Effects of zero-filling and apodization on spectral integrals in discrete Fourier-transform spectroscopy of noisy data

The influence of noise on the standard deviation of spectral integrals is examined. Calculations assuming discrete Fourier-transform data are compared with Monte-Carlo simulations. The effects of zero-filling and apodization are examined for free-induction-decay (FID) signals and for symmetric spin-echo signals in one and two dimensions, with particular attention to features not previously presented in the literature. Findings suggest that for mild apodization, the known sensitivity enhancement due to zero-filling in either the real or the imaginary part signal [E. Bartholdi, R.R. Ernst, Fourier spectroscopy and the causality principle, J. Magn. Reson., 11 (1973) 9-19] is maintained; however, for stronger apodization filters, this enhancement can be obliterated completely. It is shown that results obtained by analysis of one-dimensional signals can be readily applied to multi-dimensional data. Furthermore, zero-filling has a negligible effect for symmetric spin-echo signals with implications for signal averaging in magnetic resonance imaging and spectroscopic imaging.