Transforms and its Applications: UNIT 4: Fourier Transform
Fourier Sine Transform (FST)
Fourier Transform: Formula, Statement, Example Important Solved Problems with formula, steps, derivation and answer based on Fourier Sine Transform (F.S.T).
FOURIER
SINE TRANSFORM [F.S.T]:
The infinite Fourier sine transform of f(x) is defined by
Formula:
Problems Based on Fourier Sine Transform. [F.S.T]
Example 1: Find the Fourier sine transform of
f(x) = e‒x cos x.
Solution:
We know that,
Example 2: Find the Fourier sine transform of
Solution:
We know that,
Example 3: Find the Fourier sine transform of
Solution:
We know that,
Example 4: Find the Fourier sine transform of
1/x.
Solution:
We know that,
Example 5: Find the Fourier sine transform of
3e‒5x + 5e‒2x.
Solution:
We know that, Fs [f(x)]
Example 6: Find the Fourier sine transforms
of f(x) = e‒ax.
Solution:
We know that,
Example 7: Find the Fourier sine transform of
the function f(x) = e‒ax /
x and hence find 
.
Solution:
We know that,
Example 8: Find the Fourier sine transform of
xn-1. Deduce that 1/√x is self reciprocal under Fourier sine
transform.
Solution:
Example 9: Find the Fourier sine transform of
x/(a2+x2).
Solution:
We know that, Fs [f(x)]
Transforms and its Applications: UNIT 4: Fourier Transform : Tag: Engineering mathematics, Maths : - Fourier Sine Transform (FST)
Transforms and its Applications: UNIT 4: Fourier Transform
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