On properties of information matrices of delta-operator based adaptive signal processing algorithms

In this paper, we study the properties of information matrices of the difference operator or the so-called delta (δ) operator-based algorithms for adaptive signal processing. We show that the conditioning of a transformed information matrix in the δ domain is always better than that of the original information matrix in the conventional q domain for ill-conditioned problems. The results obtained in this paper give an explanation of the advantages of using delta operator algorithms for adaptive signal processing that have been developed. The analysis in this paper also helps to clarify the problem about the effect of Δ in the delta operator algorithms and justify the use of sampling interval as Δ in most cases when the ill conditioning is caused by fast sampling of continuous time systems