# R/dwpt_sim.R In waveslim: Basic Wavelet Routines for One-, Two- and Three-dimensional Signal Processing

```dwpt.sim <- function(N, wf, delta, fG, M=2, adaptive=TRUE, epsilon=0.05) {
M <- M*N
J <- log(M, 2)
jn <- rep(1:J, 2^(1:J))
jl <- length(jn)

Basis <- find.adaptive.basis(wf, J, fG, epsilon)
} else {
Basis <- numeric(jl)
a <- min((1:jl)[jn == J])
b <- max((1:jl)[jn == J])
Basis[a:b] <- 1
}

Index <- (1:jl)[as.logical(Basis)]
Length <- 2^jn

variance <- bandpass.var.spp(delta, fG, J, Basis, Length)
z <- vector("list", jl)
class(z) <- "dwpt"
attr(z, "wavelet") <- wf

for(i in Index)
z[[i]] <- rnorm(M/Length[i], sd=sqrt(Length[i]*variance[i]))

x <- idwpt(z, Basis)
xi <- trunc(runif(1, 1, M-N))
return(x[xi:(xi+N-1)])
}

find.adaptive.basis <- function(wf, J, fG, eps) {
H <- function(f, L) {
H <- 0
for(l in 0:(L/2-1))
H <- H + choose(L/2+l-1,l) * cos(pi*f)^(2*l)
H <- 2 * sin(pi*f)^L * H
return(H)
}

G <- function(f, L) {
G <- 0
for(l in 0:(L/2-1))
G <- G + choose(L/2+l-1,l) * sin(pi*f)^(2*l)
G <- 2 * cos(pi*f)^L * G
return(G)
}

L <- wave.filter(wf)\$length
jn <- rep(1:J, 2^(1:J))
jl <- length(jn)
U <- numeric(jl)
U[1] <- G(fG, L)
U[2] <- H(fG, L)
for(j in 2:J) {
jj <- min((1:jl)[jn == j])
jp <- (1:jl)[jn == j-1]
for(n in 0:(2^j/2-1)) {
if (n%%2 == 0) {
U[jj + 2 * n + 1] <- U[jp[n+1]] * H(2^(j-1)*fG, L)
U[jj + 2 * n] <- U[jp[n+1]] * G(2^(j-1)*fG, L)
} else {
U[jj + 2 * n] <- U[jp[n+1]] * H(2^(j-1)*fG, L)
U[jj + 2 * n + 1] <- U[jp[n+1]] * G(2^(j-1)*fG, L)
}
}
}
return(ortho.basis(U < eps))
}

bandpass.var.spp <- function(delta, fG, J, Basis, Length) {
a <- unlist(sapply(2^(1:J)-1, seq, from=0, by=1)) / (2*Length)
b <- unlist(sapply(2^(1:J), seq, from=1, by=1)) / (2*Length)
bp.var <- rep(0, length(Basis))
for(jn in (1:length(Basis))[as.logical(Basis)]) {
if(fG < a[jn] | fG > b[jn])
bp.var[jn] <- 2*integrate(spp.sdf, a[jn], b[jn], d=delta, fG=fG)\$value
else {
result1 <- 2*integrate(spp.sdf, a[jn], fG, d=delta, fG=fG)\$value
result2 <- 2*integrate(spp.sdf, fG, b[jn], d=delta, fG=fG)\$value
bp.var[jn] <- result1 + result2
}
}
return(bp.var)
}
```

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waveslim documentation built on May 2, 2019, 4:41 p.m.