Transfer Function
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1. Is the linear time-invariant continuous-time system with the impulse response h(t) = sin 2t for t ≥ 0 BIBO is stable? Explain.
2. Determine if the linear time-invariant continuous-time system defined by:
is stable, marginally stable, unstable, or marginally unstable. Show work.
3. Compute the steady-state response for the linear time-invariant continuous-time system with the transfer function:
when the input is x(t) = cos(t), t ≥ 0 and no initial energy.
4. A linear time-invariant continuous-time system has transfer function:
Compute the transient response resulting from the input x(t)=2cos(4t), t>=0, with zero initial conditions.
5. The response of a system to an input is:
What is the steady-state response?
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Solution Summary
The expert examines a linear time-invariant continuous-time system.
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1. Is the linear time-invariant continuous-time system with the impulse response h(t) = sin 2t for t ≥ 0 BIBO is stable? Explain.
Solution:
We can solve the BIBO stability of the impulse response if it is absolutely integrable using the integral form:
Substituting, we have:
Since both and does not have a unique value in the range of -1 to +1, then they have no unique value. Therefore, the impulse response in not integrable and therefore BIBO unstable.
2. Determine if the linear time-invariant continuous-time system defined by:
is ...
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