Answered: 1. Calculate Fourier transform of the…

1. Calculate Fourier transform of the following functions (1) f₁(t) = (1; -1≤t≤1 (0; otherwise (ejant; -1≤t≤ 1 0; otherwise (2) f₂(t) = (3) f(t) = f₁(t) * f₁(t)

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.

Chapter9: Multivariable Calculus

Section9.2: Partial Derivatives

Problem 33E

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Question

Please show solution on how to get the Fourier Transform. Thank you

1. Calculate Fourier transform of the following functions
(1) f₁ (t)
(2) f₂ (t)
=
=
1;−1≤t≤1
(0; otherwise
ej4πt ; − 1 ≤ t ≤1
{e'n
0; otherwise
(3) ƒ3(t) = f₁(t) * f₁(t)

Expert Solution

Step 1

Definition of Fourier transform of a function $f$ :

$\hat{f} (ξ) = \int_{ℝ} f (t) e^{- 2 π j ξ t} d t$ .

We will use this definition to solve the given problem.

Step by step

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