State the definitions of direct and inverse Fourier transforms. Then, compute the Fourier transforms of the following functions: - x| : (i) f(x) = { 1¹7 0 (ii) ƒ(x) = xe¯x²/4 x ≤ 1 : |xc|>1
State the definitions of direct and inverse Fourier transforms. Then, compute the Fourier transforms of the following functions: - x| : (i) f(x) = { 1¹7 0 (ii) ƒ(x) = xe¯x²/4 x ≤ 1 : |xc|>1
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:5. State the definitions of direct and inverse Fourier transforms. Then, compute the Fourier transforms
of the following functions:
(1) f(x) = {
|1 − x|
0
(ii) f(x) = xe¯x²/4
:
:
|x| ≤ 1
|x| > 1 '
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