Continuation of discrete Fourier spectra using a minimum-negativity constraint
Samuel J. Howard · Journal of the Optical Society of America · 1981
A method for continuing Fourier spectra applicable to spectra given by the discrete Fourier transform is presented. From the principle of minimizing the sum of the square of the negative values of the restored function, a set of simultaneous nonlinear equations is obtained. The only means of solution at present is iterative, but computational time is comparable with that for noniterative methods. Excellent restoration is obtained for the sharply attenuated spectrum of deconvolved infared peaks. The numerical procedure developed here lends itself easily to the inclusion of additional constraints to enhance resolution further. The constraints of minimum negativity and finite extent may both be enforced together on pertinent data with only slight modification of the procedure.