#
# Written by:
# -- 
# John L. Weatherwax                2009-04-21
# 
# email: wax@alum.mit.edu
# 
# Please send comments and especially bug reports to the
# above email address.
# 
#-----

N=200

fs = seq(0,1/2,length.out=N)
gf = 2 / ( 9/4 -3 * cos( 2 * pi * fs ) + cos( 4 * pi * fs ) )

#postscript("../../WriteUp/Graphics/Chapter3/prob_7_plot.eps", onefile=FALSE, horizontal=FALSE)
plot( fs, gf, pch=c("o"), col=c("black"), xlab="frequency", ylab="g(f)" )
#dev.off()

# find the location of the maximum and the frequency there 
#
mv = max(gf)
mi = which.max(gf)
mf = fs[mi]

# then dominant period is given by
#
1/mf

# Integrate to get the part of the total variance in this frequency range
#
myFn <- function(fs) {2 / ( 9/4 -3 * cos( 2 * pi * fs ) + cos( 4 * pi * fs ) )}
int = stats::integrate(myFn,0,0.2)

sigma_z2 = 12/5