dopler<-function(x){
20*sqrt(x*(1-x))*sin(2*pi*1.05/(x+0.05))
}
dataset.dopler<-function(N,sigma=1){
set.seed(0)
x<-sort(runif(N,min=0.12,max=1))
y<-dopler(x)+rnorm(N,sd=sigma)
x.ts<-sort(runif(N,min=0.12,max=1))
y.ts<-dopler(x.ts)
list(x=x,y=y,x.ts=x.ts,y.ts=y.ts)
}
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