On the convergence speed of adaptive IIR filters with rational spectrum input signals

A previously presented framework for the convergence speed analysis of adaptive IIR filters considered white input signals and an identification configuration. In this framework, a local model was built and the Hankel singular values of the system being identified had a fundamental role. It also led to the successive approximations (SA) algorithm, attaining a large speed gain. Here, an approach to extend this framework is presented, allowing more general rational spectrum input signals and unifying the analysis of the identification and inverse identification configurations. It leads to a model that has the same form and depends on the same number of Hankel singular values as in the white input case. The singular values, however, refer now to the result of a certain degree-preserving transformation of the system being identified. Conditions for faster convergence as well as the application of the SA algorithm follow naturally from the extended framework.