These expressions can be put into the form of Equation (1.12) if fictitious spin systems having zero relaxation rates are included in each dimension. For the longitudinal relaxation dimension, this zerorelaxation rate component accommodates the non-zero equilibrium magnetization. For the transverse relaxation dimension, this zero-relaxation rate component can accommodate an offset that is often added to the data to facilitate numerical analysis. In the implementation of the Matrix Pencil Method used here, ambiguities sometimes arise when decay curves cross zero. The difficulty originates within the Matrix Pencil implementation during a singular value decomposition step, where zero crossings in the data sometimes lead to problematic cusps in numerically identified singular vectors. Adding an otherwise inconsequential shift so the entire data set is non-negative eliminates this effect.