#
# 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.
# 
#-----

Z = c( 3.4, 4.5, 4.3, 8.7, 13.3, 13.8, 16.1, 15.5, 14.1, 8.9, 7.4, 3.6 )

# length(Z)=12 is even 
N = length(Z)
q = N/2

a0 = mean(Z)

ts = 1:N 

ai = c()
bi = c()
for( ii in 1:(q-1) ){
  fii = ii/N
  ai = c( ai, 2 * sum( cos( 2 * pi * fii * ts ) * Z ) / N )
  bi = c( bi, 2 * sum( sin( 2 * pi * fii * ts ) * Z ) / N )
}

# Fill in the last coefficients:
#
aq = sum( ( (-1)^ts ) * Z )
bq = 0

ai = c( ai, aq )
bi = c( bi, bq )