Problem 2 Fourier Transfer
$ x(t) = \cos{\pi t} $
$ F(x(t)) = \int_{-\infty}^\infty x(t) e^{-j\omega t}dt $
$ \chi(\omega) = \int_{-\infty}^\infty \cos{(\pi t)} e^{-j\omega t} dt $
$ \chi(\omega) = \int_{-\infty}^\infty \cos{(\pi t)} e^{-j\omega t} dt $
$ = \int_{-\infty}^\infty{ \frac{1}{2} e^{-j\pi t} dt} + \int_{-\infty}^\infty{ \frac{1}{2} e^{-j\pi t} dt} $
