f <- function(x)
{
  noise <- rnorm(1,0,0.05)
  a <-   sin(10*x)     
  b <-2*sin(   x)
  a+b
}

xr <- 20
res <- 10240

x <- seq(0,xr*2*pi,length.out=res)
y <- rep(0, length(x))
for( i in 0:length(x))
{
  y[i] <- f(x[i])
} 

ft <- abs(fft(y))

old.par <- par(mfrow=c(2, 1), yaxt="n", mgp=c(2,1,0), bty='l')

tToIndex = xr/res
tValues = ((1:length(y))-1) * tToIndex
plot(tValues,y,t='l', xlab="Zeit in s", ylab="signal",xlim=c(1,6),main="signal = 2 sin x  +  sin 10x ")

freqToIndex = xr
xvalues = ((1:length(ft))-1) / freqToIndex

plot(xvalues, ft,type='l'
     ,xlim=c(0,11), xlab='Frequenz in Hz', ylab="