#' S3 class for transfer functions
#' 
#' \code{tf} is an S3 class for defining transfer functions.
#' 
#' @param num coefficients of the numerator plynomial in q^{-1}
#' @param den coefficients of the denominator plynomial in q^{-1}
#' @param Ts sampling time
#' 
#' @return an object of class tf
#' @export
tf <- function(num=c(1),den=c(1),Ts=1){
  out <- list(num=num,den=den,Ts=Ts)
  class(out) <- "tf"
  return(out)
}

#' Display the Transfer Function
#' 
#' Printing method for objects inheriting from class \code{tf}
#' 
#' @param G an object of class \code{tf}
#' @export
print.tf <- function(G){ 
  cat("Transfer Function \nG(q^{-1}) = B(q^{-1})/A(q^{-1}) \n\n")
  cat("A(q^{-1}) = ")
  for(i in seq_along(G$den)){
    if(i-1==0){
      cat(G$den[i])
    } else{
      if(G$den[i]>0)
        cat("+")
      cat(G$den[i],"q^{-",i-1,"}",sep="")
    }
    cat("\t")
  }
  cat("\n")
  cat("B(q^{-1}) = ")
  for(i in seq_along(G$num)){
    if(i-1==0){
      cat(G$num[i])
    } else{
      if(G$num[i]>0)
        cat("+")
      cat(G$num[i],"q^{-",i-1,"}",sep="")
    }
    cat("\t")
  }
}