Q.2 We know that the output of a continmuo us-time LTI system, whose inmput x(t) and impuke response h(t) are nonzero for -o st s o, is given by the convohution integral y(t) = x(t) * h(t) = x(t – t)h(t)dr. (1) a) Now ket h(t) be given as h(t) = e-stu(t). Giving the mathematical justification, make the required change in the integral limits of the convohution integral given in (1) according to the signal h(t) given above and rewrite (1). b) Now ket x(t) = 5u(t), (2) the unit-step signal, which implies another change in the integral limits in (1). Giving the mathematical justification, make the change in the integral limits of (1) according to (2). c) Now substirute h(t) given above and (2) into (1) and find y(t) by taking the integral given in (1) with the modified limits and show that y(t) = (1– e-s)u(t). Hint: u(t -T) = 1 for OstSt.

Q.2 We know that the output of a continmuo us-time LTI system, whose inmput x(t) and impuke response h(t) are nonzero for -o st s o, is given by the convohution integral y(t) = x(t) * h(t) = x(t – t)h(t)dr. (1) a) Now ket h(t) be given as h(t) = e-stu(t). Giving the mathematical justification, make the required change in the integral limits of the convohution integral given in (1) according to the signal h(t) given above and rewrite (1). b) Now ket x(t) = 5u(t), (2) the unit-step signal, which implies another change in the integral limits in (1). Giving the mathematical justification, make the change in the integral limits of (1) according to (2). c) Now substirute h(t) given above and (2) into (1) and find y(t) by taking the integral given in (1) with the modified limits and show that y(t) = (1– e-s)u(t). Hint: u(t -T) = 1 for OstSt.

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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