A study on an estimation system of inverse transfer function using adaptive filter estimating minimum‐phase and allpass transfer function

Abstract

A structure is proposed for an adaptive system with an adaptive filter located before the unknown system (pre-inverse adaptive system) for estimation of the inverse of the transfer function (inverse transfer function) of the unknown system. In general, when an adaptive transversal filter is used as an adaptive filter, the delay signal of the output of the unknown system is needed in the adaptive algorithm for the weights. Since an adaptive filter is inserted in the front stage, this signal cannot be observed, so that a replica of the unknown system is needed. In this paper, an adaptive system that does not require this replica is discussed. Estimation of the inverse transfer function of the minimum phase of the unknown system is performed by an adaptive exponential filter and an inverse copy of the weights of the exponential filter placed in front of the unknown system. The signal within the adaptive algorithm consists of the observable input signal to the adaptive exponential filter and the estimation error. Estimation of the inverse transfer function for the allpass transfer function of the unknown system is performed by the adaptive transversal filter and the reversing copy of the weight to the transversal filter located before the unknown system. The signal in the adaptive system consists of the observable input signal to the exponential filter and the estimation error. Convergence of the weight is studied from the point of view of monotonic increase of the gradient. The unique feature of the approach is that the algorithm of the two adaptive filters consists of a gradient algorithm with guaranteed convergence for the weights and of copies of the weights after updating. Finally, a performance evaluation of the adaptive system and a comparison with conventional systems are performed by numerical simulation. © 2007 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 90(9): 10– 17, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20305