Deconvolution and measurement of spin-spin splittings by modified J doubling in the frequency domain

A new implementation of J doubling in the frequency domain is proposed. This modified J doubling uses novel sets of delta functions [..., +1, -1, +1, +1, -1, +1, ...] for in-phase multiplets and [..., -1, -1, -1, +1, +1, +1, ...] for antiphase multiplets. The convolution process together with the couplings found by it generates a deconvoluted multiplet that preserves the integral and the position of the original one. If the number of delta functions tends to infinity, the whole operation behaves like a formal deconvolution of the multiplet, which is a linear process. Modified J doubling allows for multistage procedures. This makes it possible to analyze 2D multiplets and to measure coupling constants as small as 0.11 Hz with an accuracy of +/-0.03 Hz.