half cosine pulse - 3

[logistic_guy]

Find the Fourier transform of the half-cosine pulse shown.

 

[khansaheb]

Find the Fourier transform of the half-cosine pulse shown.

View attachment 39574

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Please share your work/thoughts about this problem

 

[khansaheb]

Find the Fourier transform of the half-cosine pulse shown.

View attachment 39574

That is a half-sine pulse

 

[logistic_guy]

That is a half-sine pulse

You are not only an expert in Beams but also in Signals. Fascinating!

 

[logistic_guy]

This signal looks like the original signal, except it is shifted to the left by $\displaystyle \frac{T}{2}$ and flipped upside down.

This is a hint to use the time-shifting property and multiply the whole expression by negative one. Then, the answer to this problem is:

$\displaystyle G(f) = -\frac{A}{2\pi}\left(\frac{\cos \pi fT}{f + \frac{1}{2T}} - \frac{\cos \pi fT}{f - \frac{1}{2T}}\right)e^{j\pi fT}$

A full explanation of how to use the time-shifting property can be found in this link below.

half cosine pulse - 2

Find the Fourier transform of the half-cosine pulse shown.

www.freemathhelp.com

And the original signal can be found here.

half cosine pulse

Find the Fourier transform of the half-cosine pulse shown.

www.freemathhelp.com