Fig1.2 <- function()
{
#  postscript(file = "Fig1.2.ps", height = 6.5, width = 6.5, horiz = F)
  par(mfrow = c(2, 2), mar = c(1.5, 1.5, 1.5, 0.5), mgp = c(5, 0.4, 0))
  x <- seq( - pi, pi, by = 0.01)        
                                        # Create example function on grid
  ex <- sapply(x, examplef)     
                                        # Compute basis functions (also on
                                        #   grid)
  c1 <- cos(x)
  c2 <- cos(2 * x)
  c3 <- cos(3 * x)      
                                        # Compute coefficients numerically
  a0 <- (sum(ex) * 0.01)/pi
  a1 <- (sum(ex * c1) * 0.01)/pi
  a2 <- (sum(ex * c2) * 0.01)/pi
  a3 <- (sum(ex * c3) * 0.01)/pi        
                                        # Plotting of various reconstructions
  plot(x, ex, type = "l", ylim = c(0, 1.8))
  mtext("Example function", side = 3, line = 0.1)
  plot(x, a0/2 + a1 * c1, type = "l", ylim = c(0, 1.8))
  mtext("Reconstruction with J=1", side = 3, line = 0.1)
  plot(x, a0/2 + a1 * c1 + a2 * c2, type = "l", ylim = c(0, 1.8))
  mtext("Reconstruction with J=2", side = 3, line = 0.1)
  plot(x, a0/2 + a1 * c1 + a2 * c2 + a3 * c3, type = "l", ylim = c(0, 1.8))
  mtext("Reconstruction with J=3", side = 3, line = 0.1)
#  graphics.off()
  NULL
}

examplef <- function(x)
{
  if(x <=  - pi/2 && x >= -pi)
    return(x + pi)
    else if(x > pi/2 && x<= pi)
      return(pi - x)
    else if(x < -pi || x >pi)
      return(0)
    else
      return(pi/2)
}