Find Fourier Transform of Rectangular Pulse w(t)

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SUMMARY

The discussion revolves around finding the Fourier transform of a rectangular pulse, denoted as w(t). The user seeks clarification on simplifying their solution, particularly regarding the transformation involving the sine function and its coefficients. Key points include the simplification of the numerator to "sin(wT/2)*2*j" and the relationship of "sin(x)/x" to the sinc function, Sa(x). The user expresses confusion about the derivation of the coefficient "T" in the denominator during the transformation process.

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  • Understanding of Fourier transforms and their applications
  • Familiarity with rectangular pulse functions
  • Knowledge of trigonometric identities, specifically sine functions
  • Basic grasp of the sinc function and its properties
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  • Learn about the properties and applications of the sinc function
  • Explore simplification techniques in Fourier analysis
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Homework Statement




I have a rectangular train wave pulse, w(t). I needed to find the Fourier transform. My work can done can be seen in the attachment.

Homework Equations



My question is, is there a further way to simplify my solution.

The Attempt at a Solution



See attachment.
 
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Homework Statement



I know I posted a similar question elsewhere, but the real problem I am having comes from an example I don't quite understand. There is some little math trick in it that I just don't understand.

The example can be seen in the attachment.

Homework Equations



I understand the first step, but some confusion arises during the second step.

The Attempt at a Solution



I know that the "e's" in the numerator can simplify to "sin(wT/2)*2*j, and that sin (x)/x is equal to Sa(x), but in the second step, I do not understand how the coeficient "T" and the denominator came to be.
 
You have not attached anything to neither post, so it is not possible to help you in any way. Feel free to contact me by PM if you need assistance.
 

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