ex <- function(n=400, beta=c(0,0,.5), alpha=c(.5,.25),
               sig=0, ioptw=4, M=36)
# -----------------------------------------------------
# 
#  Interpreting the phase spectrum
# 
# -----------------------------------------------------
{ 
  k <- length(beta)
  z <- arima.sim(list(order(length(alpha),0,0),ar=alpha),n=n+k)
  fz <- filter(z,beta,sides=1)    # fz = beta(B)*z(t)
  fz <- fz[(1+k):(n+k)]           # the first k-1 are NA's
  fz <- fz + sig*rnorm(n)
  z <- z[(1+k):(n+k)]             # align them
  coher(z,fz,ioptw,M)
}