Derive Orthonormal Basis from Wavelet Packet Tree
An orthonormal basis for the discrete wavelet transform may be characterized via a disjoint partitioning of the frequency axis that covers [0,1/2). This subroutine produces an orthonormal basis from a full wavelet packet tree.
ortho.basis(xtree)
xtree |
is a vector whose entries are associated with a wavelet packet tree. |
A wavelet packet tree is a binary tree of Boolean variables. Parent nodes are removed if any of their children exist.
Boolean vector describing the orthonormal basis for the DWPT.
B. Whitcher
data(japan)
J <- 4
wf <- "mb8"
japan.mra <- mra(log(japan), wf, J, boundary="reflection")
japan.nomean <-
ts(apply(matrix(unlist(japan.mra[-(J+1)]), ncol=J, byrow=FALSE), 1, sum),
start=1955, freq=4)
japan.nomean2 <- ts(japan.nomean[42:169], start=1965.25, freq=4)
plot(japan.nomean2, type="l")
japan.dwpt <- dwpt(japan.nomean2, wf, 6)
japan.basis <-
ortho.basis(portmanteau.test(japan.dwpt, p=0.01, type="other"))
# Not implemented yet
# par(mfrow=c(1,1))
# plot.basis(japan.basis)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.