Exact Interpolation of Fourier Transform Spectra

Abstract

A systematic study of interpolation of Fourier transform (FT) spectra is reported. Interpolation errors are examined for both frequency determination and intensity determination for different interpolation procedures for both absorption mode and magnitude mode FT spectra. The errors are presented in both analytical and graphical form as functions of the number of zero-fillings and ( T/τ), the ratio of the acquisition time to the relaxation time of the time domain signal. For interpolation of absorption mode spectra, parabolic interpolation is superior to Lorentzian interpolation if T/τ < 2. For T/τ > 2, Lorentzian interpolation is superior. For small values of T/τ, both parabolic interpolation and Lorentzian interpolation of the absorption line shape give greater errors than no interpolation. For interpolation of the magnitude lineshape, interpolation with the “magnitude-Lorentzian” function gives the exact frequency of the continuous spectrum. This interpolation procedure permits exact determination of the true frequency and true intensity for both absorption mode and magnitude mode FT spectra.