FUND.OF ELECTRIC CIRCUITS (LL)-W/ACCESS
FUND.OF ELECTRIC CIRCUITS (LL)-W/ACCESS
6th Edition
ISBN: 9781260405927
Author: Alexander
Publisher: MCG
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Question
Chapter 18, Problem 1RQ
To determine

Choose the correct option which does not have a Fourier transform.

Expert Solution & Answer
Check Mark

Answer to Problem 1RQ

The correct option is (c)1t_ that does not have a Fourier transform.

Explanation of Solution

Formula used:

Consider the general form of Fourier transform of f(t) is represented as F(ω).

F(ω)=f(t)ejωtdt (1)

Calculation:

The Fourier transform is defined as, it is an integral transformation of f(t) from time domain to frequency domain.

Refer to Table 18.2 in the textbook for Fourier transform pairs.

Option (a):

Substitute etu(t) for f(t) in equation (1).

F(ω)=(etu(t))ejωtdt=11jω

Option (b):

Substitute te3tu(t) for f(t) in equation (1).

F(ω)=(te3tu(t))ejωtdt=1(3+jω)2

Option (d):

Substitute |t|u(t) for f(t) in equation (1).

F(ω)=(|t|u(t))ejωtdt=2ω2

Therefore options (a), (b) and (d) has Fourier transform and option (c) does not have a Fourier transform.

Conclusion:

Thus, the correct option is (c)1t_ that does not have a Fourier transform.

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Chapter 18 Solutions

FUND.OF ELECTRIC CIRCUITS (LL)-W/ACCESS

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