1 [1 0Sx<1 If f(x) = find the (a) Fourier sine transform, (b) Fourier cosine transform of f(x). x21 each case obtain the graph of f(x) and its transform. (1- cosa sina Ans. (a) (6)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Question
1
J1 05x<1
If f(x) =
x21
find the (a) Fourier sine transform, (b) Fourier cosine transform of f(x).
each case obtain the graph of f(x) and its transform.
1-cosa
2 sin a
Ans. (a)
(b)
2
(a) Find the Fourier transform of f(x) = {
|x[ < 1
|x[ > 1
x COS X - sin
(b) Evaluate
dx.
COS
a cos a-
sin
Ans.
(а) 2,
(b)
16
Transcribed Image Text:1 J1 05x<1 If f(x) = x21 find the (a) Fourier sine transform, (b) Fourier cosine transform of f(x). each case obtain the graph of f(x) and its transform. 1-cosa 2 sin a Ans. (a) (b) 2 (a) Find the Fourier transform of f(x) = { |x[ < 1 |x[ > 1 x COS X - sin (b) Evaluate dx. COS a cos a- sin Ans. (а) 2, (b) 16
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