R: Derive Orthonormal Basis from Wavelet Packet Tree

ortho.basis {waveslim} | R Documentation

## Derive Orthonormal Basis from Wavelet Packet Tree

### Description

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.

### Usage

    ortho.basis(xtree)

### Arguments

`xtree` | is a vector whose entries are associated with a wavelet packet tree.

### Details

A wavelet packet tree is a binary tree of Boolean variables. Parent nodes are removed if any of their children exist.

### Value

Boolean vector describing the orthonormal basis for the DWPT.

### Author(s)

B. Whitcher

### Examples

    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)

[Package waveslim version 1.7.5 Index]