Description Usage Arguments Value See Also Examples
theoreticalWaveletVar
calculates the theoretical wavelet coefficients'
variance of a fractional Brownian motion (fBm) with known parameters.
1 | theoreticalWaveletVar(H, sigma2, family, filter_number, nlevels)
|
H |
The Hurst exponent of the fBm. |
sigma2 |
Variance of the fractional Gaussian noise that results after differentiating the fBm. |
family |
Specifies the family of wavelets used in the computation of the
wavelet transform. See |
filter_number |
An integer identifying the concrete filter used within the
|
nlevels |
Number of resolution levels to compute. Thus, the resulting wavelet coefficients' variances are the expected ones from a fBm of length 2 ^ n. |
A waveletVar
object with the theoretical wavelet variance.
1 2 3 4 5 6 7 8 9 10 11 | use_H = 0.3
fbm = fbmSim(n = 2 ^ 10, H = use_H)
w_fbm = wd(fbm, bc = "symmetric")
vpr = waveletVar(w_fbm)
plot(vpr)
# the theoreticalWaveletVar also returns a 'waveletVar' object:
theo_vpr = theoreticalWaveletVar(H = use_H, sigma2 = 1,
family = wtInfo(vpr)[["family"]],
filter_number = wtInfo(vpr)[["filter_number"]],
nlevels = length(vpr))
points(theo_vpr, col = "red")
|
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