Signal Reconstruction from Partial Fourier Domain Information*

There are a variety of practical problems in which only the phase or magnitude of the Fourier transform of a signal is known and it is desired to reconstruct the signal. In this talk, a number of results developed in the Digital Signal Processing Group at M.I.T. over the past several years will be described. The work discussed began initially with an exploration of the intelligibility of phase-only signals, that is ones for which the correct Fourier transform phase is combined with a constant or characteristic Fourier transform magnitude function. Motivated by the importance of Fourier transform phase in relation to Fourier transform magnitude, a theory and associated algorithms were then developed for the exact reconstruction of finite length signals from phase information alone.