Question
Asked Oct 26, 2019
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1
. For input
S+3
3. A linear, time invariant system has a transfer function H(s) and H(s)=
xt)(ee)u(t)
_
1;t0
(4()
0;t 0
(1) Calculate the Laplace transform (X(s)) of x(t) (specify region of convergence)
(2) Calculate Y(s), system output in Laplace domain
(3) Calculate y(t) by taking inverse (unisided) Laplace transform for Y(s)
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1 . For input S+3 3. A linear, time invariant system has a transfer function H(s) and H(s)= xt)(ee)u(t) _ 1;t0 (4() 0;t 0 (1) Calculate the Laplace transform (X(s)) of x(t) (specify region of convergence) (2) Calculate Y(s), system output in Laplace domain (3) Calculate y(t) by taking inverse (unisided) Laplace transform for Y(s)

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Expert Answer

Step 1

The input of the given  L.T.I system is:

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xt)(ee2u(t) (1,t20 ut) 0,1<0f L{x(t)}= X(s).. ...1

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Step 2

(1)

Calculation of the Laplace transform of the input of the given L.T.I system. The Laplace transform of the given L.T.I system is given by the equation 1, which is calculated as shown below:

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xt)(eeu(€) x(t) (e)u(t)eu(t) X(s) L{e)u(t)+e2*u{t)} X(s) L{e)u(t)} + L{eu(t)} 1 X(s) 1 {L{e*)u)} S+1 2 S+1

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Step 3

The area of the convergence of the abov...

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1 1 X(s) {s ajo jo j@+2 to converge a+10and o+2 > 0 Re[s]lando Re[s]>-2 taking intersection of both the conditions Re[s]-2

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