Higher-order spectrum factorization in one and two dimensions with applications in signal modeling and nonminimum phase system identification

The problem of modeling a given higher-order spectrum as that of the output of a linear time-invariant (LTI) system driven by a higher-order white random signal is discussed. This can be posed as a higher-order spectrum factorization problem. A theorem is provided to discuss the existence of such a factorization. A fast algorithm for efficient implementation of the higher-order spectrum factorization, if it exists, is then proposed. The results are extended to two dimensions straightforwardly. The relationship of the higher-order spectrum factorization problem to the well-known power spectrum factorization is also discussed. As applications, the problems of identification of nonminimum-phase LTI systems given the higher-order statistics of both input and output processes and phase reconstruction are presented. Experimental results are provided for the one-dimensional case