1) Determine the z-Transform for the following signals. In each case specify the region of convergence for the transform.
(a) 
(b) 
(c) 
(d) 
(e) 
2) Using long-division, determine the inverse z-transform of
(a) if x(n) is causal and (b) x(n) is anticausal.
[Ans: (1+3n)u(n), [2- 3(n- 1)]u(-n- 1)]
3) Determine the causal signal x(n) if its z-transform X(z) is given by:
(a) 
[Ans: u(n-
6) + u(n-
7)]
(b) 
(c) 
(d) 
4) (a) An LTI system has a unit impulse response given by h(n) = (0.5)n u(n). Using the z-transform, find the output of this system to an excitation given by x(n) = (n+1)(0.25)n u(n).
(b) Confirm the result obtained in (a) above using convolution, given that
5) Evaluate the z-transform for the signal x(n) = (-1)n 2-|n|. Hence or otherwise determine its autocorrelation.
6) Consider the system
Determine:
(a) The impulse response
(b) The zero-state step response
(c) The step response if y(-1) = 1, y(-2) = 2, y(-n) = 0 for n > 2.
