Find Fourier Transform of Rectangular Pulse w(t)

[Natalie89]

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.

 

[Natalie89]

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.

 

[Borek]

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.