Physics Help Forum Fourier Transforms
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 Dec 2nd 2010, 02:43 PM #1 Junior Member   Join Date: Dec 2010 Posts: 2 Fourier Transforms First let me apologize if I'm posting this in the wrong place. I'm new to the forums, and would love to be a normal participant in discussions, but have to get started somewhere. Also forgive me as I am not experienced in using mathematics in forums other than what you will see posted here. If there are better ways, please let me know. Thank you I'm studying for a test that I have tomorrow, and one of our homework assignments over the past couple of weeks was from Essential Mathematical Methods for Physicists; Weber and Arfken. (This is the alternative edition.) Pg 694. # 15.2.4 Find the Fourier sine and cosine transforms of e^(−a|t|) I know the Fourier sine and cosine transforms are as follows Fs(ω) = Sqrt(2/π) Integrate[f(t)sin(ωt), 0, infinity]dt Fc(ω) = Sqrt(2/π) Integrate[f(t)cos(ωt), 0, infinity]dt I think the issue that I am having is simply how to address the exp[-a|t|] where |t| is abs[t] or the "absolute value of t." I'm not sure how to start the integral for e^(−a|t|) sin(ωt) and e^(−a|t|) cos(ωt). Might I be better off converting sine and cosine to their exponential forms? Thanks in advance.
 Dec 2nd 2010, 03:10 PM #2 Junior Member   Join Date: Dec 2010 Posts: 2 Something my professor mentioned was that for integrating e^(−a|t|) sin(ωt) and e^(−a|t|) cos(ωt) you end up with integral of e^(−a|t|) sin(ωt) from 0 to infinity = ω / (a^2 + ω^2) and integral of e^(−a|t|) cos(ωt) from 0 to infinity = a / (a^2 + ω^2) I'm not sure how she got these though.

 Tags fourier, transforms