Description Usage Arguments Details Value References See Also Examples
The discrete wavelet transform using convolution style filtering and periodic extension.
Let j, t be the decomposition level, and time index, respectively, and s(0,t)=X(t) for t=0,...,N-1 where X(t) is a real-valued uniformly-sampled time series. The jth level DWT wavelet coefficients (d(j,t)) and scaling coefficients (s(j,t)) are defined as d(j,t)=sum(h(l) s(j-1, t - 2t+1-l) mod N(j-1)) and s(j,t)=sum(g(l) s(j-1, t - 2t+1-l mod N(j-1))) for j=1,...,J where h(l) and g(l) are the jth level wavelet and scaling filter, respectively, and Nj=2^(j-1). The DWT is a collection of all wavelet coefficients and the scaling coefficients at the last level: d(1),d(2),...,d(J),s(J) where d(j) and s(j) denote a collection of wavelet and scaling coefficients, respectively, at level j.
1 2 3 |
x |
a vector containing a uniformly-sampled real-valued time series. |
documentation |
a character string used to describe the input
|
keep.series |
a logical value. If |
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 |
This DWT imposes an ad hoc storage sytem for odd length scaling coefficient crystals: if the length of a scaling coefficient crystal is odd, the last coefficient is "stored" in the extra crystal. During reconstruction, any extra scaling coefficients are returned to their proper location. Such as system imposes no spurious energy in the transform coefficients at the cost of a little bookkeeping.
an object of class wavTransform
.
D. B. Percival and A. T. Walden, Wavelet Methods for Time Series Analysis, Cambridge University Press, 2000.
reconstruct
, wavDaubechies
, wavMODWT
, wavMODWPT
, wavMRD
, wavDictionary
, wavIndex
, wavTitle
, wavBoundary
, wavShrink
.
1 2 3 4 5 6 7 8 9 10 11 12 13 | ## calculate the DWT of linear chirp
linchirp <- make.signal("linchirp", n=1024)
result <- wavDWT(linchirp, wavelet="s8", n.levels=5, keep.series=TRUE)
## plot the transform shifted for approximate zero
## phase alignment
plot(wavShift(result))
## plot summary
eda.plot(result)
## summarize the transform
summary(result)
|
Min 1Q Median 3Q Max Mean SD Var MAD Energy %
d1 -0.144 -0.005 0.000 0.005 0.130 0.000 0.037 0.001 0.008 0.141
d2 -1.265 -0.103 0.000 0.091 1.271 0.001 0.425 0.181 0.146 9.194
d3 -2.529 -0.615 -0.001 0.603 2.629 -0.035 1.236 1.529 0.918 38.804
d4 -3.585 -0.820 -0.001 0.171 3.212 -0.224 1.422 2.023 0.661 26.092
d5 -5.140 -0.307 0.000 0.112 2.812 -0.372 1.422 2.022 0.259 13.404
s5 -3.880 -0.092 0.005 0.059 5.373 0.170 1.403 1.967 0.133 12.365
Energy Distribution:
1st 1% 2% 3% 4% 5% 10% 15% 20%
Energy % 5.766 30.760 44.093 55.435 65.202 73.154 90.550 96.581 98.902
|coeffs| 5.373 2.812 2.489 2.312 2.110 1.787 0.974 0.593 0.344
#coeffs 1.000 11.000 21.000 31.000 41.000 52.000 103.000 154.000 205.000
25%
Energy % 99.631
|coeffs| 0.202
#coeffs 256.000
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