Question

Q-1) A causal and stable LTI system has the frequency response $$H(j\omega) = \frac{j\omega}{6 - \omega^2 + 5j\omega}$$ (a) Determine a differential equation relating the input $x(t)$ and output $y(t)$. (b) Determine the impulse response $h(t)$. (c) What is the output of S when the input is $$x(t) = e^{-t}u(t)?$$

Name: q 1 a causal and stable lti system has the frequency response hjomega fracjomega6 omega2 5jomega a determine a differential equation relating the input xt and output yt b determine the impul 11574
Uploaded: 2024-04-29T06:35:04-08:00
Duration: 3 min 44 s
Channel: Adi S
Description: q 1 a causal and stable lti system has the frequency response hjomega fracjomega6 omega2 5jomega a determine a differential equation relating the input xt and output yt b determine the impul 11574

          Q-1) A causal and stable LTI system has the frequency response
$$H(j\omega) = \frac{j\omega}{6 - \omega^2 + 5j\omega}$$
(a) Determine a differential equation relating the input $x(t)$ and output $y(t)$.
(b) Determine the impulse response $h(t)$.
(c) What is the output of S when the input is
$$x(t) = e^{-t}u(t)?$$

$q 1 a causal and stable lti system has the frequency response hjomega fracjomega6 omega2 5jomega a determine a differential equation relating the input xt and output yt b determine the impul 11574$

Added by Richard W.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Adi S

04/29/2024

Step 1

Let $Y(s)$ be the Laplace transform of $y(t)$ and $X(s)$ be the Laplace transform of $x(t)$. Then $$H(s) = \frac{Y(s)}{X(s)} = \frac{s}{-(s-6)(s+1)}$$ $$Y(s)(s^2 - 5s - 6) = -sX(s)$$ Taking the inverse Laplace transform, we get $$\frac{d^2y(t)}{dt^2} - Show more…

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Q-1) A causal and stable LTI system has the frequency response $$H(j\omega) = \frac{j\omega}{6 - \omega^2 + 5j\omega}$$ (a) Determine a differential equation relating the input $x(t)$ and output $y(t)$. (b) Determine the impulse response $h(t)$. (c) What is the output of S when the input is $$x(t) = e^{-t}u(t)?$$