How to solve the Fast Fourier transform?

Fourier Transform of 1/(cosh x)?

• What is the Fourier Transform of 1/(cosh x). I am studying for a test, and I don't quite understand how to do this. Here is a link: http://www.cs.berkeley.edu/~oholtz/121A/solll.pdf The solution for the Fourier transform of 1/(cosh (ax)) is on the problem 7 (scroll all the way down). I am guessing its the same problem and I just have to make a = 1. However, I don't understand the solution. I learned that the Fourier transform was integral (-infty to infty) of f(x)*e^(-iwx) dx. I made the substitution w = 2*pi*f (angular frequency) into integral (-infty to infty) of f(x)*e^(-i*2*pi*f*x). However, on the solutions, it seems like its using my way, except that there is a 1/sqrt(2pi) in front. Where do they get that? Also, can someone show me a solution that maybe is clearer than the one in the link. ALSO: it says on my practice test that in order to do this, I have to show that the inverse Fourier transform applies here? How do I do that?

• Answer:

  http://easycalculation.com/physics/physics.php