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.
1 2 3 |
x |
a vector containing a uniformly-sampled real-valued time series. |
documentation |
a character string used to describe the input
|
n.levels |
the number of decomposition levels.
Default: |
position |
a |
title.data |
a character string representing the name of the input
|
units |
a string denoting the units of the time series. Default: |
wavelet |
a character string denoting the filter type. See |
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
.
1 2 3 4 5 6 7 8 9 10 |
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
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