A discrete-time system is given by the input/output difference equation
y(n+1) =0.5y(n) + x(n+1)
a) What is the order of the system ?
b) Compute y(nT) iteratively for n=0, 1, 2, when, y(-T)=2, and x(nT) = u(n) Hint: the initial conditions are given for negative n. Shift the equation to the right to express x() and y() to eliminate all advances and end up with x(n), y(n), and delayed terms.
c) Transform the equation and find the Transfer function H(z), of the system above, the characteristic polynomial and its poles. Indicate the zero input and the zero state part of the response, Yoi(z) and Yos(z) respectively.
d) Is the system BIBO stable? Justify your answer.
e) Find the impulse response h(n) using H(z).
f) Find y(n) if x(n)=u(n) using the z-transform.