Signal Reconstruction from the Phase of the Bispectrum

In this paper, we first present a simple procedure to recover the Fourier phase of a signal from the phase of its bispectrum; namely the bispectrum signal reconstruction (BSR) algorithm. By simple analogy, a procedure that recovers the Fourier magnitude of a signal from the magnitude of its bispectrum is also presented. In addition, we also propose in this paper an iterative scheme, the bicepstrum iterative reconstruction algorithm (BIRA), for the reconstruction of a FIR sequence from only the phase of its bispectrum, and we demonstrate how some a priori information on the energy of the cepstra coefficients can improve significantly the convergence rate of the algorithm. Both schemes are based on the key observation that the differences of the bicepstrum coefficients contain all the information concerning the Fourier phase of the signal, whereas their sums contain the Fourier-magnitude information.