#AR(2)-Spektren
#Mit dem eingegeben Wert A1 werden drei Spektren gezeichnet
#Fuer alpha1=A1, alpha1=0, alpha1=-A1   (jedesmal alpha2=A2)

postscript(file="AR2Spec.ps", height=10, width=12, horizontal=F)

Pi<- 3.14159
x<- seq(0,Pi,by=0.001)

A1<- 1   ; A2<- -0.5
#A1<- 1.33; A2<- -0.66 

y<- 1/(1 + A1*A1 +2*(A1*A2 - A1)*cos(x) - 2*A2*cos(2*x) + A2*A2)  #mit A1
My<- max(y); MyA<- y[1] 

plot(x,y,type="l",lty=1,xlab="",ylab="AR(2)-Spektren",
     xlim=c(-0.2,Pi),cex=1)  
 
y<- 1/(1 + A1*A1 +2*(-A1*A2 + A1)*cos(x) - 2*A2*cos(2*x) + A2*A2) #mit -A1
MymA<- y[1]
lines(x,y,type="l",lty=1)

y<- 1/(1 - 2*A2*cos(2*x) + A2*A2)                                 #mit 0
My0<- y[1]
lines(x,y,type="l",lty=2)
               
text(-0.03,My,"a1 =",font=13,cex=1.2)

text(-0.1,MyA,A1,cex=1)
text(-0.1,My0,"0",cex=1)
text(-0.1,MymA,-A1,cex=1)

text(Pi/2,-0.0,"p/2",font=13,cex=1)
text(Pi,-0.0,"p", font=13,cex=1)
#text(Pi/2,-0.8,"w",font=13,cex=1)

text(1.5,My,"a2 =",font=13,cex=1.2)
text(1.8,My,A2,cex=1.2)
 

dev.off()

rm(x,y,Pi,A1,A2,My,MyA,MymA,My0)