Significance of group delay functions in signal reconstruction from spectral magnitude or phase

Abstract

In this paper we discuss the problem of signal reconstruction from spectral magnitude or phase using group delay functions. We define two separate group delay functions for a signal, one is derived from the magnitude and the other from the phase of the Fourier transform of the signal. The group delay functions offer insight into the problem of signal reconstruction and suggest methods for reconstructing signals from partial information such as spectral magnitude or phase. We examine the problem of signal reconstruction from spectral magnitude or phase on the basis of these two group delay functions and derive the conditions for signal reconstruction. Based on existing iterative and noniterative algorithms for signal reconstruction, we propose new algorithms for some special classes of signals. The algorithms are illustrated with several examples. Our study shows that the relative importance of spectral magnitude and phase depends on the nature of signals. Speech signals are used to illustrate the importance of spectral magnitude and picture signals are used to illustrate the importance of phase in signal reconstruction problems. Using the group delay functions, we explain the convergence behavior of the existing iterative algorithms for signal reconstruction.