This function performs a level J decomposition of the input vector or time series using the pyramid algorithm (Mallat 1989).
1 2  dwt(x, wf="la8", n.levels=4, boundary="periodic")
dwt.nondyadic(x)

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

The code implements the onedimensional 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 nondyadic 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, CBMSNSF 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, No. 7, 674693.
Percival, D. B. and A. T. Walden (2000) Wavelet Methods for Time Series Analysis, Cambridge University Press.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35  ## 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(52,4,42,2))
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(52,4,42,2))
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))

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