R: (Inverse) Discrete Wavelet Packet Transforms

dwpt {waveslim} | R Documentation

## (Inverse) Discrete Wavelet Packet Transforms

### Description

All possible filtering combinations (low- and high-pass) are performed to decompose a vector or time series. The resulting coefficients are associated with a binary tree structure corresponding to a partitioning of the frequency axis.

### Usage

    dwpt(x, wf = "la8", n.levels = 4, boundary = "periodic")
    idwpt(y, y.basis)
    modwpt(x, wf = "la8", n.levels = 4, boundary = "periodic")

### Arguments

`x` | a vector or time series containing the data be to decomposed. This must be a dyadic length vector (power of 2).
`wf` | Name of the wavelet filter to use in the decomposition. By default this is set to `"la8"`, the Daubechies orthonormal compactly supported wavelet of length L=8 (Daubechies, 1992), least asymmetric family.
`n.levels` | Specifies the depth of the decomposition. This must be a number less than or equal to log2[length(x)].
`boundary` | Character string specifying the boundary condition. If `boundary=="periodic"` the default, then the vector you decompose is assumed to be periodic on its defined interval, if `boundary=="reflection"`, the vector beyond its boundaries is assumed to be a symmetric reflection of itself.
`y` | Object of S3 class `dwpt`.
`y.basis` | Vector of character strings that describe leaves on the DWPT basis tree.

### Details

The code implements the one-dimensional DWPT using the pyramid algorithm (Mallat, 1989).

### Value

Basically, a list with the following components

`w?.?` | Wavelet coefficient vectors. The first index is associated with the scale of the decomposition while the second is associated with the frequency partition within that level.
`wavelet` | Name of the wavelet filter used.
`boundary` | How the boundaries were handled.

### Author(s)

B. Whitcher

### References

Mallat, S. G. (1989) A theory for multiresolution signal decomposition: the wavelet representation, IEEE Transactions on Pattern Analysis and Machine Intelligence, 11, No. 7, 674-693.

Percival, D. B. and A. T. Walden (2000) Wavelet Methods for Time Series Analysis, Cambridge University Press.

Wickerhauser, M. V. (1994) Adapted Wavelet Analysis from Theory to Software, A K Peters.

### See Also

`dwt`, `modwpt`, `wave.filter`.

### Examples

    data(mexm)
    J <- 4
    mexm.mra <- mra(log(mexm), "mb8", J, "modwt", "reflection")
    mexm.nomean <- ts(
      apply(matrix(unlist(mexm.mra), ncol=J+1, byrow=FALSE)[,-(J+1)], 1, sum),
      start=1957, freq=12)
    mexm.dwpt <- dwpt(mexm.nomean[-c(1:4)], "mb8", 7, "reflection")

[Package waveslim version 1.8.3 Index]