Q1: (10 Marks) Compute the 4 -point DFT of the signal x(n)={5,6,12,16} a)by definition b) by matrix Q2: (15 Marks) X(z)=(12z1)(3z1)5z1 a) How many zeros and poles and write them b) Find Z-transform by partial fraction c) Find all possibly for x(n): causal, anti-causal and mixed. Give the overall ROC , determine it is stable or not and the discrete time signal equation x(n) Q3: (10 Marks) Consider the system function H(z)=(z2)2z1 for a causal system : a) Using long division method find the first five values of the causal discrete - time impulse response of the system. b) Using the z - transform pairs and properties find the impulse response h(n). c) Indicate the region of convergence. Is the system stable? Why