Before revision:  We provide several important results which were missing in the early derivation: i) a rigorous proof of the converge of the SINC formula to the correct option price when the support growths and the number of Fourier frequencies increases;
After revision:  We provide several important results which were missing in the early derivation: i) a rigorous proof of the converge of the SINC formula to the correct option price when the support grows and the number of Fourier frequencies increases;