Find the inverse Fourier transform of 2 rect(w).
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
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Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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![**Problem: Find the Inverse Fourier Transform**
Determine the inverse Fourier transform of \(2 \, \text{rect}(\omega)\).
**Options:**
(a) \(\frac{1}{2\pi} \, \text{sinc}(t)\)
(b) \(\frac{1}{\pi} \, \text{sinc}(t)\)
(c) \(\frac{1}{2\pi} \, \text{sinc}(t/2)\)
(d) \(\frac{1}{\pi} \, \text{sinc}(t/2)\)
**Explanation:**
The options provided involve the sinc function, which is defined as:
\[
\text{sinc}(x) = \frac{\sin(\pi x)}{\pi x}
\]
This problem involves identifying which version of the sinc function corresponds to the inverse Fourier transform of a rectangular function in the frequency domain.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F79b292ff-e294-4445-84a4-2da9891a32be%2F82955613-8be8-4220-be9b-79e1d6827611%2Fc860arv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem: Find the Inverse Fourier Transform**
Determine the inverse Fourier transform of \(2 \, \text{rect}(\omega)\).
**Options:**
(a) \(\frac{1}{2\pi} \, \text{sinc}(t)\)
(b) \(\frac{1}{\pi} \, \text{sinc}(t)\)
(c) \(\frac{1}{2\pi} \, \text{sinc}(t/2)\)
(d) \(\frac{1}{\pi} \, \text{sinc}(t/2)\)
**Explanation:**
The options provided involve the sinc function, which is defined as:
\[
\text{sinc}(x) = \frac{\sin(\pi x)}{\pi x}
\]
This problem involves identifying which version of the sinc function corresponds to the inverse Fourier transform of a rectangular function in the frequency domain.
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