# Problem Statement: Find the Fourier transform of \( \text{sinc}^2(2t) \). ## Options: (a) \( 2\pi \Delta(\omega/2) \) (b) \( \pi \Delta(\omega/4) \) (c) \( \frac{\pi}{2} \Delta(\omega/8) \) (d) \( \frac{\pi}{4} \Delta(\omega/16) \) --- ### Note: In this context, \( \Delta(\omega) \) refers to the Delta function, and \(\text{sinc}(t) = \frac{\sin(\pi t)}{\pi t}\). The problem is asking which option correctly represents the Fourier transform of the given function \(\text{sinc}^2(2t)\). ### Instruction: Choose the correct option by selecting the corresponding letter (a, b, c, or d). *Reminder: Moving to the next question prevents changes to this answer.*
# Problem Statement: Find the Fourier transform of \( \text{sinc}^2(2t) \). ## Options: (a) \( 2\pi \Delta(\omega/2) \) (b) \( \pi \Delta(\omega/4) \) (c) \( \frac{\pi}{2} \Delta(\omega/8) \) (d) \( \frac{\pi}{4} \Delta(\omega/16) \) --- ### Note: In this context, \( \Delta(\omega) \) refers to the Delta function, and \(\text{sinc}(t) = \frac{\sin(\pi t)}{\pi t}\). The problem is asking which option correctly represents the Fourier transform of the given function \(\text{sinc}^2(2t)\). ### Instruction: Choose the correct option by selecting the corresponding letter (a, b, c, or d). *Reminder: Moving to the next question prevents changes to this answer.*
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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
Transcribed Image Text:# Problem Statement:
Find the Fourier transform of \( \text{sinc}^2(2t) \).
## Options:
(a) \( 2\pi \Delta(\omega/2) \)
(b) \( \pi \Delta(\omega/4) \)
(c) \( \frac{\pi}{2} \Delta(\omega/8) \)
(d) \( \frac{\pi}{4} \Delta(\omega/16) \)
---
### Note:
In this context, \( \Delta(\omega) \) refers to the Delta function, and \(\text{sinc}(t) = \frac{\sin(\pi t)}{\pi t}\). The problem is asking which option correctly represents the Fourier transform of the given function \(\text{sinc}^2(2t)\).
### Instruction:
Choose the correct option by selecting the corresponding letter (a, b, c, or d).
*Reminder: Moving to the next question prevents changes to this answer.*
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