Magnitude in frequency domain of Fourier Transform situation

1. Nov 14, 2012

toneboy1

Hi All, I'm just trying to practice graphing signals in frequency domain and I came across a stiuation I wasn't familiar with. If the exp() has a constant*t in it I'm not sure how to graph it, I remember that just cos it like a double sided exp(jwt) but with half the magnitude. I've attached a drawing to better illustrate the question of how to graph X(w),
I've worked out that X(w) = 1/2[1/(3+j(w-10)) + 1/(3+j(w+10))] from x(t) but not sure what that magnitude in frequency domain looks like.

Thanks heaps!

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Last edited: Nov 14, 2012
2. Nov 15, 2012

toneboy1

Did I post this in the wrong section or what?

3. Nov 18, 2012

toneboy1

Can someone tell me if I wrote the question poorly (i.e my fault) or it is just not interesting enough to respond to?

4. Nov 18, 2012

AlephZero

I can recognise the words taken one at a time, and I know what Fourier transforms are about, but I can't figure out what your question is.

If might help if you wrote some actual equations, rather than things like "just cos it like a double sided exp(jwt)".

5. Nov 19, 2012

toneboy1

Hi,
On the picture attached, you'll notice the bottom frequency graph is of the magnitude of a cos function, and it is a double sided peak, this is the sort of result I'm trying to graph for the function on the top of the picture. Where I typed the question's text I gave the fourier transformation of this function, but this is what I'm unsure how to graph, like the afformentioned magnitude of a cos function (on the bottom of the picture). I.e X(w) = 1/2[1/(3+j(w-10)) + 1/(3+j(w+10))] from x(t) in the picture.
Thanks

6. Nov 19, 2012

milesyoung

If you're trying to graph the magnitude of the Fourier transform of the damped cosine at the top, then you have pretty much succeeded with the lower plot (the magnitude needs to tend to 0 as the frequency goes to +- infinity).

The lower magnitude plot is thus not correct for cos(10t) - that would just be a couple of points (usually pictured as vertical lines) at +- 10 rad/s.

Last edited: Nov 19, 2012
7. Nov 19, 2012

toneboy1

Ah, ok, and would those vertical lines have a magnitude of 1/2 each?

RIGHT so that is pretty much the graph for the damped cos, so w at +/- infinity it tends to zero, what about at w is zero, is the magnitude zero?

THANKS!