Synthesis of fixed-point low roundoff noise digital filters with no limit cycle

A simple method is described for the design of scaled fixed-point limit-cycle free, recursive digital filters with low roundoff noise. The method is based on reducing to zero as much as possible of the entries of the filter´s state matrices. An optimization procedure is developed to get the optimum value of a linear transformation that minimizes the total output noise power, while keeping the norm of the state matrix A bounded to unity. Illustrative examples are also given to show the simplicity and efficiency of the proposed method