.104  3.594  47.684  0.000  7.565   57.227  5.522
w2.2 -30.407 -3.035 -0.007  3.053  28.690  0.000  6.170   38.075  4.520
w2.3 -24.602 -2.776 -0.020  2.785  21.956  0.000  5.290   27.989  4.124
w3.0  -1.219 15.599 43.886 72.339 211.179 51.266 41.405 1714.363 42.054
w3.1 -37.484 -3.307 -0.058  3.144  34.673  0.000  7.082   50.160  4.783
w3.2 -26.621 -2.824 -0.003  2.770  35.649  0.000  5.608   31.455  4.145
w3.3 -24.007 -2.576 -0.023  2.540  29.002  0.000  5.077   25.772  3.792
w3.4 -21.595 -2.333 -0.026  2.356  21.961  0.000  4.550   20.699  3.471
w3.5 -22.008 -2.251 -0.059  2.159  19.835  0.000  4.168   17.376  3.266
w3.6 -19.652 -1.996  0.019  1.955  19.629  0.000  3.723   13.861  2.936
w3.7 -18.203 -1.951  0.016  1.914  17.866  0.000  3.759   14.127  2.856
     Energy %
w0.0   25.000
w1.0   24.634
w1.1    0.366
w2.0   24.318
w2.1    0.317
w2.2    0.211
w2.3    0.155
w3.0   24.040
w3.1    0.278
w3.2    0.174
w3.3    0.143
w3.4    0.115
w3.5    0.096
w3.6    0.077
w3.7    0.078

Energy Distribution:
             1st      1%      2%       3%       4%       5%      10%      15%
Energy %   0.126  23.723  38.499   49.582   58.288   65.259   85.708   94.739
|coeffs| 253.800 144.605 123.270  108.497   96.244   86.900   56.921   36.229
#coeffs    1.000 423.000 846.000 1269.000 1692.000 2115.000 4230.000 6345.000
              20%       25%
Energy %   97.770    98.706
|coeffs|   18.843    12.216
#coeffs  8460.000 10575.000