R/PS.VarUntilF.R

Defines functions PS.VarUntilF

Documented in PS.VarUntilF

#' @title Variance of a powerlaw process if integrated from until frequency f
#' @description Integral of PSD=f^(-beta) from f1=1/N to f2=f
#' this equals the variance of a lowpass filtered powerlaw process
#' WARNING: The result is not normalized
#' @param f frequency until which to integrate
#' @param beta powerlaw slope
#' @param N length of the timeseries
#' @return non-normalized variance
#' @export
#' @examples
#' beta <- 1
#' signal <- ts(SimPowerlaw(beta,100000))
#' spec <- SpecMTM(signal)
#' v1 <- GetVarFromSpectra(spec,f=c(1/length(signal),0.5))
#' v2 <- GetVarFromSpectra(spec,f=c(1/length(signal),0.01))
#' PS.VarUntilF(0.01,beta,length(signal))/PS.VarUntilF(0.5,beta,length(signal))
#' v2$var/v1$var
#' @author Thomas Laepple
PS.VarUntilF <- function(f, beta, N) {
  if (beta == 1)
    return(log(f) - log(1/N)) else
      return((f^(1 - beta) - (1/N)^(1 - beta))/(1 - beta))
}
EarthSystemDiagnostics/paleospec documentation built on Feb. 17, 2024, 4:36 p.m.