dwt {waveslim} | R Documentation |
This function performs a level J
decomposition of the input vector or
time series using the pyramid algorithm (Mallat 1989).
dwt(x, wf = "la8", n.levels = 4, boundary = "periodic")
dwt.nondyadic(x)
idwt(y)
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 |
n.levels |
Specifies the depth of the decomposition. This must be a number less than or equal to log(length(x),2). |
boundary |
Character string specifying the boundary condition. If
|
y |
An object of S3 class |
The code implements the one-dimensional DWT using the pyramid algorithm (Mallat, 1989). The actual transform is performed in C using pseudocode from Percival and Walden (2001). That means convolutions, not inner products, are used to apply the wavelet filters.
For a non-dyadic length vector or time series, dwt.nondyadic
pads
with zeros, performs the orthonormal DWT on this dyadic length series and
then truncates the wavelet coefficient vectors appropriately.
Basically, a list with the following components
d? |
Wavelet coefficient vectors. |
s? |
Scaling coefficient vector. |
wavelet |
Name of the wavelet filter used. |
boundary |
How the boundaries were handled. |
B. Whitcher
Daubechies, I. (1992) Ten Lectures on Wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics, SIAM: Philadelphia.
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(7), 674–693.
Percival, D. B. and A. T. Walden (2000) Wavelet Methods for Time Series Analysis, Cambridge University Press.
## Figures 4.17 and 4.18 in Gencay, Selcuk and Whitcher (2001).
data(ibm)
ibm.returns <- diff(log(ibm))
## Haar
ibmr.haar <- dwt(ibm.returns, "haar")
names(ibmr.haar) <- c("w1", "w2", "w3", "w4", "v4")
## plot partial Haar DWT for IBM data
par(mfcol=c(6,1), pty="m", mar=c(5-2,4,4-2,2))
plot.ts(ibm.returns, axes=FALSE, ylab="", main="(a)")
for(i in 1:4)
plot.ts(up.sample(ibmr.haar[[i]], 2^i), type="h", axes=FALSE,
ylab=names(ibmr.haar)[i])
plot.ts(up.sample(ibmr.haar$v4, 2^4), type="h", axes=FALSE,
ylab=names(ibmr.haar)[5])
axis(side=1, at=seq(0,368,by=23),
labels=c(0,"",46,"",92,"",138,"",184,"",230,"",276,"",322,"",368))
## LA(8)
ibmr.la8 <- dwt(ibm.returns, "la8")
names(ibmr.la8) <- c("w1", "w2", "w3", "w4", "v4")
## must shift LA(8) coefficients
ibmr.la8$w1 <- c(ibmr.la8$w1[-c(1:2)], ibmr.la8$w1[1:2])
ibmr.la8$w2 <- c(ibmr.la8$w2[-c(1:2)], ibmr.la8$w2[1:2])
for(i in names(ibmr.la8)[3:4])
ibmr.la8[[i]] <- c(ibmr.la8[[i]][-c(1:3)], ibmr.la8[[i]][1:3])
ibmr.la8$v4 <- c(ibmr.la8$v4[-c(1:2)], ibmr.la8$v4[1:2])
## plot partial LA(8) DWT for IBM data
par(mfcol=c(6,1), pty="m", mar=c(5-2,4,4-2,2))
plot.ts(ibm.returns, axes=FALSE, ylab="", main="(b)")
for(i in 1:4)
plot.ts(up.sample(ibmr.la8[[i]], 2^i), type="h", axes=FALSE,
ylab=names(ibmr.la8)[i])
plot.ts(up.sample(ibmr.la8$v4, 2^4), type="h", axes=FALSE,
ylab=names(ibmr.la8)[5])
axis(side=1, at=seq(0,368,by=23),
labels=c(0,"",46,"",92,"",138,"",184,"",230,"",276,"",322,"",368))