Please do the following questions with full handwritten working out 2. If the Fourier transform of f(x) is ƒ(k):(a) Find the Fourier transform of f() in terms of ƒ(k).xUse this general result to find the Fourier transforms of:(b) 1/x(c) e-x²/x

Given that the Fourier transform of is .We need to find the Fourier transform of in terms of .We…

Answered: If the Fourier transform of f(x) is…

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

Please do the following questions with full handwritten working out

2. If the Fourier transform of f(x) is ƒ(k):
(a) Find the Fourier transform of f() in terms of ƒ(k).
x
Use this general result to find the Fourier transforms of:
(b) 1/x
(c) e-x²/x

Expert Solution

Step 1: Introduction

Given that the Fourier transform of $f open parentheses x close parentheses$ is $f with hat on top open parentheses k close parentheses$ .

We need to find the Fourier transform of $fraction numerator f open parentheses x close parentheses over denominator x end fraction$ in terms of $f with hat on top open parentheses k close parentheses$ .

We know that the Fourier transform of $f open parentheses x close parentheses$ is calculated as $f with hat on top open parentheses k close parentheses equals integral subscript negative infinity end subscript superscript infinity f open parentheses x close parentheses e to the power of negative i k x end exponent d x$ .