demo.dirichlet <- function(K=10){
  x <- seq(-pi, pi, length=300)
  y <- 1/(2*pi) * sin(K*x/2) / sin(x/2)
  plot(x, y, type="l", lwd=2,
       main=paste("Dirichlet_{", K, "} Kernel", sep=""))
  abline(h=0)
  abline(v=0)
}

demo.fejer <- function(K=10){
  x <- seq(-pi, pi, length=300)
  y <- 1/(2*pi *K) * (sin(K*x/2) / sin(x/2))^2
  plot(x, y, type="l", lwd=2,
       main=paste("Fejer_{", K, "} Kernel", sep=""))
  abline(h=0)
  abline(v=0)
}

demo.turkey <- function(a = 0.25, M=10){
  x <- seq(-pi, pi, length=300)
  D <- function(x) 1/(2*pi) * sin((2*M+1)*x/2) / sin(x/2)
  y = a*D(x - pi/M) + (1-2*a)*D(x) + a*D(x + pi/M)
  if(a==0.25){
    tit <- paste("Turkey-Hanning Kernel with M=", M, sep="")
  } else if(a==0.23){
    tit <- paste("Turkey-Hamming Kernel with M=", M, sep="")
  } else {
    tit <- paste("Turkey Kernel with M=", M, " a=", a, sep="")
  }
  plot(x, y, type="l", lwd=2,  main=tit)
  abline(h=0)
  abline(v=0)
}

demo.parzen <- function(M=10){
  x <- seq(-pi, pi, length=300)
  y <- ((3/(8*pi*M^3)) * (sin(M*x/4) / (sin(x/2)/2))^4 *
        (1 - 2/3*sin(x/2)^2))
  plot(x, y, type="l", lwd=2,
       main=paste("Parzen_{", M, "} Kernel", sep=""))
  abline(h=0)
  abline(v=0)
  
}




demo08 <- function(){
  demos <- list("DirichletºË"=demo.dirichlet,
                "FejerºË"=demo.fejer,
                "Turkey´°"=demo.turkey,
                "Parzen´°"=demo.parzen
                )
  ndemos <- length(demos)
  prompts <- paste("   ", seq(ndemos), ". ", names(demos), "\n", sep="")
  cat("µÚ8ÕÂÑÝʾ:\n",
      prompts)
  sel <- scan(n=1, quiet=TRUE)
  demos[[sel]]()
}