Magnitude in frequency domain of Fourier Transform situation

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  • #1
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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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  • #2
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Did I post this in the wrong section or what?
 
  • #3
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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
AlephZero
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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 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
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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)".

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
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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.
 
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  • #7
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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.
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!
 

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