System identification using the complex cepstrum and the evolutionary spectral theory

Using the complex cepstrum technique, a new method of reconstructing the impulse response of a nonminimum-phase linear time-invariant (LTI) system is proposed. In this method, the input and the output of the LTI system are considered to be non-stationary processes, and hence are expressed using the Wold-Cramer representation of a non-stationary signal. It is shown that the complex cepstrum preserves nonminimum-phase information and thus the actual system characteristics can be recovered. The results also extend to the case when signals are embedded in noise. Some numerical results are given to illustrate the algorithm