This is a Demonstration of signal processing in Fourier-transform nuclear magnetic resonance (NMR) spectroscopy. The time-domain, free induction decay signal for two coupled spins-1/2 is plotted in red. The Fourier transform frequency domain spectrum is shown in blue. The spin Hamiltonian is given by , where the sum and difference of the chemical shifts are given by and , respectively, and is the scalar coupling constant (all in Hertz). Zero and first-order phasing of the spectrum are controlled by and .