Suppose f(t) = Fne²int, where F S then what is 3 (a) 24π (b) -8T (c) 24 n=-3 F(w)dw? (-2) ein. If F(w) is the Fourier transform of f(t),
Suppose f(t) = Fne²int, where F S then what is 3 (a) 24π (b) -8T (c) 24 n=-3 F(w)dw? (-2) ein. If F(w) is the Fourier transform of f(t),
Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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![## Fourier Series and Integral Calculations
Consider a function \( f(t) \) that is represented by the following series:
\[ f(t) = \sum_{n=-3}^{3} F_n e^{2jnt}, \]
where the coefficients \( F_n \) are given by:
\[ F_n = (-2)^n e^{j\pi n}. \]
Given that \( F(\omega) \) is the Fourier transform of \( f(t) \), we are interested in determining the integral:
\[ \int_{3}^{7} F(\omega) \, d\omega. \]
**Possible Answers:**
- (a) \( 24\pi \)
- (b) \(-8\pi \)
- (c) 24](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F66bc14d7-9bd5-4ef7-a060-9dc8d70059dc%2F162f0272-c50d-4bb7-8ac6-94e0e7c6827b%2F5r3qiak_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Fourier Series and Integral Calculations
Consider a function \( f(t) \) that is represented by the following series:
\[ f(t) = \sum_{n=-3}^{3} F_n e^{2jnt}, \]
where the coefficients \( F_n \) are given by:
\[ F_n = (-2)^n e^{j\pi n}. \]
Given that \( F(\omega) \) is the Fourier transform of \( f(t) \), we are interested in determining the integral:
\[ \int_{3}^{7} F(\omega) \, d\omega. \]
**Possible Answers:**
- (a) \( 24\pi \)
- (b) \(-8\pi \)
- (c) 24
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