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# the impulse response of a system is w(t)=ε(t)e^(-3t). decide whether the system is BIBO stable or not. Explain

the impulse response of a system is w(t)=ε(t)e^(-3t). decide whether the system is BIBO stable or not. Explain your answer

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- 1 decade ago
BIBO (Bounded Input/Bounded Output)

You just need to integrate the absolute value of w(t) over the time from -infty to infty, if this integration is bounded, then your system is BIBO stable. Look that

| w(t) | = | ε(t) e^(-3t) | = | ε(t) | | e^(-3t) | = | ε(t) |

so, if the integral of | ε(t) | dt from -infinity to infinity is bounded, the system is BIBO stable. when this integral diverges the system is BIBO unstable.

By the way, I didn't found the way to write the integral symbol. Sorry.

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