### some R basics (see also Appendix A of `An Introduction to R')
###
### create 2 vectors, each containing 50 random deviates
### from a standard normal distribution
x <- rnorm(64)
y <- rnorm(64)
### examine contents of x
x
### create 2 more vectors containing sums and products
a <- x + y
b <- x * y
### plot y versus x
plot(x,y)
### plot b versus a
plot(a,b)
### set up window to hold 2 plots at a time,
### one on top of the other
par(mfrow=c(2,1))
plot(x,y)
plot(a,b)
### 2 plots at a time, one next to the other
par(mfrow=c(1,2))
plot(x,y)
plot(a,b)
### back to just one plot per window
par(mfrow=c(1,1))
plot(x,y)
### list all active plotting devices
dev.list()
### create a new plotting device (window)
quartz()  ### works on a Mac - need to adjust for Windows etc
plot(a,b)
dev.list()
### go back to plotting on first window (device 2)
dev.set(2)
plot(a,b)

### load `waveslim' module
library(waveslim)
### look at contents of module
objects(2)
### get documentation for function called wavelet.filter
?wavelet.filter
### look at definition for wavelet.filter
wavelet.filter
### create impulse response sequence for LA(8) wavelet
### filter of unit level and for equivalent wavelet filters
### of levels j = 2, 3 and 4
irs.la8w   <- wavelet.filter("la8","H")
irs.la8w.2 <- wavelet.filter("la8","HL")
irs.la8w.3 <- wavelet.filter("la8","HLL")
irs.la8w.4 <- wavelet.filter("la8","HLLL")
### look at values making up basic filter (unit level)
irs.la8w
### plot the filters
par(mfrow=c(4,1))
plot(irs.la8w)
plot(irs.la8w.2)
plot(irs.la8w.3)
plot(irs.la8w.4)
### check that filters sum to zero ...
sum(irs.la8w)
sum(irs.la8w.2)
sum(irs.la8w.3)
sum(irs.la8w.4)
### ... and have unit energy
sum(irs.la8w^2)
sum(irs.la8w.2^2)
sum(irs.la8w.3^2)
sum(irs.la8w.4^2)
### create vectors with 106 zeros
filter.1 <- rep(0,106)
filter.2 <- rep(0,106)
filter.3 <- rep(0,106)
filter.4 <- rep(0,106)
### define function that returns width of
### equivalent filter of level j for
### wavelet filter of width L at level 1
Lj <- function(L,j) (2^j - 1) * (L - 1) + 1
Lj(8,1)
Lj(8,2)
Lj(8,3)
Lj(8,4)
### store filters in lower part of vectors
filter.1[1:8] <- irs.la8w
filter.2[1:Lj(8,2)] <- irs.la8w.2
filter.3[1:Lj(8,3)] <- irs.la8w.3
filter.4[1:Lj(8,4)] <- irs.la8w.4
stack.plot(data.frame(cbind(filter.1,filter.2,filter.3,filter.4)))
### create a simliar plot for the scaling filter
irs.la8s   <- wavelet.filter("la8","L")
irs.la8s.2 <- wavelet.filter("la8","LL")
irs.la8s.3 <- wavelet.filter("la8","LLL")
irs.la8s.4 <- wavelet.filter("la8","LLLL")
filter.1[1:8] <- irs.la8s
filter.2[1:Lj(8,2)] <- irs.la8s.2
filter.3[1:Lj(8,3)] <- irs.la8s.3
filter.4[1:Lj(8,4)] <- irs.la8s.4
stack.plot(data.frame(cbind(filter.1,filter.2,filter.3,filter.4)))