1-D Discrete Wavelet Transform
Compute the single-level discrete wavelet transform of a signal
dwt(x, wname = "d8", lo = NULL, hi = NULL) wfilters(wname)
x |
input data, specified as a numeric vector. |
wname |
analyzing wavelet, specified as a character string consisting of
a class name followed by the wavelet length Only two classes of wavelets
are supported; Daubechies (denoted by the prefix |
lo |
scaling (low-pass) filter, specified as an even-length numeric
vector. |
hi |
wavelet (high-pass) filter, specified as an even-length numeric
vector. |
This function is only included because of compatibility with the 'Octave'
'signal' package. Specialized packages exist in R to perform the discrete
wavelet transform, e.g., the wavelets package [1]. this function
recognizes only a few wavelet names, namely those for which scale
coefficients are available (Daubechies [2] and Coiflet [3]).
The wavelet and scaling coefficients are returned by the function
wfilters, which returns the coefficients for reconstruction filters
associated with the wavelet wname. Decomposition filters are the time
reverse of the reconstruction filters (see examples).
A list containing two numeric vectors:
approximation (average) coefficients, obtained from convolving
x with the scaling (low-pass) filter lo, and then
downsampled (keep the even-indexed elements).
detail (difference) coefficients, obtained from convolving
x with the wavelet (high-pass) filter hi, and then
downsampled (keep the even-indexed elements).
The notations g and h are often used to denote low-pass
(scaling) and high-pass (wavelet) coefficients, respectively, but
inconsistently. Ref [4] uses it, as does the R wavelets package.
'Octave' uses the reverse notation. To avoid confusion, more neutral terms
are used here.
There are two naming schemes for wavelet names in use. For instance for Daubechies wavelets (d), dN using the length or number of taps, and dbA referring to the number of vanishing moments. So d4 and db2 are the same wavelet transform. This function uses the formed (dN) notation; 'Matlab' uses the latter (dbA).
Lukas F. Reichlin.
Conversion to R by Geert van Boxtel, G.J.M.vanBoxtel@gmail.com.
# get Coiflet 30 coefficients
wv <- wfilters('c30')
lo <- rev(wv$lo)
hi <- rev(wv$hi)
# general time-varying signal
time <- 1
fs <- 1000
x <- seq(0,time, length.out=time*fs)
y <- c(cos(2*pi*100*x)[1:300], cos(2*pi*50*x)[1:300],
cos(2*pi*25*x)[1:200], cos(2*pi*10*x)[1:200])
op <- par(mfrow = c(3,1))
plot(x, y, type = "l", xlab = "Time", ylab = "Amplitude",
main = "Original signal")
wt <- dwt(y, wname = NULL, lo, hi)
x2 <- seq(1, length(x) - length(hi) + 1, 2)
plot(x2, wt$a, type = "h", xlab = "Time", ylab = "",
main = "Approximation coefficients")
plot(x2, wt$d, type = "h", xlab = "Time", ylab = "",
main = "Detail coefficients")
par (op)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.