$ \chi(\omega) = 2\pi \sigma(\omega - \pi) <\math> <math> x[n] = frac{1}{2\pi}\int_{-\infty}^{\infty} \delta (\omega - \pi)e^{j\omega t} dw $
$ x[n] = \int_{-\infty}^\infty \delta (\omega - \pi)e^{j\omega t} dw $
