A Study on Pre-Inverse Adaptive System Based on Estimation of Minimum-Phase and Allpass Transfer Function

In this paper, we discuss a pre-inverse adaptive system in which the adaptive filter is located before the unknown system. We then propose an adaptive system that does not require a replica of the unknown system, as in the case of the filtered-x adaptive system. With the proposed method, we can therefore avoid the instability that arises from error in the replica of the unknown system. In the proposed method, the inverse transfer function of the minimum-phase part of the unknown system is estimated by an adaptive exponential filter. The inverse transfer function of the allpass part of the unknown system is estimated by an adaptive transversal filter, whose inverse can be easily realized by reversing the order of the weights. Finally, a numerical verification of the analytical results, the convergence performance of the adaptive systems, and a performance comparison with the filtered-x adaptive system are obtained by computer simulation