ABSTRACT
This chapter reviews the basic notions underlying realizations and parametrizations and a filter with rational transfer function. It also reviews first the direct form filter around which the bulk of adaptive infinite impulse response (IIR) filtering has evolved. The chapter describes recursive lattice filters, along with their connections with many results of modern analysis. The overall realization consists of the interconnection of first- and second-order filter sections, whose sensitivities to coefficient quantization and roundoff error effects tend to be less drastic in comparison to higher order direct form filters. Closely connected with Schur's test is, for rational functions, the bounded real lemma, which states the bounded real property in terms of state space descriptions. McMillan deduced the minimum number of energy storage elements necessary to synthesize a given impedance matrix, and the essence of his results were shown to carry through with Ho-Kalman work, in connection with controllability and observability concepts.
