Consider the causal linear shift-invariant system with system function
H(z) =
1 - a-1 z -1
1 - az -1
where 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.
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(c) H(z) is to be cascaded with a system H(z) so that the overall system function is unity. With 0 < a < 1
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ˆand H(z) specified to be a stable system, determine its impulse response h(n).