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Simulate a random timeseries consistent with an arbitrary numerical power spectrum

SimFromEmpiricalSpec.Rd

Adapted from SimPowerlaw

Usage

SimFromEmpiricalSpec(spec, N)

Arguments

spec

Numerical power spectrum consisting of a list with components $freq and $spec

N

length of timeseries to be generated

Value

vector containing the timeseries

See also

Other functions to generate timeseries with powerlaw like spectra: SimPLS(), SimPowerlaw(), SimProxySeries()

Author

Thomas Laepple and Andrew Dolman

Examples

# Create a piecewise spectrum

## helper function to generate continuous piecewise spectrum

PiecewiseLinear <- function(x, val.at.min.x, breaks, slopes){

breaks <- c(-Inf, breaks, Inf)
slp.vec <- slopes[findInterval(x, breaks)]
d.x <- diff(x)
d.y <- c(d.x * tail(slp.vec, -1))

y <- cumsum(c(val.at.min.x, d.y))

data.frame(x, y)

}
slps <- c(-1, -0.5, -1)
brks <- c(1e-03, 1e-02)
emp.spec <- PiecewiseLinear(log(seq(1/1e05, 1/2, 1/1e05)), 0, log(brks), slps)
emp.spec <- exp(emp.spec)
names(emp.spec) <- c("freq", "spec")

plot(emp.spec, type = "l", log = "xy")


# Sample consistent with spectrum
ts1 <- ts(SimFromEmpiricalSpec(emp.spec, 50000))

# re-estimate power spectrum
spec1 <- SpecMTM(ts1)
LPlot(spec1)
lines(emp.spec, col = "Red")
abline(v = brks, col = "Green")