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Consider the causal linear shift-invariant system with system functionH(z) =1 - a-1 z -11 - az -1where a is real
(a) For what range of values of a is the system stable?(b) If 0 < a < 1, plot the pole-zero diagram and shade the region of convergence. Do the same for a > 1.ˆ(c) H(z) is to be cascaded with a system H(z) so that the overall system function is unity. With 0 < a < 1ˆˆand H(z) specified to be a stable system, determine its impulse response h(n).
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