Discrete Wavelet Transform and Maximal Overlap Discrete Wavelet Tranform Forward and Backward Pyramid Algorithm
Implementation of DWT and MODWT forward and backward pyramid algorithms.
dwt.forward(V, filter) dwt.backward(W, V, filter) modwt.forward(V, filter, j) modwt.backward(W, V, filter, j)
W |
A vector of wavelet coefficients. |
V |
A vector of scaling coefficients. |
filter |
A |
j |
The level of wavelet and scaling coefficients to compute (for forward algorithm) or the level of wavelet and scaling coefficient inputs (for inverse algorithm). |
An implementation of the DWT and MODWT forward and backward
pyramid algorithms using pseudocode written by Percival and Walden
(2000), pp. 100-101, 177-178. These functions are intended primarily
as helper functions for the dwt, modwt, idwt and
imodwt functions.
dwt.forward and modwt.forward return a list of two
elements containing vectors of wavelet and scaling coefficients for
the subsequent level of analysis. dwt.backward and
modwt.backward return a vector of scaling coefficients for the
previous level of analysis.
Eric Aldrich. ealdrich@gmail.com.
Percival, D. B. and A. T. Walden (2000) Wavelet Methods for Time Series Analysis, Cambridge University Press.
# obtain the two series listed in Percival and Walden (2000), page 42 X1 <- c(.2,-.4,-.6,-.5,-.8,-.4,-.9,0,-.2,.1,-.1,.1,.7,.9,0,.3) X2 <- c(.2,-.4,-.6,-.5,-.8,-.4,-.9,0,-.2,.1,-.1,.1,-.7,.9,0,.3) # compute the LA8 wavelet filter for both DWT and MODWT la8.dwt <- wt.filter() la8.modwt <- wt.filter(modwt=TRUE) # compute the DWT and MODWT level one wavelet and scaling coefficients wt.dwt <- dwt.forward(X1, la8.dwt) wt.modwt <- modwt.forward(X2, la8.modwt, 1) # compute the original series with the level one coefficients newX.dwt <- dwt.backward(wt.dwt$W, wt.dwt$V, la8.dwt) newX.modwt <- modwt.backward(wt.modwt$W, wt.modwt$V, la8.modwt, 1)
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