\hat{f}\left(\omega\right)=\int_{-\infty}^{\ \ \infty}{\ f\left(\tau\right)}{\cdot e}^{-i\cdot \omega\cdot \tau}d\tau=\int_{-a}^{\ \ a}{\ f\left(\tau\right)}{\cdot e}^{-i\cdot \omega\cdot \tau}d\tau=\int_{-a}^{\ \ a}{\ e^{i\omega_0t}}{\cdot e}^{-i\cdot \omega\cdot \tau}d\tau