Concept explainers
(a)
Find the Fourier transform of
(a)
Answer to Problem 35P
The Fourier transform of
Explanation of Solution
Given data:
Formula used:
Consider the general form of Fourier transform of
Consider the general form of inverse Fourier transform of
Consider scaling property.
Consider Time shift property.
Calculation:
Modify equation (1) as follows.
Substitute
From scaling and time shift property, equation (1) can be write as follows.
Substitute
Conclusion:
Thus, the Fourier transform of
(b)
Find the Fourier transform of
(b)
Answer to Problem 35P
The Fourier transform of
Explanation of Solution
Given data:
Formula used:
Consider Modulation property.
Calculation:
Modify equation (1) as follows.
Substitute
From modulation property, equation can be write as follows.
Conclusion:
Thus, the Fourier transform of
(c)
Find the Fourier transform of
(c)
Answer to Problem 35P
The Fourier transform of
Explanation of Solution
Given data:
Formula used:
Consider Time differentiation property.
Calculation:
Modify equation (1) as follows:
Substitute
From modulation property, equation can be write as follows:
Conclusion:
Thus, the Fourier transform of
(d)
Find the Fourier transform of
(d)
Answer to Problem 35P
The Fourier transform of
Explanation of Solution
Given data:
Formula used:
Consider Convolution in t property.
Calculation:
Modify equation (1) as follows.
Substitute
From Convolution in t property, equation can be write as follows.
Conclusion:
Thus, the Fourier transform of
(e)
Find the Fourier transform of
(e)
Answer to Problem 35P
The Fourier transform of
Explanation of Solution
Given data:
Formula used:
Consider Frequency differentiation property.
Calculation:
Modify equation (1) as follows.
Substitute
From Frequency differentiation property, equation can be write as follows.
Simplify the equation as follows.
Conclusion:
Thus, the Fourier transform of
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Chapter 18 Solutions
Fundamentals of Electric Circuits
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