Optimal signal reconstruction from spectral amplitude

The iterative algorithm for signal reconstruction from spectral amplitude is investigated. The MSE is used for indication of the convergence rate, and the characteristics of signals most efficiently reconstructed by the iterative algorithm are presented. It is concluded that signals of geometric form are most efficiently reconstructed by the algorithm. Unlike recent reports on optimal phase-only representation, in the case of amplitude-only reconstruction, signals of symmetric form have good convergence characteristics as well. The results provide a new insight into the analysis of different methods for reconstructing signals from their spectral transform