Consider an LTI system with frequency response $H(j\omega) = \frac{j\omega + 4}{(j\omega + 2)(j\omega + 5)}$ and the input signal $x(t) = e^{-2t}u(t)$. Please determine the system output $y(t)$. (20 Pts)
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The Fourier Transform of e^(-2t)u(t) can be found using the formula: X(jw) = ∫[e^(-2t)u(t)]e^(-jwt) dt Since the unit step function u(t) is 1 for t ≥ 0 and 0 for t < 0, we can rewrite the integral as: X(jw) = ∫[e^(-2t)]e^(-jwt) dt Now, let's solve this Show more…
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