Question: Consider a system for which the input x[n] and output y[n] satisfy the difference equation y[n] y[n 1] = x[n] and for

Consider a system for which the input x[n] and output y[n] satisfy the difference equation

y[n] – ½ y[n – 1] = x[n]

and for which y [–1] is constrained to be zero for every input. Determine whether or not the system is stable. If you conclude that the system is stable, show your reasoning. If you conclude that the system is not stable, give an example of a bounded input that result in an unbounded output.

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