matlab

Use the Matlab function recur to calculate the response of the system to a unit step input, x[n]=u[n].  Again consider

 % x0 contains the initial conditions on x, in order

%    i.e., x0 = [x[n0-M],...,x[n0-1]]

% the output, y, has length(n)

%

N = length(a);

M = length(b)-1;

if length(y0) ~= N,

  error('Lengths of a and y0 must match')

end

if length(x0) ~= M,

  error('Length of x0 must match length of b-1')

end

y = [y0 zeros(1,length(n))];

x = [x0 x];

a1 = a(length(a):-1:1);             % reverses the elements in a

b1 = b(length(b):-1:1);      

fori=N+1:N+length(n),

  y(i) = -a1*y(i-N:i-1)' + b1*x(i-N:i-N+M)';

end

y = y(N+1:N+length(n));

To get information on how to use the function, at the Matlab prompt, type:

EDU>>help recur

It might be helpful to change the index of the difference equation such that the highest index is n rather than n+2.

 Are your plots the same?  If not, why not?