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.<>