Vaughan Rojas
08/25/2023 · Junior High School
P. 5 Consider an LTI system whose input \( \mathrm{x}[\mathrm{t}] \) and output \( \mathrm{y}[\mathrm{t}] \) are related by the differential equation \( \quad \frac{d y(t)}{d t}+3 y(t)=x(t) \) The system also satisfies the condition of initial rest \( (\mathrm{y}(0)=0) \).
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The transfer function of the system is \( H(s) = \frac{1}{s + 3} \), and the impulse response is \( h(t) = e^{-3t} u(t) \).
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