Transforms and its Applications: UNIT 4: Fourier Transform
Fourier Sine Transform and its Inversion formula
Fourier Transform: Formula, Statement, Example Important Solved Problems with formula, steps, derivation and answer based on Fourier Sine transform and its inversion formula.
Fourier
sine transform and its inversion formula
INVERSION FORMULA FOR FOURIER SINE TRANSFORM
Let
F(s) denote the F.S.T of f(x). Then
Proof:
By the definition of F.S.T
Formula:
Problems based on Fourier sine transform and its inversion formula
Example 1: Find Fourier sine transform of e‒ax,
a > 0 and deduce that 
.
Solution:
We know that,
Example 2: Find the Fourier sine transform of
e‒x, Hence show that 
, m > 0.
Solution:
We know that, FS [f(x)]
Example 3: Find f(x) if its sine transform is e‒sa /s . Hence, find Fs‒1[1/s].
Solution:
Given Fs [f(x)] = e‒sa /s
By
inversion formula, we get
Example 4: Solve the integral equation
Solution:
Transforms and its Applications: UNIT 4: Fourier Transform : Tag: Engineering mathematics, Maths : - Fourier Sine Transform and its Inversion formula
Transforms and its Applications: UNIT 4: Fourier Transform
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Transforms and its Applications
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