Hello.

I'm trying to manually calculate the spectrum of a hyperbolic secant function. It's well known that

$\displaystyle \int_{-\infty }^{\infty } \text{sech} (t \alpha) \exp (- i \omega t)d t = \frac{\pi}{\alpha} \text{sech} \left(\frac{\pi^2}{\alpha} \omega\right).$

How exactly is this expression obtained? All of my atempts to integrate this equation were unsuccessful. What measures should be taken in this particular case?