#
# Let us create the discrete autocorrelation wavelets for the Haar wavelet.
# We shall create up to scale 4.
#
haardw4<-PsiJ(-4, filter.number=1, family="DaubExPhase", verbose=TRUE)
haardw4
#Computing PsiJ
#Returning precomputed version
#Took 0.00999999 seconds
#
#[[1]]:
#[1] -0.5 1.0 -0.5
#
#[[2]]:
#[1] -0.25 -0.50 0.25 1.00 0.25 -0.50 -0.25
#
#[[3]]:
# [1] -0.125 -0.250 -0.375 -0.500 -0.125 0.250 0.625 1.000 0.625 0.250
#[11] -0.125 -0.500 -0.375 -0.250 -0.125
#
#[[4]]:
# [1] -0.0625 -0.1250 -0.1875 -0.2500 -0.3125 -0.3750 -0.4375 -0.5000 -0.3125
#[10] -0.1250 0.0625 0.2500 0.4375 0.6250 0.8125 1.0000 0.8125 0.6250
#[19] 0.4375 0.2500 0.0625 -0.1250 -0.3125 -0.5000 -0.4375 -0.3750 -0.3125
#[28] -0.2500 -0.1875 -0.1250 -0.0625
#
#
# You can plot the fourth component to get an idea of what the
# autocorrelation wavelet looks like.
#
# Note that the previous call stores the autocorrelation wavelet
# in D1Psi.4.1.DaubExPhase in the environment DWEnv. This is mainly so that it doesn't have to
# be recomputed.
#
# Note that the x-coordinates in the following are approximate.
#
plot(seq(from=-1, to=1, length=length(haardw4[[4]])),haardw4[[4]], type="l",
xlab = "t", ylab = "Haar Autocorrelation Wavelet")
#
#
# Now let us repeat the above for the Daubechies Least-Asymmetric wavelet
# with 10 vanishing moments.
# We shall create up to scale 6, a higher resolution version than last
# time.
#
PsiJ(-6, filter.number=10, family="DaubLeAsymm", OPLENGTH=5000)
#[[1]]:
# [1] 3.537571e-07 5.699601e-16 -7.512135e-06 -7.705013e-15 7.662378e-05
# [6] 5.637163e-14 -5.010016e-04 -2.419432e-13 2.368371e-03 9.976593e-13
#[11] -8.684028e-03 -1.945435e-12 2.605208e-02 6.245832e-12 -6.773542e-02
#[16] 4.704777e-12 1.693386e-01 2.011086e-10 -6.209080e-01 1.000000e+00
#[21] -6.209080e-01 2.011086e-10 1.693386e-01 4.704777e-12 -6.773542e-02
#[26] 6.245832e-12 2.605208e-02 -1.945435e-12 -8.684028e-03 9.976593e-13
#[31] 2.368371e-03 -2.419432e-13 -5.010016e-04 5.637163e-14 7.662378e-05
#[36] -7.705013e-15 -7.512135e-06 5.699601e-16 3.537571e-07
#
#[[2]]
# scale 2 etc. etc.
#
#[[3]] scale 3 etc. etc.
#
#scales [[4]] and [[5]]...
#
#[[6]]
#...
# remaining scale 6 elements...
#...
#[2371] -1.472225e-31 -1.176478e-31 -4.069848e-32 -2.932736e-41 6.855259e-33
#[2376] 5.540202e-33 2.286296e-33 1.164962e-42 -3.134088e-35 3.427783e-44
#[2381] -1.442993e-34 -2.480298e-44 5.325726e-35 9.346398e-45 -2.699644e-36
#[2386] -4.878634e-46 -4.489527e-36 -4.339365e-46 1.891864e-36 2.452556e-46
#[2391] -3.828924e-37 -4.268733e-47 4.161874e-38 3.157694e-48 -1.959885e-39
#
#
# Let's now plot the 6th component (6th scale, this is the finest
# resolution, all the other scales will be coarser representations)
#
# Note that the previous call stores the autocorrelation wavelet
# in D1Psi.6.10.DaubLeAsymm in the DWEnv environment.
#
# Note that the x-coordinates in the following are non-existant!
#
#
LA10l6<-get("D1Psi.6.10.DaubLeAsymm",envir=DWEnv)
plot(seq(from=-1, to=1, length=length(LA10l6[[6]])),LA10l6[[6]], type="l",
xlab="t", ylab ="Daubechies N=10 least-asymmetric Autocorrelation Wavelet")
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