A general formalism is presented for the analysis of NMR spin imaging spectra obtained with magnetic field modulation during the free induction decay. We show that weighted integrals of the spin density distribution are measured by this technique and deduce a prescription for reconstructing this distribution from the recorded free induction decay signal. The formalism is applied to two-dimensional imaging with one static and one modulated gradient field. For square-wave and cosine-wave modulation the transformations needed to calculate the image from the spectrum are given explicitly, and their effect is illustrated with computer-simulated pictures. We show how resolution and maximum allowable object size depend on the experimental parameters and argue that even two-dimensional imaging of a 32 cm×32 cm specimen with a resolution of 1 cm in each direction will be difficult to attain in practice, mainly because of the required strength of the modulated magnetic field.