(iii) 2 SEMESTER EXAMINATIONS ENSC3015: SIGNALS AND SYSTEMS NOVEMBER 2015 PAGE NO 6 QUESTION 4: (10 marks) (Z-Transform and Sampling) (i) If algebraic expression for the z-transform of x[n] is X(z) = (1-22") (1+0.52") Specify all the possible ROCs. Find z- inverse of X(2) corresponding to the ROC for which the system is causal. (3 marks) (ii) The signal y(r) is generated by convolving a band-limited signal x,(t) with another band limited signal x,(r), that is, where y(t) = x(t)*x(t) X,(jo)=0 for >1000 X,(jo)=0 for le> 2500x Impulse train sampling is performed on y(t) to obtain the sequence y[n]. Specify the range of sampling period 7, which ensures that y(t) is recoverable from y[n]. (3 marks) For the block diagram of a system is given below. Find the pole locations. Is the inverse of this system a stable system? Justify your answer. X(z) -2 3 120 > 0.5 Z Y(z) (4 marks)