Support-limited extrapolation of offset Fourier data

We investigate the usefulness of support-limited extrapolation as a tool for improving the estimate of the magnitude of a finite extent complex-valued signal from samples of its Fourier transform that are offset from the origin. The motivating application is spotlight mode synthetic aperture radar where the complex-valued signal to be recovered is microwave reflectivity and the measured Fourier samples of this reflectivity constitute the signal to be extrapolated. Both analytical and simulation results are presented supporting an earlier conjecture that extrapolation will be of little benefit unless the width of the known Fourier data is less than or equal to the bandwidth of just the magnitude of the reflectivity.