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Stability

Stability. Bounded input  bounded output. Absolutely summable Absolutely integrable. Stability. Examples: y(t) = 2 t Unstable y(t) = x 2 (t) Stable y(t) = 2 t x(0) Unstable y(t) = 2 t x(t) Unstable

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Stability

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  1. Stability • Bounded input  bounded output Absolutely summable Absolutely integrable

  2. Stability • Examples: • y(t) = 2t Unstable • y(t) = x2(t) Stable • y(t) = 2t x(0) Unstable • y(t) = 2t x(t) Unstable • y(t) = (1/2)t x(t) Unstable, t -1 blows up, y(t) = (1/2)t u(t) is stable

  3. Causality • Output does not depend on future values of the input: • Examples • y(t) = x(t+1) Not Causal • y(t) = x(t) et+1 Causal • y[n] = x[n] + x[n+1] Not Causal

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