AbstractA novel generalized processing system is described whereby, using time‐varying gradients, simultaneous data acquisition can be provided for all points in a volume. This is in sharp distinction to the sensitive‐point method where only the null region is imaged. It is shown that time‐varying gradients systems provide unique phase modulation functions which, when appropriately decoded, enable every point in the volume to be simultaneously imaged from a single FID signal. Methods are shown using the technique to provide simultaneously acquired, localized NMR spectra. Alternative gradient signals are considered including both periodic and aperiodic wave