#Parámetros genéricos
N=500
t=(1:N)/N

#Modelos de crecimiento
a=10
b=0.1
c=3
d=0.3
y=a/(1+exp(-(b+c*t)))^d
plot(t,y,col="blue",type="l")

#Función armónica
w=20
fase=runif(1,-pi,pi)
f1=cos(w*t+fase)
fase=runif(1,-pi,pi)
f2=cos(w*t+fase)
fase=runif(1,-pi,pi)
f3=cos(w*t+fase)
s=0.2
e=rnorm(N,0,s)
y=f+e
plot(t,f1,type="l",col="blue",ylim=c(-1.5,1.5))
lines(t,f2,col="red")
lines(t,f3,col="green")

points(t,y,col="red")

#Superposición de armónicos
A=c(5,1,10)
w=c(20,100,10)
sf=0
f=NULL
for(i in 1:3)
  {
    fase=runif(1,-pi,pi)
    g=A[i]*cos(w[i]*t+fase)
    f=c(f,g)
    sf=sf+g
  }
dim(f)=c(N,3)
ysf=sf+rnorm(N,0,0.9)

plot(t,sf,type="n")
lines(t,ysf,col="red")

lines(t,f[,1],col="green")
lines(t,f[,2],col="blue")
lines(t,f[,3],col="red")
    

#Señal de Doppler
doppler=function(t,e)
  sqrt(t*(1-t))*sin(2*pi*(1+e)/(t+e))
a=0.05
f=doppler(t,a)
s=0.25
e=rnorm(N,1,s)
y=f*e
plot(t,f,type="l",col="blue")
lines(t,y,col="red")

#Modelo para una señal
a=10
b=1
c=0.08
d=0.5
n=300
t=seq(1:n)/n
f=a*(t-t^2)*sin(b/(d*t^2+t+c))
s=0.2
e=rnorm(n,0,s)
y=f+e
fa=nls(y ~ a*(t-t^2)*sin(b/(t+c)),start=list(a=5,b=0.5,c=0.01))
summary(fa)
ff=predict(fa)

plot(t,f,col="blue",type="l",ylim=c(-2,3))
points(t,y,col="green")
lines(t,ff,col="red")

db=data.frame(t,f,y)
write.table(db,"c://datos//simu1.txt",row.names=F,col.names=F)