Concept explainers
(a)
Find the inverse Fourier transform of
(a)
Answer to Problem 32P
The inverse Fourier transform of
Explanation of Solution
Given data:
Formula used:
Consider the general form of inverse Fourier transform of
Calculation:
Modify equation (1) as follows.
Since
From Reversal property,
Therefore,
Apply inverse Fourier transform to equation (1) as follows.
Conclusion:
Thus, the inverse Fourier transform of
(b)
Find the inverse Fourier transform of
(b)
Answer to Problem 32P
The inverse Fourier transform of
Explanation of Solution
Given data:
Calculation:
Since
From Reversal property,
Therefore,
Apply inverse Fourier transform to equation (2) as follows.
Conclusion:
Thus, the inverse Fourier transform of
(c)
Find the inverse Fourier transform of
(c)
Answer to Problem 32P
The inverse Fourier transform of
Explanation of Solution
Given data:
Calculation:
Modify equation (3) as follows.
Substitute
Take partial fraction for the equation.
Find the partial fraction coefficients.
Substitute
Substitute
Apply inverse transform on both sides of equation.
Conclusion:
Thus, the inverse Fourier transform of
(d)
Find the inverse Fourier transform of
(d)
Answer to Problem 32P
The inverse Fourier transform of
Explanation of Solution
Given data:
Calculation:
Apply inverse Fourier transform to equation (5) as follows.
Conclusion:
Thus, the inverse Fourier transform of
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Chapter 18 Solutions
Fundamentals of Electric Circuits
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