Q3) Verify that the Fourier transform of the function [1–|x|, 1-|x|, |x|<1 |x|>1 ƒ (x) = = { 1 + 0 is ƒ (k)= sin³ (2) (1/2) k

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.4: Derivatives Of Exponential Functions
Problem 14E
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Q3) Verify that the Fourier transform of the function
x<1
|x|>1
f(x)=
=
1-x,
{ 1 +
0
5
is
2
sin' (k/₂)
(k/₂)²
2
ƒ (k)=-
Transcribed Image Text:Q3) Verify that the Fourier transform of the function x<1 |x|>1 f(x)= = 1-x, { 1 + 0 5 is 2 sin' (k/₂) (k/₂)² 2 ƒ (k)=-
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