Fast imaging trajectories are used in MRI to speed up the acquisition process, but imperfections in the gradient system create artifacts in the reconstructed images. Artifacts result from the deviation between k-space trajectories achieved on the scanner and their original prescription. Measuring or approximating actual k-space trajectories with predetermined gradient timing delays reduces the artifacts, but are generally based on a specific trajectory and scan orientation. A single linear time-invariant characterization of the gradient system provides a method to predict k-space trajectories scanned in arbitrary orientations through convolution. This is done efficiently, by comparing the Fourier transforms of the input and measured waveforms of a single high-bandwidth test gradient waveform. This new method is tested for spiral, interleaved echo-planar, and three-dimensional cones imaging, demonstrating its ability to reduce reconstructed image artifacts for various k-space trajectories. Magn Reson Med, 2012. © 2011 Wiley Periodicals, Inc.