dwt.forward {wavelets} | R Documentation |
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)