One Dimensional Tdm Signal Reconstruction from Its Fourier Transform Phase or Magnitude

Unlike multidimensional signals, reconstruction of one dimensional signals from their Fourier phase or magnitude is faced with an inherent dilemma. In this paper, the reconstruction of 1D Time Division Multiplexing (TDM) signals (which are sparse in time) is discussed. We will show that such signals can be uniquely reconstructed from their Fourier phase; on the other hand, reconstruction from the Fourier magnitude results in a class of signals. For reconstruction of the mentioned signals, we propose a method followed by a modification inspired by the Hayes uniqueness theorems for recovery of the 2D signals from their Fourier phase or magnitude. In contrast to the previous works which consider criterion in frequency-domain, this work aims to recover the signals using the knowledge of the non-zero sample locations in timedomain. Simulation results confirm the performance of the proposed methods.