SMME (version 1.1.1)

wt: Discrete wavelet transform

Description

This function performs a level J wavelet transform of the input array (1d, 2d, or 3d) using the pyramid algorithm (Mallat 1989).

Usage

wt(x, wf = "la8", J = NULL)

Value

...

An array with dimensions equal to those of x.

Arguments

x

a 1, 2, or 3 dimensional data array. The size of each dimension must be dyadic.

wf

the type of wavelet family used. See R-package waveslim for options.

J

is the level (depth) of the decomposition. For default NULL the max depth is used making wt(x) equal to multiplying x with the corresponding wavelet matrix.

Author

Adam Lund, Brandon Whitcher

Details

This is a C++/R wrapper function for a C implementation of the discrete wavelet transform by Brandon Whitcher, Rigorous Analytics Ltd, licensed under the BSD 3 license https://cran.r-project.org/web/licenses/BSD_3_clause, see the Waveslim package; Percival and Walden (2000); Gencay, Selcuk and Whitcher (2001).

Given a data array (1d, 2d or 3d) with dyadic sizes this transform is computed efficiently via the pyramid algorithm see Mallat (1989).

This functionality is used in the computations underlying softmaximin to perform multiplications involving the wavelet (design) matrix efficiently.

References

Gencay, R., F. Selcuk and B. Whitcher (2001) An Introduction to Wavelets and Other Filtering Methods in Finance and Economics, Academic Press.

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.

Examples

###1d
x <- as.matrix(rnorm(2^3))
range(x - iwt(wt(x)))

###2d
x <- matrix(rnorm(2^(3 + 4)), 2^3, 2^4)
range(x - iwt(wt(x)))

###3d
x <- array(rnorm(2^(3 + 4 + 5)), c(2^3, 2^4, 2^5))
range(x - iwt(wt(x)))