Fourier Transform of delta functions
$ x(t) = \delta (t+1) + \delta (t-1) <\math> <math> X(\omega) = \int_{-\infty}^{\infty} \delta (t+1)e^{-j \omega t} + \int_{-\infty}^{\infty} \delta (t-1)e^{-j \omega t} dt <\math> <math> X(\omega) = e^{j \omega}+ e^{-j \omega} = \frac{1}{2} (e^ {j \omega} + e^ {-j \omega})^2 <\math> <math> X(omega) = 2cos(\omega) <\math> $
