This paper analyzes the steady-state properties of a CORDIC-based adaptive ARMA lattice filter. In our previous study, the convergence properties of the filter in the non-steady state were clarified; however, its behavior in the steady state was not discussed. Therefore, we develop a distinct analysis technique based on a Markov chain in order to investigate the steady-state properties of the filter. By using the proposed technique, the relationship between step size and coefficient estimation error is revealed.

This paper presents a theoretical convergence analysis of a CORDIC-based adaptive ARMA lattice filter. In previous literatures, several investigation methods for adaptive lattice filters have been proposed; however, they are available only for AR-type filters. Therefore, we have developed a distinct technique that can reveal the convergence properties of the CORDIC ARMA lattice filter. The derived technique provides a quantitative convergence analysis, which facilitates an efficient hardware design for the filter. Moreover, our analysis technique can be applied to popular multiplier-based filters by slight modifications. Hence, the presented convergence analysis is significant as a leading attempt to investigate ARMA lattice filters.

This paper proposes a method to transform a CORDIC ARMA lattice filter, which is originally realized for signal analysis, into a signal synthesis lattice filter (CORDIC ARMA lattice synthesis filter). In order to perform such a transformation and then obtain the CORDIC ARMA lattice synthesis filter, we must implement the followings with CORDIC: (1) the structure of the altered lattice filter; and (2) an angle calculation module. However, we cannot achieve such an implementation as an extension of the CORDIC ARMA lattice filter algorithm. Therefore, this paper proposes CORDIC implementation schemes for both the structure and module, and then we realize the CORDIC ARMA lattice synthesis filter. By using CORDIC processors, the elementary sections of the CORDIC ARMA lattice synthesis filter are efficiently implemented without any multipliers. Since the obtained signal synthesis lattice filter consists of dedicated CORDIC processors, it keeps the advantage of the CORDIC ARMA lattice filter, that is a simple structure.

This letter proposes a method to transform normalized ARMA lattice filters, which are originally realized for signal analysis, into signal synthesis lattice filters. Although the transformation method has been proposed for normalized ARMA lattice filters with the MA order which is greater than or equal to the AR order, it has not been done when the AR order is greater than the MA order. With the proposed method, once an ARMA lattice filter with the AR order greater than the MA order is realized, then it can be transformed to the signal synthesis filter.