If the function of is odd function (i.e. f(-x) = - f cx)) then, the Fourier transform of f(x) is called Fourier sine transform and denoted by Fs { fcx)}, which is defined by: @ Fs (P) = √√ = √²f α) simpx dx = Fs [f(x)} © £ ²x1 = F5¹ { Fs (²) { = √ = {Fs (p) sin p x dp

If the function of is odd function (i.e. f(-x) = - f cx)) then, the Fourier transform of f(x) is called Fourier sine transform and denoted by Fs { fcx)}, which is defined by: @ Fs (P) = √√ = √²f α) simpx dx = Fs [f(x)} © £ ²x1 = F5¹ { Fs (²) { = √ = {Fs (p) sin p x dp

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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Question

2) If the function of is odd function (i-e. f(-x) =
- f (x)) then, the Fourier transform of f(x) is
called Fourier sine transform and denoted by
Fs { fcx)}, which is defined by:
@F₁ (P) = √
Fs
Ⓒf ²x1 = F5¹ { Fs (²) { = √
[fu) sixpx dx = Fs [f(x)}
[Fs (p) si px dp
proof: Howo

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