Ex (3): Find The Fourier Transform for this function 0. 1 f(x) = x< 0 x = 0 %3D x > 0
Ex (3): Find The Fourier Transform for this function 0. 1 f(x) = x< 0 x = 0 %3D x > 0
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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Ex (3): Find The Fourier Transform for this function
0.
1
f(x) =
x < 0
x = 0
x > 0
Solution:
00
F(u) =
e-iux f(x)dx
e-iux e-xdx
-00
e-x(1+iu) dx
-00
-1
e-(1+iu)
1+ iu
1- iu
1- iu
%3D
1+ iu
1-iu 1+u2
Go
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