Signal synthesis and reconstruction from partial Fourier-domain information

Abstract

We review and interpret previous results of Fourier synthesis of a signal from its partial Fourier-domain information. Specifically, the high intelligibilities of the phase-only, signed-magnitude-only, and one-bit–phase-only signals are shown to be closely related to one another. In addition, we review and interpret previous results and develop new results on exact reconstruction of a signal from its partial Fourier-domain information.