Computationally efficient low roundoff noise second-order digital filter sections with no overflow oscillations

An algebraic technique for the synthesis of state-space realizations of second-order digital filter sections having complex-conjugate poles is introduced. The technique provides realizations that are as computationally efficient as possible subject to preserving low roundoff noise, low coefficient sensitivity, and freedom form zero-input and overflow limit cycles. It is found that this technique virtually always provides a realization with the same number of nontrivial multiples as the canonical direct form. The synthesis techniques is based on the selection of three real design parameters. Equations are developed which give the acceptance ranges of these parameters and guide in the selection process. Numerical examples are included to illustrate the design process