7.1.1. Find the Fourier transform of the following functions: (a) e−(x+4)², (b) e¯\x+¹, x, |x|<1, (c) (d) 0, otherwise, - 2x 3x 2 x ≥ 0, x ≤ 0,
7.1.1. Find the Fourier transform of the following functions: (a) e−(x+4)², (b) e¯\x+¹, x, |x|<1, (c) (d) 0, otherwise, - 2x 3x 2 x ≥ 0, 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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Solve first four parts
Transcribed Image Text:7.1.1. Find the Fourier transform of the following functions:
(a) e¯(x+4)²
(b) e-x+¹, (c)
| x | < 1,
Jx,
(c) {
(d)
9
0,
otherwise,
X
e
|x|≥ 1,
sin x,
(e)
{
(f)
x > 0,
{&
e
|x ≤ 1,
x ≤ 0,
9
9
(g)
{
- 2x
3 x
e
9
1−|x|,
0,
9
x ≥ 0,
x ≤ 0,
|x|≤ 1,
otherwise.
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