\text { An LTI system with transfer function } H(z)=\frac{1-z^{-1}}{1-2 z^{-1}} \text { cannot be stable. } \text { Let } \left.\left.X_{1}(z), X_{2}(z) \text { be the rational } z \text {-transforms of } x_{1} n\right], x_{2} n\right] \text {. Then the poles of } X_{1}(z) \text { and } X_{2}(z) \text { must be poles of the } z \text {-transform of } x[n]=x_{1}[n]+x_{2}[n] \text {. } Cascade of two BIBO unstable LTI systems cannot be stable. \text { A causal LTI system with transfer function } H(z)=\frac{z^{-1}}{1-z^{-1}} \text { produces an unbounded output for } \text { input } x[n]=u[n]

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\text { An LTI system with transfer function } H(z)=\frac{1-z^{-1}}{1-2 z^{-1}} \text { cannot be stable. } \text { Let } \left.\left.X_{1}(z), X_{2}(z) \text { be the rational } z \text {-transforms of } x_{1} n\right], x_{2} n\right] \text {. Then the poles of } X_{1}(z) \text { and } X_{2}(z) \text { must be poles