Nuclear magnetic resonance signal decay in the presence of a background gradient: Normal and anomalous diffusion

A novel way for calculating the diffusion-weighted nuclear magnetic resonance (NMR) attenuation signal expression in the presence of a background gradient is developed. This method is easily applicable to NMR-attenuated signals arising from any pulse field gradient sequence experiments. Here, we provide detailed calculations for the classical pulsed gradient stimulated echo and the pulsed gradient spin echo, as the particular cases. Within this general theoretical framework, devised for Gaussian processes with stationary increments, we recover and extend the previous Stejskal-Tanner results in the case of normal diffusion and we furnish a new expression in the case of anomalous diffusion.