2

Question 3A function is given by (1-< 0 < I < 1 f(e) -2-1 -<2< 0 (o krl > 1 Choose A-E such that the following are correct: J (1 cJe-ikds = 4 +} 5...

Question

Question 3A function is given by (1-< 0 < I < 1 f(e) -2-1 -<2< 0 (o krl > 1 Choose A-E such that the following are correct: J (1 cJe-ikds = 4 +} 51( 1)e-ibdz = &+& and hence the Fourier transform of flx) is {() = €+8A = [Select ][Selcct |Scicct |D= (Selec |[Select |ska |

Question 3 A function is given by (1-< 0 < I < 1 f(e) -2-1 -<2< 0 (o krl > 1 Choose A-E such that the following are correct: J (1 cJe-ikds = 4 +} 51( 1)e-ibdz = &+& and hence the Fourier transform of flx) is {() = €+8 A = [Select ] [Selcct | Scicct | D= (Selec | [Select | ska |



Answers

Given the function
$$ f(x)=\operatorname{rect}\left|\frac{x-a}{a}\right|+\operatorname{rect}\left|\frac{x+a}{a}\right| $$ determine its Fourier transform. (See Problem 11.14 .)

Okay. Yeah. Here, for the solution Step one We consider the following function that is for practical to a cost cannot X. Now we use the identity that cause X equal to It was the power I explicitly to the power -1X. All divided by two. So by using that identity, the function becomes F of X equal to a into the power I cannot express into the power I cannot. Each of the power minus I cannot X all divided by two. Okay, now, for your transform is given by that type of equal to limit minus infinity to plus infinity app of X to the power iK X dx. For the next step we substitute A into the power I cannot express into the power minus. I cannot X divided by 24 ffx. So by substituting we get F K equal to limit minus infinity to plus infinity A It took the power minus into the power cannot express into the power minus. I cannot X divided by two. To the power Ik X d X or a by two. As we bring out it out of the limit. So we get a bye to limit minus infinity to plus infinity. And bracket E to the power I I cannot express it to the power -1 cannot x whole multiple E to the power ik X dx or a buy to limit minus infinity to plus infinity in bracket D to the power I k. Not X plus. It was the power I cannot x minus. I cannot X. All the X or it will be a by two in bracket to buy by K plus K. Not plus two by by k minus cannot. But for this old half of the equal to by a bracket, two divided by k square minus, cannot square. So therefore the required for transform is a type of K equal to by a two K, divided by k squared minus, can or square just a final answer. So this is a complete solution for the calculation step by step in detail. Please go through this. Thank you.


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