A brief and approximate justification of the method, different from that presented in Part 2, begins by examining the coefficients for constructing ill-defined parameter combinations. These coefficients have fluctuating signs when arrayed along the relaxation rate axis, leading to near cancellation of intensities in the resulting curves along the time axis. The fluctuations have frequency components above that set by the resolution of the measurements. Dealing with rapidly fluctuating ill-defined components is straightforward in the Fourier domain because such high frequency components can be trivially identified and damped or zeroed. Transforming back to the relaxation rate domain produces quasicontinuous renderings having the reasonably expected properties listed above. The resolution of the rendering in the rate domain can be controlled through the number of Fourier components used and the way they are damped.