$$f(t) = \frac{1}{2\pi} \int_{-\infty}^{\infty} F(\omega)e^{i\omega t}d\omega$$
$$F(\omega) = \int_{-\infty}^{\infty} f(t)e^{-i\omega t}dt$$ fourier transform and its applications bracewell pdf
Bracewell, R. N. (1986). The Fourier Transform and Its Applications. McGraw-Hill. fourier transform and its applications bracewell pdf