Q3) Verify that the Fourier transform of the function [1-x|, |x|<1 10₂ |x|>1 f(x)= a. Then Show that 2 sin u u b. Compute the integral 2 du sinu u is T 4 4 du ƒ (k)= f sin² (1/2)²

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
Q3) Verify that the Fourier transform of the function
[1-x|, |x|<1
f(x)=
10₂
|x|>1
a. Then Show that
2
sin u
sin
u
b. Compute the integral
2
du
sinu
u
is
T
4
4
du
sin²
2² (k/2)
(4/2)²
ƒ(k)=
Transcribed Image Text:Q3) Verify that the Fourier transform of the function [1-x|, |x|<1 f(x)= 10₂ |x|>1 a. Then Show that 2 sin u sin u b. Compute the integral 2 du sinu u is T 4 4 du sin² 2² (k/2) (4/2)² ƒ(k)=
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