show that f1 equals f2 (a) ["_ (21 – 3)5(31 – 2)kt ; (b) [,(3- 2)e*s(2+r\dt; (c) f,(4– 21)' sin 5-5(1 – 3 dt2

Answered: (a) [*_ (21 – 3)»(31 – 2)dt ; (b) [ (3…

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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show that f1 equals f2

(a) ["_ (21 – 3)5(31 – 2)kt ; (b) [,(3- 2)e*s(2+r\dt; (c) f,(4– 21)' sin 5
-5(1 – 3 dt
2

Expert Solution

Step 1

Here we need to calculate integrals (Area) of given signals :

$a . I_{a} = \int_{- \infty}^{\infty} (2 t - 3) δ (3 t - 2) d t b . I_{b} = \int_{- 3}^{\infty} (3 t - 2) e^{t - 2} δ (2 + t) d t c . I_{c} = \int_{- 1}^{2} {(4 - 2 t)}^{2} \sin (\frac{π t}{2}) δ (t - 3) d t$

we know by impulse signal property:

$\int_{- \infty}^{\infty} x (t) δ (t - t_{0}) d t = x (t_{0}) . . . . . (i) a n d w e k n o w, b y s c a l i n g p o p e r t y : δ [a (t - t_{0})] = \frac{1}{| a |} δ (t - t_{0})$

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