Problem 6. (C05) Show that the convolution z of the following two signals¤(t) = e-ale|(6a)y(t) = e-ble|(6b) where a, b > 0 and a + b + 0, is given by(6c)262a-히티a #b+z(t)(비 + 공) e-c비(6d)a = b = c> 0Hint: Use the fact that any signal of the form e-alel can be written as eatu(-t) +e-atu(t) (verifythis!) and then use convolution properties to minimize the amount of convolutions you need tocalculate.

Answered: Problem 6. (C05) Show that the…

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Electrical Engineering

Problem 6. (C05) Show that the convolution z of the following two signals #(t) = e-a!4| =e-ble|

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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Question

Problem 6. (C05) Show that the convolution z of the following two signals
¤(t) = e-ale|
(6a)
y(t) = e-ble|
(6b)

where a, b > 0 and a + b + 0, is given by
(6c)
26
2a
-히티
a #b
+
z(t)
(비 + 공) e-c비
(6d)
a = b = c> 0
Hint: Use the fact that any signal of the form e-alel can be written as eatu(-t) +e-atu(t) (verify
this!) and then use convolution properties to minimize the amount of convolutions you need to
calculate.

Expert Solution

Step 1

We are given two functions:

$x (t) = e^{- a |t|}; y (t) = e^{- b |t|}$

We have to find convolution of x(t) and y(t) for two cases:

when $a \neq b$ .
when a=b=c>0.

Step by step

Solved in 7 steps

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