Consider a continuous time LTI system described by $\dfrac {dy(t)}{dt} + 2y=x(t). $

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Consider a continuous time LTI system described by

$\dfrac {dy(t)}{dt} + 2y=x(t).$

written 8.5 years ago by

teamques10 ★ 69k

• modified 6.4 years ago

Using the Fourier transform, find out output to each of the following input signals.

$i) \space\space x(t) = e^{-t} u(t) \\ ii) \space x(t) = u(t)$

Mumbai University > EXTC > Sem 4 > Signals and Systems

Marks : 10

Year : DEC 2014

signals and systems

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1 Answer

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written 8.5 years ago by

teamques10 ★ 69k

Given

$\dfrac {dy(t)}{dt}+2y=x(t)$

By Laplace transform,

$s\space y(s) + 2 y(s) = x (s) \\ y (s) (s+2) = x (s) \\ \dfrac {y(s)}{x(s)} = \dfrac 1{(s+2)} \\ H(s) = \dfrac 1{(s+2)} \\ (i)\space x(t) = e^{-t} u(t) \\ X (s) =\dfrac 1{(s+1)}$

By Laplace transform,

$Y (s) = …

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