Concept explainers
(a)
Find the Fourier transform of
(a)
Answer to Problem 23P
The Fourier transform of
Explanation of Solution
Given data:
Formula used:
Consider the general form of Fourier transform of
Consider the scaling property of the Fourier transform.
Calculation:
Find
Conclusion:
Thus, the Fourier transform of
(b)
Find the Fourier transform of
(b)
Answer to Problem 23P
The Fourier transform of
Explanation of Solution
Formula used:
Consider the Time shift property of the Fourier transform.
Consider the scaling property of the Fourier transform.
Calculation:
Find
Conclusion:
Thus, the Fourier transform of
(c)
Find the Fourier transform of
(c)
Answer to Problem 23P
The Fourier transform of
Explanation of Solution
Formula used:
Consider the Modulation property of the Fourier transform.
Calculation:
Find
Conclusion:
Thus, the Fourier transform of
(d)
Find the Fourier transform of
(d)
Answer to Problem 23P
The Fourier transform of
Explanation of Solution
Formula used:
Consider the Time differentiation property of the Fourier transform.
Calculation:
Find
Conclusion:
Thus, the Fourier transform of
(e)
Find the Fourier transform of
(e)
Answer to Problem 23P
The Fourier transform of
Explanation of Solution
Formula used:
Consider the Time integration property of the Fourier transform.
Calculation
Find
Conclusion:
Thus, the Fourier transform of
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Chapter 18 Solutions
FUNDAMENTALS OF ELECTRIC...(LL)>CUSTOM<
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- 1. Discrete Fourier Transform: Use the Fast Fourier Transform algorithm to compute the 8-point Dis- crete Fourier Transforms of sequences (1,0,1,0,1,0, 1,0) and (1,1,1,1,0,0,0,0). Provide detailed calculations with intermediate steps rather than just the results.arrow_forwardUse the Laplace transform to find the Fourier transform for each of thefollowing functions: f(t)=0,t≤0−;f(t)=e−at cos ω0t, t≥0+.arrow_forwardIf g(k) = F{f(x)} where F is the Fourier transform, show (a), (b) and (c) when a>0 and a<0arrow_forward
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