Reconstruction of mixed-phase signals from sum-of-autotriplecorrelations using least squares

A least squares minimization technique for the reconstruction of a real, discrete-time signal from a sum-of-autotriplecorrelations (SOA) sequence is presented. Compared with other methods, our approach has many advantages. First, the reconstruction is based on simple one-dimensional (1-D), instead of two-dimensional (2-D), time-domain operations. Moreover, unlike some current methods, it is possible to perform the reconstruction even if the z transform of the signal has roots on the unit circle. We present the derivation of the approach and simulation results.