A bi-symmetric log transformation for wide-range data

The logarithmic transformation has long been used to present data that have both large and small components that are significant, such as neutron scattering data, or to present data that perhaps cover a wide range of time-scales, such as NMR relaxation data. A more general transformation, which is applicable to many different disciplines, is offered here, and is particularly suitable for representing wide-range data that have both positive and negative (or zero) components. The proposed transform smoothly modifies the gradient of the transformation so that in the region near zero it remains finite. A single constant is provided to tune this behavior, so as to adjust the meaning of 'region near zero'. This modified logarithmic transformation can be one-sided or symmetric, and thus can transform negative data to scaled negative data. It can be applied to both the X and Y data, when it becomes a bi-symmetric log transform. (technical design note)