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^(−at)
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[at] where t is abs[t] or the "absolute value of t."
I'm not sure how to start the integral for e^(−at) sin(ωt) and e^(−at) cos(ωt).
Might I be better off converting sine and cosine to their exponential forms?
Thanks in advance.
