Q3) Verify that the Fourier transform of the function [1–|x|, 1-|x|, |x|<1 |x|>1 ƒ (x) = = { 1 + 0 is ƒ (k)= sin³ (2) (1/2) k
Q3) Verify that the Fourier transform of the function [1–|x|, 1-|x|, |x|<1 |x|>1 ƒ (x) = = { 1 + 0 is ƒ (k)= sin³ (2) (1/2) k
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:Q3) Verify that the Fourier transform of the function
x<1
|x|>1
f(x)=
=
1-x,
{ 1 +
0
5
is
2
sin' (k/₂)
(k/₂)²
2
ƒ (k)=-
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