function [x,y] = arma (u,theta,x,n,m)
%-----------------------------------------------------------------------
% Usage:       [x,y] = arma (u,theta,x,n,m)
%
% Description: Compute the output of an auto-regressive moving-average
%              (ARMA) model having the following transfer function:
%
%              Y(z)      theta(n+1) + ... + theta(n+m+1)*z^(-m)
%              ---- = -------------------------------------------
%              U(z)   1 + theta(1)*z^(-1) + ... + theta(n)*z^(-n)   
%
% Inputs:      u     = system input
%              theta = (n+m+1) by 1 vector of system parameters:
%                      [a1,...,an,b0,...,bm]'
%              x     = (n+m+1) by 1 vector containing system state:
%                      [-y(k-1),...,-y(k-n),u(k),u(k-1),...,u(k-m)]'
%              n     = number of past outputs used (n >= 0)
%              m     = number of past inputs used (m >= 0)
%
% Outputs:     x     = (n+m+1) \times 1 vector containing updated
%                      system state with x(n+1) = 0. 
%              y     = the system output.  
%-----------------------------------------------------------------------
   
% Initialize

   chkvec (theta,2,'arma');
   chkvec (x,3,'arma');
   m = args (m,0,m,4,'arma');
   n = args (n,0,n,5,'arma');
   y = 0;
   r = n + m + 1;
   
% Compute y 

   x(n+1) = u;
   for i = 1 : r
      y = y + theta(i)*x(i);
   end

% Update 

   for i = r : -1 : 2
      x(i) = x(i-1);
   end
   if n > 0
      x(1) = -y;
   end
   x(n+1) = 0;
%-----------------------------------------------------------------------