Question
Asked Feb 2, 2020
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Answer Part 2 ONLY 

Determine the Fourier transform of each of the following signals:
1. x(t) =
2. 1(t - 3) + 1(t + 3)
3. 41 (4) cos(27 fot)
4. t sinct
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Determine the Fourier transform of each of the following signals: 1. x(t) = 2. 1(t - 3) + 1(t + 3) 3. 41 (4) cos(27 fot) 4. t sinct

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Expert Answer

(2.)rectangular function definition

the rectangular function is given by the expression as shown below:

the Fourier transform for the given expression is given as :

Electrical Engineering homework question answer, step 1, image 1

Here in the given problem, the shifting property is used. the variable t shifts to (t-3).

Electrical Engineering homework question answer, step 1, image 2

 

shifting property for rectangular function.

 

the Fourier transform of the rectangular function is given by: 

F(rect(t))=Electrical Engineering homework question answer, step 2, image 1

 

applying the shifting property for the given function,

 

Electrical Engineering homework question answer, step 2, image 2

 

calculation

the given problem can be broken into two parts by using Fourier distributive property. as shown below.

 

Electrical Engineering homework question answer, step 3, image 1

 

calculation for the Electrical Engineering homework question answer, step 3, image 2

Electrical Engineering homework question answer, step 3, image 3

 

The overall Fourier transform is given as 

Electrical Engineering homework question answer, step 3, image 4

...

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