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For the LTI system described by the following system functions, determine (i) the impulse response (ii)...

For the LTI system described by the following system functions, determine (i) the impulse response (ii) the difference equation representation (iii) the pole-zero plot, and (iv) the steady state output y(n) if the input is x[n] = 3cos(πn/3)u[n].

a. H(z) = (z+1)/(z-0.5), causal system (Hint: you need to express H(z) in z-1 to find the difference equation )

b. H(z) = (1 + z-1+ z-2)/(1-1.7z-1+0.6z-2), stable system

c. Is the system given in (a) stable? Is the system given in (b) causal? (Hint: to compute the steady state output of the system for the given output, you must first find the frequency response of the system by replacing z=ejω)

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