Find the response fromintugnutoranx0) - ye) - S)deh(E) = u(t)to inputsult-a),tu(t),teo(t-4)u(t-1)e-at u(t) ,tou Ct), uCt) -u(t-s)Using con volution in tegmal.b) Veri fy the results of part a) for-at uct)-26and(6+1) u(t+l)using the system eqn.IyCt)= S"x e)de

Answered: Find the response from integrator an…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Find the response from
intugnutor
an
x0) - ye) - S)de
h(E) = u(t)
to inputs
ult-a),
tu(t),
teo
(t-4)u(t-1)
e-at u(t) ,
tou Ct), uCt) -u(t-s)
Using con volution in tegmal.
b) Veri fy the results of part a) for
-at uct)
-26
and
(6+1) u(t+l)
using the system eqn.IyCt)= S"x e)de

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Given: An input $x (t)$ is feed to an integrator and gives output $y (t)$ as shown below.

$x (t) \to \int \to y (t)$ .

We know that the convolution integral is

$y (t) = \int_{- \infty}^{\infty} x (t - τ) h (τ) d τ = \int_{- \infty}^{\infty} x (t - τ) u (τ) d τ y (t) = \int_{- \infty}^{\infty} x (τ) h (t - τ) d τ = \int_{- \infty}^{\infty} x (τ) u (t - τ) d τ .$

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